# Δ-Machine Learned Potential Energy Surfaces and Force Fields

- Joel M. Bowman
*****Joel M. BowmanDepartment of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States*****Email: [email protected]More by Joel M. Bowman, - Chen Qu
- Riccardo Conte
*****Riccardo ConteDipartimento di Chimica, Università Degli Studi di Milano, via Golgi 19, 20133 Milano, Italy*****Email: [email protected]More by Riccardo Conte, - Apurba NandiApurba NandiDepartment of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United StatesMore by Apurba Nandi,
- Paul L. Houston
*****Paul L. HoustonDepartment of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United StatesDepartment of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States*****Email: [email protected]More by Paul L. Houston, and - Qi Yu
*****Qi YuDepartment of Chemistry, Yale University, New Haven, Connecticut 06520, United States*****Email: [email protected]More by Qi Yu

## Abstract

There has been great progress in developing machine-learned potential energy surfaces (PESs) for molecules and clusters with more than 10 atoms. Unfortunately, this number of atoms generally limits the level of electronic structure theory to less than the “gold standard” CCSD(T) level. Indeed, for the well-known MD17 dataset for molecules with 9–20 atoms, all of the energies and forces were obtained with DFT calculations (PBE). This Perspective is focused on a Δ-machine learning method that we recently proposed and applied to bring DFT-based PESs to close to CCSD(T) accuracy. This is demonstrated for hydronium, *N*-methylacetamide, acetyl acetone, and ethanol. For 15-atom tropolone, it appears that special approaches (e.g., molecular tailoring, local CCSD(T)) are needed to obtain the CCSD(T) energies. A new aspect of this approach is the extension of Δ-machine learning to force fields. The approach is based on many-body corrections to polarizable force field potentials. This is examined in detail using the TTM2.1 water potential. The corrections make use of our recent CCSD(T) datasets for 2-b, 3-b, and 4-b interactions for water. These datasets were used to develop a new fully ab initio potential for water, termed q-AQUA.

#### Note

## Introduction

*O*(

*N*

^{3}) whereas CCSD(T) scales as

*O*(

*N*

^{7}), where

*N*is the size of the system.

_{5}

^{+}and H

_{5}O

_{2}

^{+}, and later ones include malonaldehyde and the 10-atom formic acid dimer. (5) More recently, we have reported PIP PESs for molecules containing 10–15 atoms using enhancements to the PIP basis. (16−18) The PIP method was recently evaluated (2) against the ML methods assessed in ref (1). PIPs were shown to be as precise as the most precise methods but to run much faster both for energies and gradients with fast backward differentiation.

*V*

_{LL→CC}, is given by

*V*

_{LL}is the lower-level PES and Δ

*V*

_{CC–LL}is the correction PES. We note that previously the basic idea of using energy differences between high and low levels of ab initio theory to correct a PES can be found in refs (29) and (30) for the OH + H

_{2}and F + H

_{2}reactions, respectively.

_{3}O

^{+}, for which we have reported a CCSD(T)-based PIP PES based on tens of thousands of CCSD(T) energies. (31) Then we move to more challenging molecules, namely,

*N*-methylacetamide, ethanol, and acetylacetone for which we have reported Δ-ML PESs. Then we conclude that section of the Perspective with a discussion of tropolone, for which we have reported a DFT-based PES (18) but for which a Δ-ML PES is still a work in progress. The third section describes a new direction for us, namely, using Δ-ML to correct a force field. Preliminary work in this direction was recently reported with the goal of correcting the four-body (4-b) water interaction in the MB-pol potential; (32) the interested reader is referred to ref (33) for details. In this Perspective, we demonstrate the Δ-ML approach for the polarizable water potential TTM2.1. (34) The Perspective closes with a Discussion and Summary.

## Δ-ML PESs for a Variety of Molecular Systems

### Hydronium Ion

*V*

_{CC–LL}using different training datasets. This was done using 1000, 500, 250, and 125 configurations. The test datasets consist of the remaining data from the total of 32 142 configurations. The root-mean-square errors (RMSEs) between the

*V*

_{LL→CC}and CCSD(T) energies, given in Table 1, are similar for all of the training datasets. The result for the training set of 125 energy differences are encouraging, where the RMSE is just 32 cm

^{–1}for test energies up to 23 000 cm

^{–1}. In this case the PIP basis for Δ

*V*

_{CC–LL}contains only 51 terms. Timings for Δ

*V*

_{CC–LL}for this and other molecules are given in a subsequent section.

^{a}

Δ*V*_{CC–LL} was trained with maximum polynomial order of 7 and a basis size of 348.

^{b}

Δ*V*_{CC–LL} was trained with maximum polynomial order of 6 and a basis size of 196.

^{c}

Δ*V*_{CC–LL} was trained with maximum polynomial order of 5 and a basis size of 103.

^{d}

Δ*V*_{CC–LL} was trained with maximum polynomial order of 4 and a basis size of 51.

*V*

_{LL→CC}versus the direct CCSD(T) energy for the training set of 500 points and the corresponding test data are shown in Figure 1. Overall the correction PES reproduces the direct energies precisely. As expected, the absolute errors increase with energy and do become large for very high energies. If needed, one can always reduce these errors by adding the high-energy data points into the training dataset. Beyond the energy RMSE, we reported a test of this Δ-ML PES for the equilibrium geometries of both the global minimum and transition state (TS) and the normal mode frequencies. This corrected PES,

*V*

_{LL→CC}, produced results in excellent agreement with the direct CCSD(T) ones and also provided a significant improvement compared to the DFT PES in terms of barrier height, normal mode frequencies, and geometric parameters. Perhaps most impressive is the excellent accuracy that was achieved even with the smallest training dataset of 100 energies. The interested reader is referred to the original paper for details. (26)

### *N*-Methylacetamide

*N*-methylacetamide (NMA) molecule, which is of central interest as the smallest molecule in the peptide linkage in polypeptides and proteins. For us, the interest is the challenge to correct a DFT PES that contains the

*cis*and

*trans*isomers, two isomerization saddle points, and two threefold methyl torsional potentials. This is clearly a more complex PES than the one for H

_{3}O

^{+}and more representative of PESs of larger molecules.

*V*

_{CC–LL}was done on 4696 data points of the difference between direct CCSD(T) and DFT absolute energies. Testing of

*V*

_{LL→CC}was done on 734 energies. The PIP basis to fit Δ

*V*

_{CC–LL}was generated using MSA software with the reduced permutational symmetry of 31111113. This notation corresponds to the molecule class A

_{3}BCDEFGH

_{3}, where “A” and “H” are hydrogen atoms and “B” and “G” are carbon atoms, etc. This is the minimum symmetry that describes the identity of the hydrogen atoms within a methyl group. This is essential to get the threefold torsional barrier. The maximum polynomial order is 2. This basis leads to 569 linear coefficients. The fitting RMSE of this Δ

*V*

_{CC–LL}was 57 cm

^{–1}. Plots of

*V*

_{LL→CC}versus the direct CCSD(T) energy for the training and test data are shown in Figure 2. The RMSEs between the

*V*

_{LL→CC}and direct CCSD(T) energies for the training and test datasets are 57 and 147 cm

^{–1}, respectively.

*cis*and

*trans*isomers, and details can be found in ref (26). Here we note that the DFT PES, which predicts an incorrect minimum for the

*trans*isomer, is successfully corrected using the Δ

*V*

_{CC–LL}PES. Specifically, the DFT torsion angle of one methyl rotor (NH–CH

_{3}) is shifted by 60° relative to the CCSD(T) structure. In addition, the torsional potentials of the two methyl rotors of both the

*trans*and

*cis*isomers of NMA are improved substantially from the previously reported DFT PES results. (36)

_{3}rotors for both the

*cis*and

*trans*isomers. Overall, the Δ-ML PES barriers are significantly closer in energy to the CCSD(T) ones. To the best of our knowledge there is no experimental determination of these torsional barriers. However, a previous report of a torsional barrier of 24 cm

^{–1}for acetamide (37) is consistent with the small barriers of 34 and 74 cm

^{–1}(Δ-ML PES) for

*trans*-NMA. For more details, interested readers are referred to the original paper. (26)

method | CH_{3}–NH | CH_{3}–CO |
---|---|---|

trans-NMA | ||

DFT PES | 256 | 37 |

Δ-ML PES | 34 | 74 |

CCSD(T) | 42 | 103 |

cis-NMA | ||

DFT PES | 61 | 361 |

Δ-ML PES | 153 | 366 |

CCSD(T) | 148 | 303 |

### Ethanol

*trans*and

*gauche*) and two different methyl rotors. It is also of great applied interest in fields as diverse as combustion and astrochemistry and in the condensed phase as a solvent.

*trans*conformer but that substantial delocalization to the

*gauche*conformer is present based on rigorous quantum calculations of the vibrational zero-point state using a newly developed CCSD(T) PES. The new PES was obtained by means of a Δ-ML approach starting from a pre-existing low-level DFT surface. (2) The DFT dataset was taken from our previously reported “MDQM21” dataset, (2) where a total of 11 000 energies and their corresponding gradients were generated from ab initio molecular dynamics (AIMD) simulations at the B3LYP/6-311+G(d,p) level of theory. The DFT PES (

*V*

_{LL}) was a fit using 8500 DFT data that spanned the energy range of 0–35 000 cm

^{–1}, with a maximum polynomial order of 4 and 321111 permutational symmetry, which led to a total of 14 752 PIPs in the fitting basis set. The fitting RMSEs for energies and gradients were 40 and 73 cm

^{–1}bohr

^{–1}, respectively.

*V*

_{CC–LL}on the difference between the CCSD(T) and DFT absolute energies of 2069 geometries and tested the obtained surface on the remaining 250 geometries.

*V*

_{CC–LL}does not vary as strongly as

*V*

_{LL}with respect to the nuclear configuration. Therefore, low-order polynomial fitting was employed to fit this correction PES. The maximum polynomial order of 2 with permutational symmetry 321111 was used to fit the training dataset, leading to a total of 208 unknown linear coefficients (equivalent to the number of terms in the PIP fitting basis set). We added this correction Δ

*V*

_{CC–LL}to the low-level DFT PES,

*V*

_{LL}, to obtain the CCSD(T) energies. Plots of

*V*

_{LL→CC}versus the corresponding direct CCSD(T) energy for the training set of 2069 points and the test set of 250 points are shown in Figure 3, as recently reported. (38) As can be seen, there is overall excellent precision; however, we see a few larger errors. The RMSEs between the

*V*

_{LL→CC}and direct CCSD(T) energies for the training and test datasets are 49 and 63 cm

^{–1}, respectively.

*trans*and

*gauche*isomers and their two isomerization saddle point geometries. We found excellent accuracy with respect to the direct CCSD(T)-F12a calculations. We obtained PES optimized energies within 5 cm

^{–1}of the direct CCSD(T)-F12a calculation and found that the

*trans*isomer is lower in energy by 38 cm

^{–1}. This PES obtained barrier heights for

*trans*–

*gauche*isomerization with respect to eclipsed and syn TSs that agree well with the corresponding direct ab initio values as well the experimental barrier heights. (39) Another comparison to experiment was the torsional barrier for the methyl rotor as a function of the torsional angle for both the

*trans*and

*gauche*isomers as well as two TSs. The agreement was very good.

*trans*and

*gauche*isomers as well as singly deuterated isotopologues. In addition, it is well-known that a DMC calculation is a very challenging test to examine the quality of a PES in extended regions of the configuration space. A common issue in PES fitting is the unphysical behavior in the extrapolated regions where the fitting dataset lacks data, and this is dramatically manifested by large negative energy values with respect to the global-minimum energy. These are called “holes” in the PES. Generally, we have observed that holes occur for highly repulsive configurations, that is short internuclear distances. Therefore, one goal of presenting DMC calculations was also to demonstrate that our PES correctly describes the high-energy regions of ethanol and is therefore suitable for quantum approaches that need to sample these regions.

*trans*fingerprint even when starting from the

*gauche*conformer, an observation that revealed the ground state to be of the

*trans*type with a leak to the

*gauche*conformer. This PES was further employed to study the motions of the –CH

_{3}and –OH rotors at the quantum-mechanical level. Rigorous DMC and 1D discrete variable representation (DVR) results were in very good agreement, and the computed DVR wave functions confirm the presence of the “leak” effect. Furthermore, the previously suggested geared motion of the rotors was also confirmed by our calculations, and the 2D model of the torsions based on potential cuts through the full-dimensional potential provides reasonable energy levels compared to experiment.

### Acetylacetone

*V*

_{LL}(MP2) surface. The details of this approach have been described previously. (17,35,36,41) The permutational symmetries and atom numbers (using the scheme in Figure 4) are as follows: symmetry {1, 1, 1, 1, 1, 1, 1, 1, 1} with atoms {1, 2, 3, 4, 5, 6, 10, 11, 12}; symmetry {3, 1, 1, 1, 1, 1, 1, 1, 1} with atoms {13, 14, 15, 1, 2, 3, 4, 5, 10, 11, 12}; symmetry {3, 1, 1, 1, 1, 1, 1, 1, 1} with atoms {7, 8, 9, 1, 2, 3, 4, 5, 6, 10, 11}; and symmetry {3, 3, 1, 1} with atoms {7, 8, 9, 13, 14, 15, 6, 12}. We refer to this fragmentation as 4-(9,11,11,8), where the numbers in parentheses represent the numbers of atoms in the four fragments. Along with performance details, properties of this basis set and its fit to the dataset are shown in Table 3. Fits were inverse-energy-weighted, and gradients were weighted by a factor of

^{1}/

_{3}relative to energies.

property | value |
---|---|

monomials | 3609 |

polynomials | 24030 |

no. of fitted points | 5454 |

wRMSE (pot) | 22 |

wRMSE (grad) | 16 |

time (pot/grad) | 0.43/26.61 |

^{a}

Weighted RMSE (wRMSE) values are in cm^{–1} and cm^{–1} bohr^{–1} for potentials and gradient components, respectively. Times are in seconds for an average over 10 tests using a 2.7 GHz Intel Core i7 processor. Each test involved evaluation of 5000 configurations, and the time listed is that required for evaluation of all 5000 configurations.

*V*

_{CC–LL}was generated by MOLPRO (43) calculations to obtain LCCSD(T)-F12/cc-pVTZ energies at 2151 geometries taken from the original MP2 database. We chose 1100 geometries nearest to the global minimum (denoted GM) and the saddle point for the H-atom transfer (denoted SP), and another 1051 were taken by choosing a random integer that indicated their position on a list, discarding choices whose energies were more than 30 000 cm

^{–1}and stopping the selection when the requisite number of choices had been made. This selection produced a new PES with a barrier for H-atom transfer that is much closer to the direct LCCSD(T) one than the MP2 one, for which the barrier is underestimated by more than 1 kcal/mol. We additionally found that training with even as few as 430 energies from this database of 2151 LCCSD(T) energies still resulted in a PES with a barrier in much better agreement with the LCCSD(T) one. (41) Tunneling splittings due to H-atom transfer were calculated using this new PES, providing improved estimates over previous ones obtained using an MP2-based PES.

^{–1}(0.27 kcal/mol). Other metrics of the performance of the Δ-ML approach were presented in the Supporting Information of ref (44). For example, the harmonic frequencies of the GM and SP are similar for the lower-level and Δ-ML surfaces, with the exceptions of the high-frequency OH stretch and the imaginary frequency, where the Δ-ML values are a significant improvement over those for the low-level PES. In addition, the mean absolute errors (MAEs) of the frequencies were significantly improved by the Δ-ML method.

*V*

_{LL→CC}PESs than by the

*V*

_{LL}one.

stationary point | LCCSD(T)a | V_{LL→CC} (1935) | V_{LL→CC} (430) | V_{LL} |
---|---|---|---|---|

GM | 0 | 0 | 0 | 0 |

SP | 1234 | 1218 | 1219 | 745 |

TS(T)-I | 123 | 165 | 154 | 160 |

TS(T)-II | 488 | 477 | 481 | 399 |

TS(T)-III | 581 | 627 | 623 | 541 |

TS(HT)-I | 1434 | 1299 | 1306 | 820 |

TS(HT)-II | 1645 | 1359 | 1374 | 864 |

^{a}

From LCCSD(T)-F12 calculations at the MP2-optimized geometries.

^{–1}. The energy of the excited state for the H-transfer motion from 10 fixed-node DMC calculations is 26773 ± 10 cm

^{–1}. Consequently, the tunneling splitting is about 32 cm

^{–1}. By comparison, the splitting we obtained using the MP2-based PES (i.e.,

*V*

_{LL}) is 160 cm

^{–1}. Such a significant decrease in the tunneling splitting is expected because the barrier height of the

*V*

_{LL→CC}PES (1218 cm

^{–1}) is significantly higher than the

*V*

_{LL}barrier height (745 cm

^{–1}).

*Q*

_{im}approach. Thus, the barrier heights from these not fully relaxed potentials are 179 cm

^{–1}less than the LCCSD(T) value. Therefore, in the second step a small scaling (“morphing”) of these potentials was performed to produce the correct barrier height. Using this 1D approach, the ground-state tunneling splittings are 37.9 and 8.2 cm

^{–1}for H and D, respectively; the H splitting is in reasonably good agreement with the value of 32 cm

^{–1}obtained from the DMC calculation, and the D splitting is also consistent with the fact that it is smaller than the uncertainty of the DMC calculations.

### Tropolone

^{–1}, which is underestimated by 1.22 kcal/mol or 426 cm

^{–1}with respect to the reported CCSD(T)/aug-cc-pVDZ result. (54) This PES was applied to compute the tunneling splitting using a fast 1D

*Q*

_{im}path tunneling method (59,60) in which the potential along the imaginary-frequency normal mode of the H atom TS (

*Q*

_{im}) is fully relaxed with respect to all other modes. We obtained tunneling splittings of around 3–5 cm

^{–1}depending on the fit, whereas the experimental value is 0.96 cm

^{–1}. (51,54) As can be seen, the splitting value was much larger than the experimental value, mostly due to the error in the barrier height. In addition, a full-dimensional tunneling splitting was computed via an Instanton calculation that indicated a splitting of 2.56 cm

^{–1}(from a private communication with Jeremy Richardson), which is still higher than the experimental value. Considering these results, one concludes that the DFT surface is not accurate enough to estimate the H-transfer barrier height and tunneling dynamics of tropolone. A correction to this DFT PES is needed to achieve the CCSD(T) level of accuracy.

*N*

^{7}, where

*N*is the number of basis functions), the Δ-ML approach is a method that uses a small number (several hundreds to thousand) of CCSD(T) energies to correct a PES based on DFT electronic energies and gradients. For systems with more than 10 atoms, it becomes arduous job to compute CCSD(T) energies for a thousand geometries using a Dunning basis. For example, a single-point energy computation of the 15-atom tropolone molecule at the CCSD(T)/aug-cc-pVTZ level takes about 2063 min on a single 16-core machine. Therefore, correcting the DFT tropolone PES by using, say, 1000 CCSD(T) energies becomes computationally very expensive and even prohibitive. Of course, a local method such as the LCCSD(T) method applied for AcAc could be used. However, our research in progress uses a fragmented approach. Several fragmentation-based methods have been proposed during the last two decades for treating large molecules. These methods have been extensively tested and benchmarked for obtaining the molecular energies, gradients, and Hessian matrix. An overview of such fragmented methods is given in ref (61). One such fragmented method, namely, the molecular tailoring approach (MTA), has been developed by Gadre and co-workers and appraised for various large molecules and molecular clusters. (62−66) Very recently, this MTA method was successfully applied to develop a full-dimensional PES for the AcAc molecule, and this first-ever full-dimensional PES of a 15-atom system is reported at the CCSD(T)/aVTZ level of theory. (67) From this PES the H-transfer barrier is estimated as 3.02 kcal/mol, in excellent agreement with the benchmarked barrier of 3.19 kcal/mol. Therefore, This MTA approach is being taken to correct the DFT tropolone surface in collaboration with Gadre group.

### PES Timing Comparison

*V*

_{CC–LL}). These calculations were carried out on a single core of an Intel Xeon 2.40 GHz processor with 64 GB of RAM. Clearly, the computation of Δ

*V*

_{CC–LL}is much faster than the computation of the

*V*

_{LL}PES because less-complex and lower-order PIPs are employed to fit the correction PES. Thus, the additional cost to bring the DFT-based PES to the CCSD(T) level of accuracy is a small fraction of the cost of evaluating the DFT PES.

molecule | V_{LL} | ΔV_{CC–LL} | V_{LL→CC} |
---|---|---|---|

H_{3}O^{+} | 0.04 | 0.01 | 0.05 |

NMA | 2.05 | 0.12 | 2.17 |

ethanol | 3.12 | 0.06 | 3.18 |

## Δ-Machine Learning Polarizable Force Fields

*V*

_{MB-FF}is the force field and the Δ

*V*

_{n-b}are the many-body corrections to the MB-FF many-body terms. These are given by the difference between CCSD(T) and MB-FF

*n*-body (

*n*-b) interaction energies. In general the

*n*-b interaction energy is obtained from a cluster of

*n*monomers. For example, the 2-b interaction is obtained by calculating the total energy of the dimer (two monomers) and subtracting all of the 1-b interactions from the total energy. It should be noted that for simplicity we assume that an accurate 1-b term (e.g., the single monomer) is given in the MB-FF. It should also be noted that if the MB-FF is given by an MB expansion, the corrections Δ

*V*

_{n-b}are obvious term by term.

*V*

_{MB-FF}is

*V*

_{TTM2.1}and the 1-b term is the accurate isolated H

_{2}O potential of Partridge and Schwenke. (71) Specifically, we corrected the 2-b, 3-b, and 4-b interactions targeting the CCSD(T) level of accuracy. The datasets of CCSD(T) energies for 2-b, 3-b, and 4-b interactions were recently reported by us in developing a new water potential, q-AQUA, (72) that is exactly truncated at the 4-b level. This potential was shown to be very accurate from clusters to the condensed phase. The role of 4-b interactions has been well-established in the literature, and the interested reader is referred to recent refs (73) and (74) and references cited therein. Based on this work, we recently created a 4-b CCSD(T) energy dataset (74) that was fit using PIPs. (2,9,10,75) That fit, together with PIP fits to extensive new datasets for 2-b and 3-b CCSD(T) energies, constitute the q-AQUA potential, as noted already. However, it is certainly of interest to incorporate higher-body interactions, and that is achieved using the current approach, which relies on TTM2.1 for 5- and higher-body interactions.

*V*

_{n-b}needed here. This was done initially, but the fitting error of the dominant Δ

*V*

_{2–b}interaction was 30 cm

^{–1}. This was mainly due to the major failure of the TTM2.1 2-b interaction at short range, as shown below. Reducing the fitting error is straightforward by increasing the maximum polynomial order of the PIP basis, but this comes at a big increase in the computation time. Instead, we represent Δ

*V*

_{2-b}as the direct difference between q-AQUA and TTM2.1

*V*

_{2-b}interactions. For the 3-b and 4-b interactions, PIP fits to Δ

*V*

_{3-b}and Δ

*V*

_{4-b}were done. Briefly, the Δ-ML 3-b correction potential, Δ

*V*

_{3-b}, was fitted from a database of 42 710 reference energies of water trimer structures selected from the 3-b database in ref (72) with maximum O–O distance in the range of [2.0, 7.5] Å. For each trimer structure, the Δ

*V*

_{3-b}correction energy was computed as the difference between BSSE-corrected CCSD(T)-F12a/aVTZ and TTM2.1-F 3-b energies. Using fourth-order 222111-symmetry PIPs, the fitting RMSE for the whole dataset is 9 cm

^{–1}. For the Δ-ML 4-b correction potential, Δ

*V*

_{4-b}, we employed the same PIP bases as described in q-AQUA 4-b and the Δ-ML 4-b to MB-pol (33) using a dataset of 3692 tetramer energies computed at the CCSD(T)-F12/haTZ level of theory. The fitting RMSE for this correction potential is 6.3 cm

^{–1}. More details of the Δ

*V*

_{3-b}and Δ

*V*

_{4-b}PES fits are provided in the Supporting Information. Below we present systematic assessments of the performance of the 2-b, 3-b, and 4-b interactions from CCSD(T) energies, TTM2.1, and Δ

*V*

_{n-b}. Large differences between the former two are seen.

### Interaction Potentials

*V*

_{3-b}data (not a fit) versus the maximum O–O distance in a trimer. As can be seen, many of these are less than 1 kcal/mol; however, a large number are several kcal/mol and as large as 10 kcal/mol. These are clearly significant errors in the TTM2.1 3-b interaction. Figure 7B shows the correlation plot of the precise Δ

*V*

_{3-b}PIP fit (described in detail below). Figure 7C,D shows two 1D cuts when one of the monomers is moved away from the dimer. As one can see, the Δ

*V*

_{3-b}energy can be very large at short range, indicating the inaccuracy of the TTM2.1-F force field in this range; this is also clearly shown in the two potential cuts. The fitting brings the 3-b interaction into much better agreement with the CCSD(T) energies. Similarly, Figure 8A shows a scatter plot of the Δ

*V*

_{4-b}data (not a fit) versus the maximum O–O distance in a tetramer, and again, significant errors in the TTM2.1-F 4-b can be seen. Figure 8B shows the correlation plot of the Δ

*V*

_{4-b}PIP fit. Figure 8C,D shows two 1D cuts when one of the monomers and a dimer are moved away from the remaining water molecules; again, the Δ

*V*

_{4-b}correction brings TTM2.1-F into better agreement with CCSD(T)-F12 energies, especially at short range.

#### Energy Analysis of the Water Hexamer and 20-mer Isomers

*D*

_{e}, for the corrected FF are in much better agreement with the benchmark CCSD(T) results than the TTM2.1 ones. In particular, the Prism is incorrectly predicted to be number 4 in dissociation. The corrected FF also has unprecedented agreement with the CCSD(T) results compared to MB-pol (78) and is even slightly better than q-AQUA. (72) The detailed

*n*-body analysis presented in Table 6 shows the accuracy of the Δ-corrected FF for each

*n*, and impressively, for

*n*> 4 TTM2.1 provides the additional small term that results excellent accuracy of the Δ-ML-corrected FF. This analysis is presented graphically in Figure 9. The results shown in Table 6 are even more accurate than those from our q-AQUA potential, (72) which is truncated at the 4-b level, and also more accurate than the MB-pol potential. (78)

isomer | CCSD(T)a | Δ-ML + TTM2.1-F | TTM2.1-F | CCSD(T)b | Δ-ML + TTM2.1-F | TTM2.1-F |
---|---|---|---|---|---|---|

D_{e} | 2-b Energy | |||||

Prism | 45.92 | 45.90 | 43.95 | –38.94 | –39.07 | –38.80 |

Cage | 45.67 | 45.59 | 44.63 | –38.47 | –38.49 | –39.15 |

Book 1 | 45.20 | 45.04 | 44.28 | –36.02 | –35.97 | –37.51 |

Book 2 | 44.90 | 44.78 | 44.10 | –36.13 | –36.04 | –37.69 |

Bag | 44.30 | 44.30 | 43.38 | –35.28 | –35.38 | –37.09 |

Ring | 44.12 | 44.01 | 43.38 | –32.71 | –32.59 | –35.04 |

Boat 1 | 43.13 | 43.18 | 42.82 | –32.30 | –32.27 | –34.82 |

Boat 2 | 43.07 | 43.12 | 43.05 | –32.24 | –32.21 | –34.89 |

MAE | – | 0.07 | 0.84 | – | 0.07 | 1.64 |

3-b Energy | 4-b Energy | |||||

Prism | –8.70 | –8.73 | –6.96 | –0.66 | –0.58 | –0.69 |

Cage | –8.97 | –9.04 | –7.29 | –0.53 | –0.47 | –0.62 |

Book 1 | –10.38 | –10.36 | –8.01 | –1.08 | –1.07 | –1.05 |

Book 2 | –10.11 | –10.15 | –7.85 | –1.00 | –1.00 | –0.98 |

Bag | –10.35 | –10.36 | –7.80 | –1.16 | –1.09 | –1.03 |

Ring | –11.78 | –11.81 | –8.91 | –1.78 | –1.70 | –1.52 |

Boat 1 | –11.34 | –11.44 | –8.69 | –1.63 | –1.57 | –1.42 |

Boat 2 | –11.34 | –11.41 | –8.79 | –1.61 | –1.57 | –1.43 |

MAE | / | 0.05 | 2.33 | / | 0.05 | 0.12 |

Higher-Body (>4-b) Energy | ||||||

Prism | 0.06 | 0.06 | 0.06 | |||

Cage | 0.01 | 0.03 | 0.03 | |||

Book 1 | –0.04 | –0.06 | –0.06 | |||

Book 2 | –0.02 | –0.04 | –0.04 | |||

Bag | –0.01 | –0.06 | –0.06 | |||

Ring | –0.20 | –0.23 | –0.23 | |||

Boat 1 | –0.17 | –0.21 | –0.21 | |||

Boat 2 | –0.17 | –0.21 | –0.21 | |||

MAE | – | 0.03 | 0.03 |

*D*

_{e}of roughly 200 kcal/mol. A comparison of these benchmark energies with those from TTM2.1-F and the Δ-ML-corrected FF are given in Table 7. Using TTM2.1-F optimized geometries, the dissociation energies are very close to the MP2 benchmark ones. However, it should be noted that upon using the same MP2/aVDZ-optimized geometries, the TTM2.1-F energies are ∼9 kcal/mol higher than the MP2/aV5Z data. This indicates that the geometry optimization using the TTM2.1-F force field results in significant changes in the geometries of these isomers. With the Δ-ML-corrected TTM2.1-F potential, the structures of the three isomers do not undergo significant changes during optimization, and the dissociation energies using the optimized geometries are close to both the MP2 and CCSD(T) benchmark results.

#### Quantum Simulations of *D*_{0} Energy and IR Spectra of Gas-Phase Clusters

*D*

_{e}) and exact ZPE of the water monomer, give the exact dissociation energy

*D*

_{0}. Table 8 shows

*D*

_{e}, the ZPEs of the reactants and products, and the ZPE-corrected dissociation energy (

*D*

_{0}) for the following dissociations: (H

_{2}O)

_{2}→ 2H

_{2}O, (H

_{2}O)

_{3}→ 2H

_{2}O + H

_{2}O, and (H

_{2}O)

_{3}→ 3H

_{2}O. As can be seen, the agreement with experiment is excellent. The agreement is also excellent with DMC calculations of

*D*

_{0}for the dimer using the HBB2 (83) and MB-pol (84) potentials, both of which predict a value of 1101 cm

^{–1}. These values are also in excellent agreement with the value of

*D*

_{0}reported for the dimer (85) using the recent flexible CCpol-8sf potential. (86) For the water trimer, the present results are in excellent agreement with previous DMC calculations using WHBB (87) (2724 cm

^{–1}) and MB-pol (84) (2693 cm

^{–1}). Also there is very good agreement for dissociation to three monomers, namely, 3854 cm

^{–1}for WHBB and 3794 cm

^{–1}for MB-pol. We do not show results for TTM2.1, as the electronic dissociation eneriges for the dimer and trimer already show significant errors compared to the above potentials.

^{–1}lower than that of the Prism isomer (both ZPEs are referenced to the electronic energy of the Prism isomer), in semiquantitative agreement with the results using q-AQUA, (72) though the uncertainties here are much larger due to the smaller numbers of walkers and steps.

^{–1}is due to the overtone of the monomer bend and did settle the controversy about the origin of the experimental peak seen at around 3220 cm

^{–1}. More details and discussion can be found in ref (95). For the present purpose, we note the poor agreement with experiment using the TTM2.1 potential, with the WHBB DMS, in identical VSCF/VCI calculations. The improvement of that spectrum just using the 2-b correction (not shown) is significant but not in quantitative agreement with the Δ-ML-corrected spectrum. The corresponding comparisons with experiment for the Book isomer are given in Figure 11. As can be seen, theory, with the Δ-corrected potentials, reproduces the complex experimental spectrum well, whereas the spectrum obtained using TTM2.1 does not. For completeness we note that the dipole moment surface is a 1- and 2-body one that has been described and tested previously. (96)

### Δ-ML Correction Timings

*V*

_{n-b}is also listed. The TTM2.1-F force field code is an optimized and parallelized one that is computationally more efficient than the original TTM2.1-F force field code for gas-phase cluster calculations. The 256-water structure was chosen from an MD simulation of liquid water using our recently developed water potential, q-AQUA. (72) The number of terms given is less than the factorial result due to the use of the finite-range switching function. For example, the total number of 3-b interaction terms in this 256-mer water system is $\left(\begin{array}{c}256\\ 3\end{array}\right)=\mathrm{2,763,520}$, but only 3-b interactions with a maximum O–O distance smaller than 7.0 Å are considered for correction, which results in only 20 790 Δ

*V*

_{3-b}terms. It is also straightforward to do multicore processing (using OpenMP) of the Δ

*V*

_{n-b}terms, which is clearly effective as shown in Table 9. Using eight cores, the additional time to evaluate the Δ correction is almost negligible for energy calculations and almost 2 times the TTM2.1-F force field for gradient calculations. The corresponding timing for an energy plus gradient calculation on eight cores for the q-AQUA potential is 0.97 s on the same cluster (reported in Table S5 of ref (72)). This is similar to that for the present Δ-corrected FF.

time for energy (s) | time for energy+gradient (s) | ||||
---|---|---|---|---|---|

component | number | one core | eight cores | one core | eight cores |

TTM2.1-F | – | 1.09 | 0.28a | 1.09 | 0.28a |

ΔV_{2-b} | 3816 | 0.25 | 0.03 | 0.59 | 0.07 |

ΔV_{3-b} | 20790 | 0.58 | 0.08 | 2.47 | 0.35 |

ΔV_{4-b} | 28786 | 0.31 | 0.04 | 1.07 | 0.15 |

total | 2.23 | 0.43 | 5.22 | 0.85 |

^{a}

The current TTM2.1-F force field code calculates the gradients by default.

*V*

_{n-b}correction terms were determined. The 2-b correction Δ

*V*

_{2-b}is given explicitly by the 2-b term in our recent q-AQUA potential minus the 2-b interaction in TTM2.1. For the 3-b and 4-b corrections, the Δ

*V*

_{n-b}are permutationally invariant polynomial fits to 3-b and 4-b energy differences between the corresponding CCSD(T)and TTM2.1 energies. These fits were to high-dimensional datasets, i.e., for the 4-b correction, Δ

*V*

_{4-b}is 12-atom full-dimensional and is a function of all 66 Morse-transformed internuclear distances. The fits are invariant with respect to all permutations of monomers and with respect to the two H atoms of each monomer.

## Discussion

*Journal of Chemical Physics*, (25) the selection of configurations is driven by the goal of the usage of the PES. We generally use PESs for dynamics calculations, ranging from quantum dynamics to high-energy (quasi)classical trajectory calculations of reaction dynamics. These often require both energies at a large number of geometries and also high accuracy, particularly near barriers to reaction. The Δ-ML method allows us to combine lower-level theory (DFT, MP2) for a large number of geometries with higher-level theory (CCSD(T)) at a few geometries so that the accuracy at all geometries is greatly improved. Also, we note that a similar approach, subsequent to ours, was reported by Liu and Li, who developed a Δ-ML potential for the HO

_{2}self-reaction. (99) Finally, we note that modifying a PES has been done in the past for small molecules. A method using scaled coordinates (100) that has been called “morphing” (101) is one example.

*V*

_{n-b}potentials are based on much larger datasets, which in this case were already available from our recent work in developing the q-AQUA water potential. (72) It should also be noted that the basic approach of blending a force field with ab initio many-body potentials is not new. Again for water, this approach is the basis of the WHBB potential, (102) where 2-b and 3-b PIP PESs are combined with the TTM3F potential (103) for higher-body interactions. The subsequent MB-pol potential (104) combines ab initio PIP 2-b and 3-b PESs with the TTM4F potential. (105) It should be noted that both of these potentials also use the Partridge–Schwenke potential for the monomer, (71) as is done in the present work. Here we have extended this approach to 4-b interactions for the first time. We note that we recently corrected the MB-pol PES by adding a correction to the 4-b interaction. (33)

## Summary

_{3}O

^{+}, as a pedagogical test case, and then for nine-atom ethanol, 12-atom

*N*-methylacetamide, and 15-atom acetylacetone. We have also described work in progress for an application to 15-atom tropolone. A major extension of the Δ-machine learning approach for force fields was demonstrated in detail for the TTM2.1 force field for water. The corrected FF was shown to result in major improvements over the TTM2.1 FF for a variety of important properties of clusters.

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.2c01034.

Details of the Δ

*V*_{3-b}and Δ*V*_{4-b}PES fits and sample potential cuts for 2-b, 3-b, and 4-b interactions (PDF)

## Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

## Acknowledgments

We thank Kristina Herman and Sotiris Xantheas for sending the original version of the TTM2.1-F force field and George Fanourgakis for sending the parallelized version. J.M.B. thanks NASA (80NSSC20K0360) for financial support. R.C. thanks Università degli Studi di Milano (“PSR, Azione A Linea 2 - Fondi Giovani Ricercatori”) for support. Q.Y. thanks Professor Sharon Hammes-Schiffer and the National Science Foundation (Grant CHE-1954348) for support.

## References

This article references 111 other publications.

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(Royal Society of Chemistry)We investigate the mode-specific dynamics of the ground-state, C-Cl stretching (v10), CH2 wagging (v7), sym-CH2 stretching (v1), and sym-CH3 stretching (v3) excited F- + CH3CH2Cl(vk = 0, 1) [k = 10, 7, 1, 3] → Cl- + CH3CH2F (SN2), HF + CH3CHCl-, FH···Cl- + C2H4, and Cl- + HF + C2H4 (E2) reactions using a full-dimensional high-level anal. global potential energy surface and the quasi-classical trajectory method. Excitation of the C-Cl stretching, CH2 stretching, and CH2/CH3 stretching modes enhances the SN2, proton abstraction, and FH···Cl- and E2 channels, resp. Anti-E2 dominates over syn-E2 (kinetic anti-E2 preference) and the thermodynamically-favored SN2 (wider reactive anti-E2 attack angle range). The direct (a) SN2, (b) proton abstraction, (c) FH···Cl- + C2H4, (d) syn-E2, and (e) anti-E2 channels proceed with (a) back-side/backward, (b) isotropic/forward, (c) side-on/forward, (d) front-side/forward, and (e) back-side/forward attack/scattering, resp. The HF products are vibrationally cold, esp. for proton abstraction, and their rotational excitation increases for proton abstraction, anti-E2, and syn-E2, in order. Product internal-energy and mode-specific vibrational distributions show that CH3CH2F is internally hot with significant C-F stretching and CH2 wagging excitations, whereas C2H4 is colder. One-dimensional Gaussian binning technique is proved to solve the normal mode anal. failure caused by Me internal rotation.**8**Yin, C.; Tajti, V.; Czakó, G. Full-dimensional potential energy surface development and dynamics for the HBr + C_{2}H_{5}→ Br(^{2}P_{3/2}) + C_{2}H_{6}reaction.*Phys. Chem. Chem. 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The computational mathematics underlying this approach is reviewed first, followed by a review of the practical approaches used to obtain the data for the fits. A straightforward symmetrization approach is also given, mainly for pedagogical purposes. The methods are illustrated for potential energy surfaces for CH+5, (H2O)2 and CH3CHO. The relationship of this approach to other approaches is also briefly reviewed.**10***MSA Software with Gradients*, 2019. https://github.com/szquchen/MSA-2.0 (accessed 2019-01-20).Google ScholarThere is no corresponding record for this reference.**11**Györi, T.; Czakó, G. Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program System.*J. Chem. Theory Comput.*2020,*16*, 51– 66, DOI: 10.1021/acs.jctc.9b01006[ACS Full Text ], [CAS], Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MbhsFCmtQ%253D%253D&md5=b7817b4b8f54e3372c069db735ca7a91Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program SystemGyori Tibor; Czako GaborJournal of chemical theory and computation (2020), 16 (1), 51-66 ISSN:.The construction of high-dimensional global potential energy surfaces (PESs) from ab initio data has been a major challenge for decades. Advances in computer hardware, electronic structure theory, and PES fitting methods have greatly alleviated many challenges in PES construction, but building fitting sets has remained a bottleneck so far. We present the robosurfer program system that completely automates the generation of new geometries, performs ab initio computations, and iteratively improves the PES under development. Unlike previous efforts to automate PES development, robosurfer does not require any uncertainty estimate from the PES fitting method and thus it is compatible with the permutationally invariant polynomial (PIP) method. As a demonstration we have developed five related but different global reactive PIP PESs for the CH3Br + F(-) system and used them to perform quasiclassical trajectory (QCT) reaction dynamics simulations over a wide range of collision energies. The automatically developed PESs show good to excellent accuracy at known stationary points without any manual sampling, and QCT results indicate the lack of unphysical minima on the fitted surfaces. We also present evidence suggesting that the breakdown of single reference electronic structure theory may contribute significantly to the fitting errors of global reactive PESs.**12**Czakó, G.; Györi, T.; Papp, D.; Tajti, V.; Tasi, D. A. First-Principles reaction dynamics beyond six-atom systems.*J. Phys. Chem. A*2021,*125*, 2385– 2393, DOI: 10.1021/acs.jpca.0c11531[ACS Full Text ], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXkvFyisLc%253D&md5=08815ec095c5dc58b793084d6cd0e829First-Principles Reaction Dynamics beyond Six-Atom SystemsCzako, Gabor; Gyori, Tibor; Papp, Dora; Tajti, Viktor; Tasi, Domonkos A.Journal of Physical Chemistry A (2021), 125 (12), 2385-2393CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)A review. Moving beyond the six-at. benchmark systems, we discuss the new age and future of first-principles reaction dynamics which investigates complex, multichannel chem. reactions. We describe the methodol. starting from the benchmark ab initio characterization of the stationary points, followed by full-dimensional potential energy surface (PES) developments and reaction dynamics computations. We highlight our composite ab initio approach providing benchmark stationary-point properties with subchem. accuracy, the ROBOSURFRER program system enabling automatic PES development, and applications for the Cl + C2H6, F + C2H6, and OH- + CH3I reactions focusing on ab initio issues and their solns. as well as showing the excellent agreement between theory and expt.**13**Lambros, E.; Dasgupta, S.; Palos, E.; Swee, S.; Hu, J.; Paesani, F. General many-body framework for data-driven potentials with arbitrary quantum mechanical accuracy: water as a case study.*J. Chem. Theory Comput.*2021,*17*, 5635– 5650, DOI: 10.1021/acs.jctc.1c00541[ACS Full Text ], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhslahsLzO&md5=b06f7e098c2de001b980bc51c6a08a96General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case StudyLambros, Eleftherios; Dasgupta, Saswata; Palos, Etienne; Swee, Steven; Hu, Jie; Paesani, FrancescoJournal of Chemical Theory and Computation (2021), 17 (9), 5635-5650CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small mols. at an arbitrary quantum-mech. (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from d. functionals belonging to different rungs across Jacob's ladder of approxns. within d. functional theory (MB-DFT) and from Moller-Plesset perturbation theory (MB-MP2). Through a systematic anal. of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calcns., with the exception of those derived from d. functionals within the generalized gradient approxn. (GGA). The differences between the DFT and MB-DFT results are traced back to d.-driven errors that prevent GGA functionals from accurately representing the underlying mol. interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using d.-cor. functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.**14**Moberg, D. R.; Jasper, A. W. Permutationally invariant polynomial expansions with unrestricted complexity.*J. Chem. Theory Comput.*2021,*17*, 5440– 5455, DOI: 10.1021/acs.jctc.1c00352[ACS Full Text ], [CAS], Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvFWmsbzN&md5=d16d508a3685baa08aa5f706e846aac8Permutationally Invariant Polynomial Expansions with Unrestricted ComplexityMoberg, Daniel R.; Jasper, Ahren W.Journal of Chemical Theory and Computation (2021), 17 (9), 5440-5455CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chem. systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atm. chem., and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the no. of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphys. unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.**15**Moberg, D. R.; Jasper, A. W.; Davis, M. J. Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy Selection.*J. Phys. Chem. Lett.*2021,*12*, 9169– 9174, DOI: 10.1021/acs.jpclett.1c02721[ACS Full Text ], [CAS], Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitVaku77L&md5=a7948ec2233918e1617979880381ff63Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy SelectionMoberg, Daniel R.; Jasper, Ahren W.; Davis, Michael J.Journal of Physical Chemistry Letters (2021), 12 (37), 9169-9174CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Potential energy surfaces fit with basis set expansions have been shown to provide accurate representations of electronic energies and have enabled a variety of high-accuracy dynamics, kinetics, and spectroscopy applications. The no. of terms in these expansions scales poorly with system size, a drawback that challenges their use for systems with more than ~ 10 atoms. A soln. is presented here using dictionary learning. Subsets of the full set of conventional basis functions are optimized using a newly developed multipass greedy regression method inspired by forward and backward selection methods from the statistics, signal processing, and machine learning literatures. The optimized representations have accuracies comparable to the full set but are 1 or more orders of magnitude smaller, and notably, the no. of terms in the optimized multipass greedy expansions scales approx. linearly with the no. of atoms.**16**Qu, C.; Bowman, J. M. Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?.*Phys. Chem. Chem. Phys.*2019,*21*, 3397– 3413, DOI: 10.1039/C8CP04990D[Crossref], [PubMed], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitVWjurbL&md5=e5758610af64d91ef76cfa1cc9f465c7Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?Qu, Chen; Bowman, Joel M.Physical Chemistry Chemical Physics (2019), 21 (7), 3397-3413CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)A review. The subject of this Perspective is quantum approaches, beyond the harmonic approxn., to vibrational dynamics and IR spectroscopy. We begin with a pedagogical, unifying review of the most widely used quantum approaches. Some of the key details that lead to steep computational scaling of these approaches are reviewed, as well as some effective strategies to overcome or at least mitigate them. Considering in particular the application to IR spectroscopy, we stress the strength and weakness of each approach for spectral features that evolve from "simple" to "complex". We use the 10-atom formic acid dimer as an ideal example of this evolution. The IR spectrum of this dimer and two isotopologs has been obtained computationally using our software, MULTIMODE, and approaches to obtain accurate, ab initio, full-dimensional potential energy and dipole moment surfaces, also developed by our group. The IR spectra obtained with the widely used "ab initio mol. dynamics" approach are also presented and assessed. The extension of quantum approaches to mol. clusters and even condensed phase applications, where mol. dynamics approaches are typically used, is discussed mainly in the context of the local monomer model. This approach is illustrated for a methane clathrate hydrate, where vibrational energies of the sym. and asym. stretches of methane are given for a no. of water cages and compared to expt. The question about interpretation is also addressed throughout the Perspective.**17**Conte, R.; Qu, C.; Houston, P. L.; Bowman, J. M. Efficient generation of permutationally invariant potential energy surfaces for large molecules.*J. Chem. Theory Comput.*2020,*16*, 3264– 3272, DOI: 10.1021/acs.jctc.0c00001[ACS Full Text ], [CAS], Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXls12hu70%253D&md5=51e9d22fbd49e36d8fc216018c665340Efficient Generation of Permutationally Invariant Potential Energy Surfaces for Large MoleculesConte, Riccardo; Qu, Chen; Houston, Paul L.; Bowman, Joel M.Journal of Chemical Theory and Computation (2020), 16 (5), 3264-3272CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)An efficient method is described for generating a fragmented, permutationally invariant polynomial basis to fit electronic energies and, if available, gradients for large mols. The method presented rests on the fragmentation of a large mol. into any no. of fragments while maintaining the permutational invariance and uniqueness of the polynomials. The new approach improves on a previous one reported by Qu and Bowman by avoiding repetition of polynomials in the fitting basis set and speeding up gradient evaluations while keeping the accuracy of the PES. The method is demonstrated for CH3-NH-CO-CH3 (N-methylacetamide) and NH2-CH2-COOH (glycine).**18**Houston, P. L.; Conte, R.; Qu, C.; Bowman, J. M. Permutationally invariant polynomial potential energy surfaces for tropolone and H and D atom Tunneling Dynamics.*J. Chem. Phys.*2020,*153*, 024107, DOI: 10.1063/5.0011973[Crossref], [PubMed], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtlKqu7nP&md5=b1ae8cf76e76f44231a6524a74c22ffaPermutationally invariant polynomial potential energy surfaces for tropolone and H and D atom tunneling dynamicsHouston, Paul; Conte, Riccardo; Qu, Chen; Bowman, Joel M.Journal of Chemical Physics (2020), 153 (2), 024107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report permutationally invariant polynomial (PIP) fits to energies and gradients for 15-atom tropolone. These include std., augmented, and fragmented PIP bases. Approx., 6600 energies and their assocd. gradients are obtained from direct-dynamics calcns. using DFT/B3LYP/6-31+G(d) supplemented by grid calcns. spanning an energy range up to roughly 35 000 cm-1. Three fragmentation schemes are investigated with respect to efficiency and fit precision. In addn., several fits are done with reduced wt. for gradient data relative to energies. These do result in more precision for the H-transfer barrier height. The properties of the fits such as stationary points, harmonic frequencies, and the barrier to H-atom transfer are reported and compared to direct calcns. A previous 1D model is used to obtain the tunneling splitting for the ground vibrational state and qual. predictions for excited vibrational states. This model is applied to numerous fits with different barrier heights and then used to extrapolate the H and D atom tunneling splittings to values at the CCSD(T)-F12 barrier. The extrapolated values are 2.3 and 0.14 cm-1, resp. for H and D. These are about a factor of two larger than expt., but within the expected level of agreement with expt. for the 1D method used and the level of the electronic structure theory. (c) 2020 American Institute of Physics.**19**McCoy, A. B.; Braams, B. J.; Brown, A.; Huang, X.; Jin, Z.; Bowman, J. M.*Ab initio*diffusion monte carlo calculations of the quantum behavior of CH_{5}^{+}in full dimensionality.*J. Phys. Chem. A*2004,*108*, 4991– 4994, DOI: 10.1021/jp0487096[ACS Full Text ], [CAS], Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjvVCksbo%253D&md5=ca3ca54006f02e11af63f4042e5f3340Ab Initio Diffusion Monte Carlo Calculations of the Quantum Behavior of CH5+ in Full DimensionalityMcCoy, Anne B.; Braams, Bastiaan J.; Brown, Alex; Huang, Xinchuan; Jin, Zhong; Bowman, Joel M.Journal of Physical Chemistry A (2004), 108 (23), 4991-4994CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)We report an ab initio calcn. of the potential surface, quantum structures, and zero-point energies of CH5+ and CH2D3+ in full dimensionality. This potential energy surface is a very precise fit to 20 633 ab initio energies and an even larger data set of potential gradients, obtained at the MP2/cc-pVTZ level of theory/basis. The potential, which exactly obeys the permutational symmetry of the five hydrogen atoms, is used in diffusion Monte Carlo (DMC) calcns. of the fully anharmonic zero-point energies and ground-state wave functions of CH5+ and CH2D3+. Bond length distributions are obtained from the DMC ground state and are compared to those resulting from classical mol. dynamics simulations, which are performed at the quantum zero-point energy for roughly 300 ps.**20**McCoy, A. B.; Huang, X.; Carter, S.; Landeweer, M. Y.; Bowman, J. M. Full-dimensional vibrational calculations for H_{5}O_{2}^{+}using an*ab initio*potential energy surface.*J. Chem. Phys.*2005,*122*, 061101, DOI: 10.1063/1.1857472[Crossref], [PubMed], [CAS], Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtlWrtr0%253D&md5=654dcd1d4c39944a6f2d55037198f4bdFull-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surfaceMcCoy, Anne B.; Huang, Xinchuan; Carter, Stuart; Landeweer, Marc Y.; Bowman, Joel M.Journal of Chemical Physics (2005), 122 (6), 061101/1-061101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report quantum diffusion Monte Carlo (DMC) and variational calcns. in full dimensionality for selected vibrational states of H5O2+ using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calcns. OH-stretch fundamentals are also calcd. using "fixed-node" DMC calcns. and variationally using two versions of the code MULTIMODE. These results are compared with IR multiphoton dissocn. measurements of L. I. Yeh et al. (1989). Some preliminary results for the energies of several modes of the shared hydrogen are also reported.**21**McCoy, A. B. Diffusion monte carlo approaches for investigating the structure and vibrational spectra of fluxional systems.*Int. Rev. Phys. Chem.*2006,*25*, 77– 107, DOI: 10.1080/01442350600679347[Crossref], [CAS], Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmtV2mt70%253D&md5=4e17d880afb8e5c3b3ee09b1465463edDiffusion Monte Carlo approaches for investigating the structure and vibrational spectra of fluxional systemsMcCoy, Anne B.International Reviews in Physical Chemistry (2006), 25 (1-2), 77-107CODEN: IRPCDL; ISSN:0144-235X. (Taylor & Francis Ltd.)A review. Recent advances in diffusion Monte Carlo (DMC) are reviewed within the context of the vibrational motions of systems that undergo large amplitude motions. A review. Specifically, the authors describe the DMC approach for obtaining the ground state were function and zero-point energy (ZPE) of the system of interest, as well as extensions to the method for evaluating probability amplitudes, rotational consts., vibrationally excited states and methods for obtaining vibrational spectra. The discussion is framed in terms of the properties of several systems of current exptl. and theor. interest, specifically complexes of neon atoms with OH or SH, H3O-2, H5O+2, and CH+5. The results of the DMC simulations provide the information necessary to characterize the extent of delocalization of the probability amplitudes, even in the ground vibrational states. Methods for evaluating expectation values and vibrationally excited states are explored, and, when possible, the results are compared with those from other approaches. Finally, the methods for evaluating intensities are described and existing and future challenges for the approach are reviewed.**22**Wang, Y. M.; Babin, V.; Bowman, J. M.; Paesani, F. The water hexamer: cage, prism, or both. Full dimensional quantum simulations say both.*J. Am. Chem. Soc.*2012,*134*, 11116, DOI: 10.1021/ja304528m[ACS Full Text ], [CAS], Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XptF2gsL0%253D&md5=65e5ba6199bbd78f0ca7cb64f53ddd70The Water Hexamer: Cage, Prism, or Both. Full Dimensional Quantum Simulations Say BothWang, Yimin; Babin, Volodymyr; Bowman, Joel M.; Paesani, FrancescoJournal of the American Chemical Society (2012), 134 (27), 11116-11119CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)State-of-the-art quantum simulations on a full-dimensional ab initio potential energy surface are used to characterize the properties of the water hexamer. The relative populations of the different isomers are detd. over a wide range of temps. While the prism isomer is identified as the global min.-energy structure, the quantum simulations, which explicitly include zero-point energy and quantum thermal motion, predict that both the cage and prism isomers are present at low temp. down to almost 0 K. This is largely consistent with the available exptl. data and, in particular, with recent measurements of broadband rotational spectra of the water hexamer recorded in supersonic expansions.**23**Bowman, J. M.; Czakó, G.; Fu, B. High-dimensional ab initio potential energy surfaces for reaction dynamics calculations.*Phys. Chem. Chem. Phys.*2011,*13*, 8094– 8111, DOI: 10.1039/c0cp02722g[Crossref], [PubMed], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXkvFakurs%253D&md5=fd50abf6ba72080b0220aecc71574e87High-dimensional ab initio potential energy surfaces for reaction dynamics calculationsBowman, Joel M.; Czako, Gabor; Fu, BinaPhysical Chemistry Chemical Physics (2011), 13 (18), 8094-8111CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)A review. There has been great progress in the development of potential energy surfaces (PESs) for reaction dynamics that are fits to ab initio energies. The fitting techniques described here explicitly represent the invariance of the PES with respect to all permutations of like atoms. A review of a subset of dynamics calcns. using such PESs (currently 16 such PESs exist) is then given. Bimol. reactions of current interest to the community, namely, H + CH4 and F + CH4, are focused on. Unimol. reactions are then reviewed, with a focus on the photodissocn. dynamics of H2CO and CH3CHO, where so-called "roaming" pathways have been discovered. The challenges for electronically nonadiabatic reactions, and assocd. PESs, are presented with a focus on the OH* + H2 reaction. Finally, some thoughts on future directions and challenges are given.**24**Czakó, G.; Bowman, J. M. Reaction dynamics of methane with F, O, Cl, and Br on*ab initio*potential energy surfaces.*J. Phys. Chem. A*2014,*118*, 2839– 2864, DOI: 10.1021/jp500085h[ACS Full Text ], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXjsFOlu7w%253D&md5=ef3cf173be46dd476c74a025d372705aReaction Dynamics of Methane with F, O, Cl, and Br on ab Initio Potential Energy SurfacesCzako, Gabor; Bowman, Joel M.Journal of Physical Chemistry A (2014), 118 (16), 2839-2864CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)A review. The bimol. hydrogen abstraction reactions of methane with atoms have become benchmark systems to test and extend our knowledge of polyat. chem. reactivity. We review the state-of-the-art methodologies for reaction dynamics computations of X + methane [X = F, O(3P), Cl, Br] reactions, which consist of two key steps: (1) potential energy surface (PES) developments and (2) reaction dynamics computations on the PES using either classical or quantum methods. We briefly describe the permutationally invariant polynomial approach for step 1 and the quasiclassical trajectory method, focusing on the mode-specific polyat. product anal. and the Gaussian binning (1GB) techniques, and reduced-dimensional quantum models for step 2. High-quality full-dimensional ab initio PESs and dynamical studies of the X + CH4 and CHD3 reactions are reviewed. The computed integral cross-sections, angular, vibrational, and rotational product distributions are compared with available expts. Both exptl. and theor. findings shed light on the rules of mode-selective polyat. reactivity.**25**Bowman, J. M.; Qu, C.; Conte, R.; Nandi, A.; Houston, P. L.; Yu, Q. The MD17 datasets from the perspective of datasets for gas-phase “small” molecule potentials.*J. Chem. Phys.*2022,*156*, 240901, DOI: 10.1063/5.0089200[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFOnurnJ&md5=6c228a4aec39325136eaf734f35a2e16The MD17 datasets from the perspective of datasets for gas-phase "small" molecule potentialsBowman, Joel M.; Qu, Chen; Conte, Riccardo; Nandi, Apurba; Houston, Paul L.; Yu, QiJournal of Chemical Physics (2022), 156 (24), 240901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each mol. in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three "small" mols., ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the potential energy surfaces (PESs) in mind: a rigorous calcn. of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde, and, in the case of glycine, a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-mol. but complex chem. reactions. Finally, we introduce a new database, "QM-22," which contains datasets of mols. ranging from 4 to 15 atoms that extend to high energies and a large span of configurations. (c) 2022 American Institute of Physics.**26**Nandi, A.; Qu, C.; Houston, P. L.; Conte, R.; Bowman, J. M. Δ-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theory.*J. Chem. Phys.*2021,*154*, 051102, DOI: 10.1063/5.0038301[Crossref], [PubMed], [CAS], Google Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXjsVGlsb8%253D&md5=bfe9137fc71598377f305232c3f58047Δ-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theoryNandi, Apurba; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Bowman, Joel M.Journal of Chemical Physics (2021), 154 (5), 051102CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)"Δ-Machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) d. functional theory (DFT) energies and gradients close to a coupled cluster (CC) level of accuracy. Here, we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation VLL→CC = VLL + ΔVCC-LL, and demonstrated for CH4, H3O+, and trans and cis-N-Me acetamide (NMA), CH3CONHCH3. For these mols., the LL PES, VLL, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients and ΔVCC-LL is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small no. of CCSD(T) energies. For CH4, these are new calcns. adopting an aug-cc-pVDZ basis, for H3O+, previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA, new CCSD(T)-F12/aug-cc-pVDZ calcns. are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results for the small mols., and for 12-atom NMA, training is done with 4696 CCSD(T) energies. (c) 2021 American Institute of Physics.**27**Ramakrishnan, R.; Dral, P. O.; Rupp, M.; von Lilienfeld, O. A. Big data meets quantum chemistry approximations: The Δ-machine learning approach.*J. Chem. Theory Comput.*2015,*11*, 2087– 2096, DOI: 10.1021/acs.jctc.5b00099[ACS Full Text ], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtlams7Y%253D&md5=a59b33f51a9dd6dbad95290f2642c306Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning ApproachRamakrishnan, Raghunathan; Dral, Pavlo O.; Rupp, Matthias; von Lilienfeld, O. AnatoleJournal of Chemical Theory and Computation (2015), 11 (5), 2087-2096CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Chem. accurate and comprehensive studies of the virtual space of all possible mols. are severely limited by the computational cost of quantum chem. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approx. legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger mol. sets than used for training. For thermochem. properties of up to 16k isomers of C7H10O2 we present numerical evidence that chem. accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qual. relationship between mol. entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chem. and machine learning models trained on 1 and 10% of 134k org. mols., to reproduce enthalpies of all remaining mols. at d. functional theory level of accuracy.**28**Dral, P. O.; Owens, A.; Dral, A.; Csányi, G. Hierarchical machine learning of potential energy surfaces.*J. Chem. Phys.*2020,*152*, 204110, DOI: 10.1063/5.0006498[Crossref], [PubMed], [CAS], Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVGgsrrE&md5=4b6eb648c3879342f52bc8c000ac94f6Hierarchical machine learning of potential energy surfacesDral, Pavlo O.; Owens, Alec; Dral, Alexey; Csanyi, GaborJournal of Chemical Physics (2020), 152 (20), 204110CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present hierarchical machine learning (hML) of highly accurate potential energy surfaces (PESs). Our scheme is based on adding predictions of multiple Δ-machine learning models trained on energies and energy corrections calcd. with a hierarchy of quantum chem. methods. Our (semi-)automatic procedure dets. the optimal training set size and compn. of each constituent machine learning model, simultaneously minimizing the computational effort necessary to achieve the required accuracy of the hML PES. Machine learning models are built using kernel ridge regression, and training points are selected with structure-based sampling. As an illustrative example, hML is applied to a high-level ab initio CH3Cl PES and is shown to significantly reduce the computational cost of generating the PES by a factor of 100 while retaining similar levels of accuracy (errors of ∼1 cm-1). (c) 2020 American Institute of Physics.**29**Nguyen, K. A.; Rossi, I.; Truhlar, D. G. A dual-level Shepard interpolation method for generating potential energy surfaces for dynamics calculations.*J. Chem. Phys.*1995,*103*, 5522– 5530, DOI: 10.1063/1.470536**30**Fu, B.; Xu, X.; Zhang, D. H. A hierarchical construction scheme for accurate potential energy surface generation: An application to the F + H_{2}reaction.*J. Chem. Phys.*2008,*129*, 011103, DOI: 10.1063/1.2955729[Crossref], [PubMed], [CAS], Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXosVyhtrg%253D&md5=5f12304ac43c1ededad519c07bbf3c99A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reactionFu, Bina; Xu, Xin; Zhang, Dong H.Journal of Chemical Physics (2008), 129 (1), 011103/1-011103/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a hierarchical construction scheme for accurate ab initio potential energy surface generation. The scheme is based on the observation that when mol. configuration changes, the variation in the potential energy difference between different ab initio methods is much smaller than the variation for potential energy itself. This means that it is easier to numerically represent energy difference to achieve a desired accuracy. Because the computational cost for ab initio calcns. increases very rapidly with the accuracy, one can gain substantial saving in computational time by constructing a high accurate potential energy surface as a sum of a low accurate surface based on extensive ab initio data points and an energy difference surface for high and low accuracy ab initio methods based on much fewer data points. The new scheme was applied to construct an accurate ground potential energy surface for the FH2 system using the coupled-cluster method and a very large basis set. The constructed potential energy surface is found to be more accurate on describing the resonance states in the FH2 and FHD systems than the existing surfaces. (c) 2008 American Institute of Physics.**31**Yu, Q.; Bowman, J. M.*Ab initio*potential for H_{3}O^{+}→ H^{+}+ H_{2}O: A step to a many-body representation of the hydrated proton?.*J. Chem. Theory Comput.*2016,*12*, 5284– 5292, DOI: 10.1021/acs.jctc.6b00765[ACS Full Text ], [CAS], Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFOktrzP&md5=480982a0ce8c433d2c9ed48861c52ff2Ab Initio Potential for H3O+ → H+ + H2O: A Step to a Many-Body Representation of the Hydrated Proton?Yu, Qi; Bowman, Joel M.Journal of Chemical Theory and Computation (2016), 12 (11), 5284-5292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We report a new potential energy surface (PES) for hydronium that dissocs. to H+ + H2O. The PES is a permutationally invariant fit to a data set of nearly 100,000 electronic energies, of which most are CCSD(T)-F12/aug-cc-pVQZ, plus a small set of MRCI-aug-cc-pVTZ diabatic energies in the region where the CCSD(T) method fails. The long-range part of the PES is described accurately by a classical Coulomb interaction between the proton and H2O using partial charges obtained from an accurate, full-dimensional dipole moment surface. A switching function connects the fitted PES to this long-range interaction. The fidelity of this global PES is detd. by a combination of std. geometry and harmonic analyses at the min. and inversion saddle point. In addn., VSCF/VCI calcns. of the fundamentals and tunneling splittings are reported; all of these are within 3 cm-1 or less of exptl. values. A diffusion Monte Carlo calcn. is also reported for the zero-point state. The PES is used in a two-body representation of the interaction of the proton with two water mols., including a 2-body H2O-H2O interaction, and is shown to give a realistic description of the Zundel cation H5O2+. This demonstrates that the PES may be usable as a component in a many-body potential describing the hydrated proton, esp. for vibrational calcns. of protonated water clusters.**32**Cisneros, G. A.; Wikfeldt, K. T.; Ojamäe, L.; Lu, J.; Xu, Y.; Torabifard, H.; Bartók, A. P.; Csányi, G.; Molinero, V.; Paesani, F. Modeling molecular interactions in water: From pairwise to many-body potential energy functions.*Chem. Rev.*2016,*116*, 7501– 7528, DOI: 10.1021/acs.chemrev.5b00644[ACS Full Text ], [CAS], Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XnvFeqs7w%253D&md5=69e5c66d2b4a029a4ca90b940366194aModeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy FunctionsCisneros, Gerardo Andres; Wikfeldt, Kjartan Thor; Ojamae, Lars; Lu, Jibao; Xu, Yao; Torabifard, Hedieh; Bartok, Albert P.; Csanyi, Gabor; Molinero, Valeria; Paesani, FrancescoChemical Reviews (Washington, DC, United States) (2016), 116 (13), 7501-7528CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. Almost 50 years have passed from the first computer simulations of water, and a large no. of mol. models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of anal. potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approxns. and on their ability to accurately reproduce ref. data obtained from state-of-the-art electronic structure calcns. and exptl. measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a phys. correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.**33**Qu, C.; Yu, Q.; Conte, R.; Houston, P. L.; Nandi, A.; Bowman, J. M. A Δ-machine learning approach for force fields, illustrated by a CCSD(T) 4-body correction to the MB-pol water potential.*Digital Discovery*2022,*1*, 658– 664, DOI: 10.1039/D2DD00057A**34**Fanourgakis, G. S.; Xantheas, S. S. The flexible, polarizable, Thole-type interaction potential for water (TTM2-F) revisited.*J. Phys. Chem. A*2006,*110*, 4100– 4106, DOI: 10.1021/jp056477k[ACS Full Text ], [CAS], Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhvVKlsbs%253D&md5=d088b728272fae6e49733fc1f862a5efThe Flexible, Polarizable, Thole-Type Interaction Potential for Water (TTM2-F) RevisitedFanourgakis, George S.; Xantheas, Sotiris S.Journal of Physical Chemistry A (2006), 110 (11), 4100-4106CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)We present a revision of the flexible, polarizable, Thole-type interaction potential for water [J. Chem. Phys. 2002, 116, 5115], which allows for condensed-phase simulations. The revised version (TTM2.1-F) of the potential correctly describes the individual water mol. dipole moment and alleviates problems arising at short intermol. sepns. that can be sampled in the course of mol. dynamics and Monte Carlo simulations of condensed environments. Furthermore, its parallel implementation under periodic boundary conditions enables the efficient calcn. of the macroscopic structural and thermodn. properties of liq. water, as its performance scales superlinearly with up to a no. of 64 processors for a simulation box of 512 mols. We report the radial distribution functions, av. energy, internal geometry, and dipole moment in the liq. as well as the d., dielec. const., and self-diffusion coeff. at T = 300 K from (NVT) and (NPT) classical mol. dynamics simulations by using the revised version of the potential.**35**Qu, C.; Bowman, J. M. Communication: A fragmented, permutationally invariant polynomial approach for potential energy surfaces of large molecules: Application to*N*-methyl acetamide.*J. Chem. Phys.*2019,*150*, 141101, DOI: 10.1063/1.5092794[Crossref], [PubMed], [CAS], Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXmvFWgtrw%253D&md5=5beda36666eda7f3a1c0b94b46a48225A fragmented, permutationally invariant polynomial approach for potential energy surfaces of large molecules: Application to N-methyl acetamideQu, Chen; Bowman, Joel M.Journal of Chemical Physics (2019), 150 (14), 141101/1-141101/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We describe and apply a method to extend permutationally invariant polynomial (PIP) potential energy surface (PES) fitting to mols. with more than 10 atoms. The method creates a compact basis of PIPs as the union of PIPs obtained from fragments of the mol. An application is reported for trans-N-Me acetamide, where B3LYP/cc-pVDZ electronic energies and gradients are used to develop a full-dimensional potential for this prototype peptide mol. The performance of several fragmented bases is verified against a benchmark PES using all (66) Morse variables. The method appears feasible for much larger mols. (c) 2019 American Institute of Physics.**36**Nandi, A.; Qu, C.; Bowman, J. M. Full and fragmented permutationally invariant polynomial potential energy surfaces for*trans*and*cis N*-methyl Acetamide and isomerization saddle points.*J. Chem. Phys.*2019,*151*, 084306, DOI: 10.1063/1.5119348[Crossref], [PubMed], [CAS], Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhs12jtLjN&md5=ca33c1749defcb985c9a613ce9b1140aFull and fragmented permutationally invariant polynomial potential energy surfaces for trans and cis N-methyl acetamide and isomerization saddle pointsNandi, Apurba; Qu, Chen; Bowman, Joel M.Journal of Chemical Physics (2019), 151 (8), 084306/1-084306/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report full and fragmented potential energy surfaces (PESs) for N-Me acetamide that contain the cis and trans isomers and the saddle points sepg. them. The full PES uses Permutationally Invariant Polynomials (PIPs) in reduced symmetry which describe the three-fold symmetry of each Me rotor. A more efficient PES is an extension of the fragmented PIP approach we reported recently. In this approach, the set of Morse variables is partitioned and the fragmented PIP basis is the union of the PIP basis for each set of variables. This approach is general and can be used with neural network fits. The fits are done using roughly 250 000 electronic energies and gradients obtained from direct dynamics, using the B3LYP/cc-pVDZ level of theory. The full PIP basis in 66 Morse variables, with a max. polynomial order of 3, contains 8040 linear coeffs. The fragmented PIP basis, also with a max. polynomial order of 3, contains 6121 coeffs. The root-mean-square errors of both PESs are roughly 100 cm-1 for energies and 15 cm-1/bohr per atom for gradients, for energies up to roughly 45 000 cm-1, relative to the trans min. Energies and normal mode frequencies of the cis and trans isomers for the full and fragmented PESs agree well with direct calcns. The energies of the two saddle points sepg. these min. are precisely given by both PESs. Diffusion Monte Carlo calcns. of the zero-point energies of the two isomers are also reported. (c) 2019 American Institute of Physics.**37**Suenram, R.; Golubiatnikov, G.; Leonov, I.; Hougen, J.; Ortigoso, J.; Kleiner, I.; Fraser, G. Reinvestigation of the microwave spectrum of acetamide.*J. Mol. Spectrosc.*2001,*208*, 188– 193, DOI: 10.1006/jmsp.2001.8377[Crossref], [CAS], Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXmsF2mu7c%253D&md5=5d22c08e93ce8af1602bb4c8f4c416caReinvestigation of the Microwave Spectrum of AcetamideSuenram, R. D.; Golubiatnikov, G. Yu.; Leonov, I. I.; Hougen, J. T.; Ortigoso, J.; Kleiner, I.; Fraser, G. T.Journal of Molecular Spectroscopy (2001), 208 (2), 188-193CODEN: JMOSA3; ISSN:0022-2852. (Academic Press)About 50 jet-cooled Fourier transform lines for acetamide were recorded using a new version of spectrometer, which was upgraded with a heated nozzle and an expanded automatic scanning range. Nuclear quadrupole hyperfine structure arising from the N atom was removed theor. to yield hyperfine-free center frequencies. In addn., ∼30 mm measurements were carried out. When hyperfine structure was obsd. for these lines, it was also removed theor. A set of 115 A-species and E-species rotational transitions in the torsional ground state, obtained by combining new measurements with the literature data, were fit to a model involving 28 torsion, rotation, and torsion-rotation interaction parameters to near exptl. uncertainty (i.e., to a weighted unitless std. deviation of 1.5), significantly improving on previous fits. Various theor. problems assocd. with K labels for E-species levels in this very low barrier mol. are briefly discussed and used to justify a variant of the signed Ka labels frequently used for internal-rotor E states. (c) 2001 Academic Press.**38**Nandi, A.; Conte, R.; Qu, C.; Houston, P. L.; Yu, Q.; Bowman, J. M. Quantum calculations on a new CCSD(T) machine-learned potential energy surface reveal the leaky nature of gas-phase*trans*and*gauche*ethanol conformers.*J. Chem. Theory Comput.*2022,*18*, 5527– 5538, DOI: 10.1021/acs.jctc.2c00760[ACS Full Text ], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitV2jtL3N&md5=4eb3d99f030720b57d1d9eb69e22fb4eQuantum Calculations on a New CCSD(T) Machine-Learned Potential Energy Surface Reveal the Leaky Nature of Gas-Phase Trans and Gauche Ethanol ConformersNandi, Apurba; Conte, Riccardo; Qu, Chen; Houston, Paul L.; Yu, Qi; Bowman, Joel M.Journal of Chemical Theory and Computation (2022), 18 (9), 5527-5538CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Ethanol is a mol. of fundamental interest in combustion, astrochem., and condensed phase as a solvent. It is characterized by two Me rotors and trans (anti) and gauche conformers, which are known to be very close in energy. Here we show that based on rigorous quantum calcns. of the vibrational zero-point state, using a new ab initio potential energy surface (PES), the ground state resembles the trans conformer, but substantial delocalization to the gauche conformer is present. This explains exptl. issues about identification and isolation of the two conformers. This "leak" effect is partially quenched when deuterating the OH group, which further demonstrates the need for a quantum mech. approach. Diffusion Monte Carlo and full-dimensional semiclassical dynamics calcns. are employed. The new PES is obtained by means of a Δ-machine learning approach starting from a pre-existing low level d. functional theory surface. This surface is brought to the CCSD(T) level of theory using a relatively small no. of ab initio CCSD(T) energies. Agreement between the cor. PES and direct ab initio results for std. tests is excellent. One- and two-dimensional discrete variable representation calcns. focusing on the trans-gauche torsional motion are also reported, in reasonable agreement with expt.**39**Durig, J.; Larsen, R. Torsional vibrations and barriers to internal rotation for ethanol and 2,2,2-trifluoroethanol.*J. Mol. Struct.*1990,*238*, 195– 222, DOI: 10.1016/0022-2860(90)85015-B[Crossref], [CAS], Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXhtVSqtrw%253D&md5=169af24806d8b4da302d68bcff4861b1Torsional vibrations and barriers to internal rotation for ethanol and 2,2,2-trifluoroethanolDurig, J. R.; Larsen, R. A.Journal of Molecular Structure (1990), 238 (), 195-222CODEN: JMOSB4; ISSN:0022-2860.The far-IR (370-50 cm-1) spectra of gaseous ethanol, EtOH, and the O-d compd. were recorded at a resoln. of 0.10 cm-1. Similar far-IR spectra were collected for 2,2,2-trifluoroethanol, CF3CH2OH, and the O-d, C-d2 and -d3 isotopic species. In addn., the Raman (4000-50 cm-1) and the mid-IR (5000-400 cm-1) spectra were collected for CF3CH2OH and the isotopic compds. in the vapor phase. A detailed examn. of the torsional modes was carried out and potential functions for the hindered internal rotation of the O-H and O-D groups and the CH3 and CF3 rotors were calcd. For ethanol, the fundamental O-H torsion for the trans conformer is obsd. at 202.6 cm-1 whereas for the gauche conformation, the 1-←0+ transition is found at 243.1 cm-1 and the 1+←0- transition is 195.8 cm-1. An asym. potential function utilizing these transitions gives values of 403 cm-1 (1.15 kcal mol-1) for the trans/gauche barrier and 399 cm-1 (1.14 kcal mol-1) for the gauche/gauche barrier with the trans conformer more stable by 42 cm-1 (120 cal mol-1) than the gauche conformer. Potential functions for the hydroxy torsions are also calcd. for the ethanol-O-d compd. and the four 2,2,2-trifluoroethanol isotopic mols. The CH3 torsional transitions of trans ethanol give a V3 barrier of 1185 ± 16 cm-1 (3.39 ± 0.05 kcal mol-1) and the corresponding barrier for the gauche conformer is 1251 ± 2 cm-1 (3.58 ± 0.01 kcal mol-1). Similarly, a series of CF3 torsional transitions was obsd. for the trans and gauche conformations of the CF3CH2OH mol. as well as for some of the isotopic species. In addn. to the examn. of the far-IR spectra, a series of sum and difference bands assocd. with the O-H and O-D stretching fundamentals is found in the mid-IR spectra for the 2,2,2-trifluoroethanol compds. and a possible explanation for these modes is given.**40**Wang, Y.; Braams, B. J.; Bowman, J. M.; Carter, S.; Tew, D. P. Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface.*J. Chem. Phys.*2008,*128*, 224314, DOI: 10.1063/1.2937732[Crossref], [PubMed], [CAS], Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXntFyns7c%253D&md5=bb210d3fb84a1cb7f545f6c16c72247eFull-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surfaceWang, Yimin; Braams, Bastiaan J.; Bowman, Joel M.; Carter, Stuart; Tew, David P.Journal of Chemical Physics (2008), 128 (22), 224314/1-224314/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Quantum calcns. of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcal/mol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calcns. of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calcd. using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm-1 in Cartesian coordinates and 22.6 cm-1 in normal coordinates, with an uncertainty of 2-3 cm-1. This splitting is also calcd. based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calcn. gives a tunneling splitting of 21-22 cm-1. The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm-1. These calcd. tunneling splittings agree with each other to within less than the std. uncertainties obtained with the DMC method used, which are between 2 and 3 cm-1, and agree well with the exptl. values of 21.6 and 2.9 cm-1 for the H and D transfer, resp. (c) 2008 American Institute of Physics.**41**Qu, C.; Conte, R.; Houston, P. L.; Bowman, J. M. Full-dimensional potential energy surface for acetylacetone and tunneling splittings.*Phys. Chem. Chem. Phys.*2021,*23*, 7758– 7767, DOI: 10.1039/D0CP04221H[Crossref], [PubMed], [CAS], Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvVGgs7rK&md5=fde99d4eba58249eba57685bef99d1a4Full-dimensional potential energy surface for acetylacetone and tunneling splittingsQu, Chen; Conte, Riccardo; Houston, Paul L.; Bowman, Joel M.Physical Chemistry Chemical Physics (2021), 23 (13), 7758-7767CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)We present a full-dimensional potential energy surface for acetylacetone (AcAc) using full and fragmented permutationally invariant polynomial approaches. Previously reported MP2/aVTZ energies and gradients are augmented by addnl. calcns. at this level of theory for the fits. Numerous stationary points are reported as are the usual metrics to assess the precision of the fit. The electronic barrier height for the H-atom transfer is roughly 2.2 kcal mol-1. Diffusion Monte Carlo (DMC) calcns. are used to calc. the ground state wavefunction and zero-point energy of acetylacetone. These together with fixed-node DMC calcns. for the first excited-state provide the predicted tunneling splitting due to the barrier to H-transfer sepg. two equiv. wells. Simpler 1d calcns. of this splitting are also reported for varying barrier heights including the CCSD(T) barrier height of 3.2 kcal mol-1. Based on those results the DMC splitting of 160 cm-1 with a statistical uncertainty of roughly 21 cm-1, calcd. using the MP2-based PES, is estd. to decrease to 100 cm-1 for a barrier of 3.2 kcal mol-1. The fragmented surface is shown to be fast to evaluate.**42**Meuwly, M. Atomistic simulations for reactions and vibrational spectroscopy in the era of machine learning─*quo vadis?*.*J. Phys. Chem. B*2022,*126*, 2155– 2167, DOI: 10.1021/acs.jpcb.2c00212[ACS Full Text ], [CAS], Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XmvV2hsr8%253D&md5=1adeb410ff1794f8fe5abaec37066868Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning-Quo Vadis?Meuwly, MarkusJournal of Physical Chemistry B (2022), 126 (11), 2155-2167CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)A review. Atomistic simulations using accurate energy functions can provide mol.-level insight into functional motions of mols. in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the IR spectroscopy of mols. in soln. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose mol. simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.**43**Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.*MOLPRO, a package of ab initio programs*, ver. 2015.1, 2015; http://www.molpro.net.Google ScholarThere is no corresponding record for this reference.**44**Qu, C.; Houston, P. L.; Conte, R.; Nandi, A.; Bowman, J. M. Breaking the coupled cluster barrier for machine-learned potentials of large molecules: The case of 15-Atom acetylacetone.*J. Phys. Chem. Lett.*2021,*12*, 4902– 4909, DOI: 10.1021/acs.jpclett.1c01142[ACS Full Text ], [CAS], Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhtFSitb%252FL&md5=cf8ef9d6a8f3da518260f003408922bcBreaking the Coupled Cluster Barrier for Machine-Learned Potentials of Large Molecules: The Case of 15-Atom AcetylacetoneQu, Chen; Houston, Paul L.; Conte, Riccardo; Nandi, Apurba; Bowman, Joel M.Journal of Physical Chemistry Letters (2021), 12 (20), 4902-4909CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Machine-learned potential energy surfaces (PESs) for mols. with more than 10 atoms are typically forced to use lower-level electronic structure methods such as d. functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2). While these are efficient and realistic, they fall short of the accuracy of the "gold std." coupled-cluster method, esp. with respect to reaction and isomerization barriers. We report a major step forward in applying a Δ-machine learning method to the challenging case of acetylacetone, whose MP2 barrier height for H-atom transfer is low by roughly 1.1 kcal/mol relative to the benchmark CCSD(T) barrier of 3.2 kcal/mol. From a database of 2151 local CCSD(T) energies and training with as few as 430 energies, we obtain a new PES with a barrier of 3.5 kcal/mol in agreement with the LCCSD(T) barrier of 3.5 kcal/mol and close to the benchmark value. Tunneling splittings due to H-atom transfer are calcd. using this new PES, providing improved ests. over previous ones obtained using an MP2-based PES.**45**Redington, R. L. H atom and heavy atom tunneling process in tropolone.*J. Chem. Phys.*2000,*113*, 2319– 2335, DOI: 10.1063/1.482046[Crossref], [CAS], Google Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXltFygt74%253D&md5=bbb86ee39b2783206169d815a3e26e8cH atom and heavy atom tunneling processes in tropoloneRedington, Richard L.Journal of Chemical Physics (2000), 113 (6), 2319-2335CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The min. energy pathway leading between the tautomers of tropolone was calcd. using MO methods. This, with various 1D and 2D cuts of the potential energy surface (PES) topog., reveals the {tunneling skeleton}/{tunneling H atom} mechanism for tautomerization. In the zero-point states the H atom is localized to one of the O atoms until the tropolone skeleton becomes sufficiently vibrationally displaced towards C2v configurations that near-equal double-min. potential energy functions (PEFs) arise for the H atom vibration. The resulting delocalization of the H atom between the two O atom sites allows the skeletal displacement to proceed through the barrier and the tautomerization process to be completed. The v1 (OH stretching) energies in quantum states N1 are strongly dependent on the skeletal geometry and, adiabatically sepd. from the slow v22 vibration, they contribute to markedly different 1D effective potential energy functions V22eff[N1] for v22. V22eff[N1=0] is a normal equal double min. PEF while V22eff[N1≠0] have more complex shapes. Expressed as a function of the v22 skeletal displacement ΔS, the v1 states show a nonadiabatic curve crossing E1(1) E1(2) contributing to the V22eff[N1=1 2] effective PEF for v22 vibration in the lowest excited OH stretching state. This function, rather than V22eff[N1=1], is strongly supported by the IR observations on v1. The computed effective energy barriers on the "model" tunneling path for the zero point states are 4.97 kcal/mol for the skeletal motion, and 3.22 kcal/mol for the H atom vibration at C2v skeletal geometry. Overall, the independent computational model predicts the major spectroscopic features obsd. for S0 tropolone(OH) and tropolone(OD): (a) similar IR tunneling doublets with ∼10 cm-1 splittings for the v22 skeletal vibration; (b) weak v1 IR absorbance with 20 and 5 cm-1 tunneling doublet sepns. for the isotopomers; (c) small tunneling splittings of the zero point states; and (d) unresolved vibrational state-specific IR tunneling doublets for all other fundamentals.**46**Redington, R. L.; Redington, T. E.; Montgomery, J. M. IR spectra of tropolone(OH) and tropolone(OD).*J. Chem. Phys.*2000,*113*, 2304– 2318, DOI: 10.1063/1.482045[Crossref], [CAS], Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXltFygtrc%253D&md5=1428f2b1fb3055eeef608283373e4340IR spectra of tropolone(OH) and tropolone(OD)Redington, Richard L.; Redington, Theresa E.; Montgomery, Jason M.Journal of Chemical Physics (2000), 113 (6), 2304-2318CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)IR spectra of tropolone(OH) and tropolone(OD) obtained from vapor phase, solvated, and rare gas matrix-isolated samples, and from fluorescence dip IR spectroscopy expts. by Frost et al. on jet-cooled samples, are analyzed with the guidance of high level ab initio MO computations. The anharmonicity of the double min. global potential energy surface of S0 tropolone is manifested by multistate local resonance networks coupling fundamental vibrations to nearby overtone and combination states. These resonance networks pervade the IR spectrum of tropolone >500 cm-1, and the absorbances are much more strongly perturbed from harmonic level predictions than the frequencies. Some of the IR absorbances are also sensitive to intermol. interactions. At max. spectral resolns. reaching ∼0.2 cm-1 only the v1 and v22 (OH stretching and nascent skeletal tunneling) vibrations show resolved vibrational state-specific tunneling doublets. The tunneling behavior of tropolone is analyzed in the accompanying article.**47**Redington, R. L.; Sams, R. L. N_{2}pressure broadened Q branch spikes and vibration–contortion–rotation effects in the high resolution FTIR spectrum of tropolone.*Chem. Phys.*2002,*283*, 135– 151, DOI: 10.1016/S0301-0104(02)00614-6[Crossref], [CAS], Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XntVWksLw%253D&md5=539d3e1fc2d22037d5e683953ec53043N2 pressure broadened Q branch spikes and vibration-contortion-rotation effects in the high resolution FTIR spectrum of tropoloneRedington, Richard L.; Sams, Robert L.Chemical Physics (2002), 283 (1-2), 135-151CODEN: CMPHC2; ISSN:0301-0104. (Elsevier Science B.V.)N pressure broadening effects are obsd. on the high resoln. (0.0025 cm-1) FTIR spectrum of gaseous tropolone at 298 K and 32 m of path length. Broadening observations on narrow absorption spikes contribute to understanding of the spectroscopy and dynamics of tropolone in several ways. First, they help to establish a remarkable progression of sharp peaks near 752 cm-1 as a part of the Q branch of the anharmonic ν22 (COH torsion) fundamental. The subband spacings of ∼0.005-0.010 cm-1 are too large to be detd. by harmonic vibrational differences in the rotational consts. alone and are attributed to vibration-contortion-rotation perturbations of the upper state (ν22) energy levels of this anharmonic and relatively large amplitude vibration. Second, the isolated and sharp Q branch spikes near 915 cm-1 allow 1st ests. to be made for effective composite pressure broadening coeffs. of tropolone-N2 collisions. The coeffs. for transitions within the Ncon=0 and Ncon=1 contortion states differ from each other. They are relatively small due to the preponderance of high rotational states in their compn. Third, N2 broadening effects on substructure in the Q branch doublet near 754 cm-1 help support the assignment of this doublet to tunneling structure of the ν37 fundamental (contortion or incipient skeletal tunneling). The obsd. doublet components appear as perturbatively IR enhanced 3 and 5 peak fragments of weak longer progressions. The parallel spectroscopic behaviors of the perturbed anharmonic ν22 and ν37 vibrations differ markedly from behavior obsd. for the quasiharmonic vibrations.**48**Redington, R. L.; Sams, R. L. State-specific spectral doublets in the FTIR spectrum of gaseous tropolone.*J. Phys. Chem. A*2002,*106*, 7494– 7511, DOI: 10.1021/jp0122631[ACS Full Text ], [CAS], Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXosFahu7c%253D&md5=06b6d6ba5edfc9e28001449114483accState-Specific Spectral Doublets in the FTIR Spectrum of Gaseous TropoloneRedington, Richard L.; Sams, Robert L.Journal of Physical Chemistry A (2002), 106 (33), 7494-7511CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The IR absorption spectrum of tropolone vapor at 25 °C, ∼0.01 Torr, and 32 m path length has been recorded from 960 to about 700 cm-1 at a resoln. of 0.0025 cm-1. Twenty-nine cold band and hot band spectral tunneling doublets marked by sharp type A or type C Q branch apexes protruding from the congested vibration-contortion-rotation absorption profiles are assigned. Twenty-six vibration-contortion state-specific splittings are estd. for tropolone in its ground electronic state. This no. is currently unprecedented in the literature for any sizable mol. About half of these quasiharmonic vibrational states show an appreciable quenching of tunneling due to increased effective barriers and/or path lengths and, in the case of the nominal COH torsion, the tunneling is reduced to 0.07 of the zero-point (ZP) value of 0.974 cm-1. The anal. is guided by predictions of the independent {tunneling skeleton}{tunneling H atom} tautomerization model that was previously applied to the vibrational spectrum and tautomerization mechanism of tropolone. The increase of effective tunneling path length by a few percent over the ZP path length is attributed to dynamical complexity arising from an atom-to-atom exchange of unequal vibrational displacements as a part of the tautomerization process. This aspect of tunneling quenching behavior can arise for quasiharmonic vibrations lacking direct contact to the OH···O group. For the case of tropolone, the tautomerization model advocates heavy atom tunneling as equal in importance to H atom tunneling. Heavy atom tunneling is supported by the observation of a (perturbed) spectral tunneling doublet at 754 cm-1 with the sepn. 0.80 cm-1. This doubling of the high frequency component of the previously obsd. 11 cm-1 doublet obsd. using Ne matrix-isolation sampling provides evidence for the "doublet of doublet" quartet structure predicted for the ν37 nascent skeletal tunneling (contortion) vibration. The compilation of numerous vibrational state-specific tunneling doublings for a 15-atom nonrigid mol. invites further exptl. and theor. research aimed at advancing the understanding of multidimensional intramol. tunneling dynamics, vibrational energy redistribution, and unimol. reaction kinetics. Several strong parallels are seen between the vibrational interactions arising in our studies of the tautomerization of tropolone and those appearing in recent articles discussing possible behaviors in the active sites of enzymic H transfer reactions.**49**Redington, R. L.; Redington, T. E.; Blake, T. A.; Sams, R. L.; Johnson, T. J. O18 Effects on the infrared spectrum and skeletal tunneling of tropolone.*J. Chem. Phys.*2005,*122*, 224311, DOI: 10.1063/1.1897367[Crossref], [PubMed], [CAS], Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXlsFGlsbk%253D&md5=c8442542c7d6a616260726eddcea4b3e18O effects on the infrared spectrum and skeletal tunneling of tropoloneRedington, Richard L.; Redington, Theresa E.; Blake, Thomas A.; Sams, Robert L.; Johnson, Timothy J.Journal of Chemical Physics (2005), 122 (22), 224311/1-224311/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)IR-absorption profiles obsd. for vibrational transitions of gaseous tropolone often show sharp Q branch peaks, some of them ultranarrow spikes, indicative of the band origins for vibrational state-specific spectral tunneling doublets. O isotope effects for 2 CH wagging fundamentals, the COH torsion fundamental, and the skeletal contortion fundamental are reported. They allow considerations to be given: (1) O isotope effects on the vibrational frequencies and state-specific tunneling splittings; (2) the asymmetry offset of the potential-energy min. for 16O and 18O tropolone; and (3) addnl. details concerning previously proposed high J rotation-contortion resonances in the contortional fundamental. The new results help to characterize the skeletal contortion fundamental and support the joint participation of skeletal tunneling with H tunneling in the vibrational state-specific tautomerization processes of tropolone in its ground electronic state.**50**Redington, R. L.; Redington, T. E.; Sams, R. L. Quantum tunneling in the midrange vibrational fundamentals of tropolone.*J. Phys. Chem. A*2006,*110*, 9633– 9641, DOI: 10.1021/jp062068s[ACS Full Text ], [CAS], Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmvFWhsbw%253D&md5=2cbdaf0496264daa12c7be6a49d013c1Quantum Tunneling in the Midrange Vibrational Fundamentals of TropoloneRedington, Richard L.; Redington, Theresa E.; Sams, Robert L.Journal of Physical Chemistry A (2006), 110 (31), 9633-9642CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The Fourier transform IR spectrum of tropolone(OH) vapor in the 1175-1700 cm-1 region is reported at 0.0025 and 0.10 cm-1 spectral resolns. The 12 vibrational fundamentals in this region of rapidly rising vibrational state d. are dominated by mixts. of the CC, CO, CCH, and COH internal coordinates. Ests. based on the measurement of sharp Q branch peaks are reported for 11 of the spectral doublet component sepns. DSν = |Δν ± Δ0|. Δ0 = 0.974 Cm-1 is the known zero-point splitting, and three a1 modes show tunneling splittings Δν ≈ Δ0, four b2 modes show splittings Δν ≈ 0.90Δ0, and the remaining four modes show splittings Δνv falling 5-14% from Δ0. Significantly, the splitting for the nominal COH bending mode ν8 (a1) is small, i.e., 10% from Δ0. Many of the vibrational excited states demonstrate strong anharmonic behavior, but there are only mild perturbations on the tautomerization mechanism driving Δ0. The data suggest, esp. for the higher frequency a1 fundamentals, the onset of selective intramol. vibrational energy redistribution processes that are fast on the time scale of the tautomerization process. These appear to delocalize and smooth out the topog. modifications of the zero-point potential energy surface that are anticipated to follow absorption of the νν photon. Further, the spectra show the propensity for the Δν splittings of b2 and other complex vibrations to be damped relative to Δ0.**51**Redington, R. L.; Redington, T. E.; Sams, R. L. Infrared absorption spectra in the hydroxyl stretching regions of gaseous tropolone OHO Isotopomers.*Z. Phys. Chem.*2008,*222*, 1197– 1211, DOI: 10.1524/zpch.2008.5383[Crossref], [CAS], Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhsV2js7jN&md5=69470b2468135b4a3a0feba0c8723d69Infrared absorption spectra in the hydroxyl stretching regions of gaseous tropolone OHO isotopomersRedington, Richard L.; Redington, Theresa E.; Sams, Robert L.Zeitschrift fuer Physikalische Chemie (Muenchen, Germany) (2008), 222 (8-9), 1197-1211CODEN: ZPCFAX; ISSN:0942-9352. (Oldenbourg Wissenschaftsverlag GmbH)Fourier transform IR (FTIR) absorption spectra in the 2000 to 3500 cm-1 range are reported for the gaseous 16O, 16O-, and 18O, 18O-isotopomers of tropolone[OH(OD)] at 25°. The spectral doublet component sepns. are near 20 and 19 cm-1 for 16O, 16O-, and 18O, 18O-Tp(OH), resp., and near 7 and 6.5 cm-1 for 16O, 16O-, and 18O, 18O-Tp(OD). The spectra suggest the tautomerization tunneling mechanisms in these states are complex multidimensional processes including the participation of IVR. In general, the OHO isotope effects demonstrate a mixing of O atom displacement coordinates into the intramol. dynamics for most of the vibrational states obsd. in the fundamental CH/OH(OD) stretching regions.**52**Redington, R. L.; Redington, T. E.; Sams, R. L. Tunneling splittings for “O···O stretching” and other vibrations of tropolone isotopomers observed in the infrared spectrum below 800 cm^{–1}.*J. Phys. Chem. A*2008,*112*, 1480– 1492, DOI: 10.1021/jp0757255[ACS Full Text ], [CAS], Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXps1Kjsg%253D%253D&md5=5998090839f0024081ba1a2028089b78Tunneling Splittings for "O···O Stretching" and Other Vibrations of Tropolone Isotopomers Observed in the Infrared Spectrum Below 800 cm-1Redington, Richard L.; Redington, Theresa E.; Sams, Robert L.Journal of Physical Chemistry A (2008), 112 (7), 1480-1492CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)Fourier transform IR absorption spectra contg. evidence for about two dozen spectral tunneling doublets are reported for gaseous tropolone(OH), tropolone (OD), and 18O,18O-tropolone(OH) in the 800 to 300 cm-1 spectral range. No FTIR absorption was detected in the 300-150 cm-1 range. The known zero-point (ZP) tunneling splitting values Δ0 = 0.974 cm-1 for tropolone(OH) (Tanaka et al.) and 0.051 cm-1 for tropolone(OD) (Keske et al.) allow vibrational state-specific tunneling splittings Δv to be estd. for fundamentals including three with strong O···O stretching displacements [cf. for tropolone(OH) ν13(a1) = 435.22 cm-1 with HΔ13 = 1.71 cm-1 = 1.76 HΔ0, and for tropolone(OD) ν13(a1) = 429.65 cm-1 with DΔ13 = 0.32 cm-1 = 6.27 DΔ0]. The majority of Δv splittings in the sub-800 cm-1 range are dilated relative to the isotopomer Δ0 values. The FTIR spectra demonstrate the presence of dynamic couplings and potential function anharmonicity in addn. to revealing Δv splittings and many OH/D and 18O/16O isotope effects. Approx. values are obtained for the ZP splittings 88Δ0 and 86Δ0 of the doubly and singly 18O-labeled isotopomers of tropolone(OH). The diverse values of the obsd. Δv/Δ0 splitting ratios underscore the inherent multidimensionality and corner-cutting activities entering the state-specific tunneling processes of the tropolone tautomerization reaction.**53**Frost, R. K.; Hagemeister, F. C.; Arrington, C. A.; Zwier, T. S.; Jordan, K. D. Fluorescence-dip infrared spectroscopy of tropolone and tropolone-OD.*J. Chem. Phys.*1996,*105*, 2595– 1604, DOI: 10.1063/1.472119[Crossref], [CAS], Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XltVGjtLs%253D&md5=7ea43463fa5db131e9db28f82746f114Fluorescence-dip infrared spectroscopy of tropolone and tropolone-ODFrost, Rex K.; Hagemeister, C.; Arrington, Caleb A.; Zwier, Timothy S.; Jordan, Kenneth D.Journal of Chemical Physics (1996), 105 (7), 2595-2604CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Fluorescence-dip IR spectroscopy (FDIRS) is employed to record the IR spectra of the isolated, jet-cooled tropolone mol. (TrOH) and its singly deuterated isotopomer TrOD in the O-H and C-H stretch regions. The ability of the method to monitor a single ground-state level enables the acquisition of spectra out of the lower and upper levels of the zero-point tunneling doublet free from interference from one another. The high power of the optical parametric oscillator used for IR generation produces FDIR spectra with good signal-to-noise despite the weak intensity of the C-H and O-H stretch transitions in tropolone. The expectation that both spectra will exhibit two OH stretch transitions sepd. by OH(ν = 1) tunneling splitting is only partially verified in the present study. The spectra of TrOH are compared with those form deuterated tropolone (TrOD) to assign transitions due to C-H and O-H, which are in close proximity in TrOH. The appearance of the spectra out of lower (a1 symmetry) and upper (b2 symmetry) tunneling levels are surprisingly similar. Two sharp transitions at 3134.9 cm-1 (out of the a1 tunneling level) and 3133.9 cm-1 (out of the b2 tunneling level) are sepd. by the ground-state tunneling splitting (0.99 cm-1), and thereby terminate in the same upper state tunneling level. Their similar intensities relative to the C-H stretch transitions indicate that the y- and z-polarized transitions are of comparable intensity, as predicted by ab initio calcns. The corresponding transitions to the other member of the upper state tunneling doublet are not assigned by the present study, but the broad absorptions centered about 12 cm-1 below the assigned transitions are suggested as the most likely possibility for the missing transitions.**54**Murdock, D.; Burns, L. A.; Vaccaro, P. H. Vibrational specificity of proton-transfer dynamics in ground-state tropolone.*Phys. Chem. Chem. Phys.*2010,*12*, 8285– 8299, DOI: 10.1039/c003140b[Crossref], [PubMed], [CAS], Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXoslyqu7o%253D&md5=7621de33cb289884583cb1b246bba896Vibrational specificity of proton-transfer dynamics in ground-state tropoloneMurdock, Daniel; Burns, Lori A.; Vaccaro, Patrick H.Physical Chemistry Chemical Physics (2010), 12 (29), 8285-8299CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The vibrational dependence of large-amplitude proton transfer taking place in the ground electronic state (X~1A1) of tropolone has been explored by implementing a coherent variant of the stimulated emission pumping (SEP) technique within the framework of two-color resonant four-wave mixing (TC-RFWM) spectroscopy. The lowest 1700 cm-1 portion of this potential surface has been interrogated under ambient bulk-gas conditions, enabling rotationless term energies (Tv+) and tunneling-induced bifurcations to be extd. for 43 assigned vibrational features of a1 and b2 symmetry. The resulting values of reflect the state-specificity long attributed to the hydron-migration pathways of tropolone and range in magnitude from 0.0 cm-1 to 17.8 cm-1, where the former implies essentially complete quenching of unimol. dynamics while the latter represents nearly a twenty-fold increase in reaction rate over that of the zero-point level. This vibrational mediation of tunneling behavior is discussed in terms of attendant at. displacements and permutation-inversion symmetries, with choreographed motion of the five-member reaction site () found to exert the most significant influence on the efficacy of proton transfer.**55**Vener, M. V.; Scheiner, S.; Sokolov, N. D. Theoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropolone.*J. Chem. Phys.*1994,*101*, 9755– 9765, DOI: 10.1063/1.467941[Crossref], [CAS], Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXisFChu7o%253D&md5=27a24e6b7629d64c40180f87740dc3fbTheoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropoloneVener, M. V.; Scheiner, Steve; Sokolov, N. D.Journal of Chemical Physics (1994), 101 (11), 9755-65CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Theor. models of hydrogen bonding and proton transfer in the ground (S0) and lowest excited ππ* singlet (S1) states of tropolone are developed in terms of the localized OH···O fragment model and ab initio three-dimensional potential energy surfaces (PESs). The PESs for proton transfer in the S0 and S1 states are calcd. using ab initio SCF and CIS methods, resp., with a 6031G basis set which includes polarization functions on the atoms involved in the internal H bond. The Schroedinger equation for nuclear vibrations is solved numerically using adiabatic sepn. of the variables. The calcd. values for the S0 state (geometry, relaxed barrier height, vibrational frequencies, tunnel splittings and H/D isotope effects) agree fairly well with available exptl. And theor. data. The calcd. data for the S1 state reproduce the principal exptl. trends, established for S1 ← S0 excitation in tropolone, but are less successful with other features of the dynamics of the excited state, e.g., the comparatively large value of vibrationless level tunnel splitting and its irregular increase with O···O excitation in S1. In order to overcome these discrepancies, a model 2-D PES is constructed by fitting an anal. approxn. of the CIS tropolone-OH. It is found that the specifics of the proton transfer in the S1 state are detd. by a relatively low barrier (only one doublet of the OH stretch lies under the barrier peak). Bending vibrations play a minor role in modulation of the proton transfer barrier, so correct description of tunnel splitting of the proton stretch levels in both electronic states can be obtained in terms of the two-dimensional stretching model, which includes O···O and O-H stretching vibration coordinates only.**56**Guo, Y.; Sewell, T. D.; Thompson, D. L. Semiclassical calculations of tunneling splitting in tropolone.*J. Phys. Chem. A*1998,*102*, 5040– 5048, DOI: 10.1021/jp980445y[ACS Full Text ], [CAS], Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXjs1Srs7w%253D&md5=7aa2a2e08d2c6ab12eb1e1ac079f36afSemiclassical calculations of tunneling splitting in tropoloneGuo, Yin; Sewell, Thomas D.; Thompson, Donald L.Journal of Physical Chemistry A (1998), 102 (26), 5040-5048CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)Energy-level splittings in tropolone are calcd. by using a semiclassical approach for tunneling in multidimensional systems. A potential-energy surface that includes all 39 vibrational degrees of freedom was constructed for the ground electronic state on the basis of ab initio MP2 results. Since the method incorporates tunneling within std. trajectory simulations, the full-dimensional dynamics were explicitly treated to provide a clear picture of the dynamical behavior of the system and its effect on tunneling. Level splittings for the ground states of the normal and deuterated species were calcd. The sensitivity of the splittings to the choice of tunneling path were also studied. Mode-selective excitations were used to study the effect of vibrational excitation on the tunneling. Some modes promote tunneling, some suppress it, and some do not affect it. This shows the multidimensional nature of the tunneling process and the importance of properly treating heavy-atom motions.**57**Giese, K.; Kühn, O. The all-cartesian reaction plane hamiltonian: Formulation and application to the H-atom Transfer in tropolone.*J. Chem. Phys.*2005,*123*, 054315, DOI: 10.1063/1.1978869[Crossref], [PubMed], [CAS], Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXos1egsrk%253D&md5=ee3e5631bdd34a2afd45e1c6e395ea3aThe all-Cartesian reaction plane Hamiltonian: Formulation and application to the H-atom transfer in tropoloneGiese, Kai; Kuhn, OliverJournal of Chemical Physics (2005), 123 (5), 054315/1-054315/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, i.e., the unique plane defined by the two min. and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approxn. which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calcns. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramol. O···H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm-1 for the normal and deuterated species, resp. We calcd. IR-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm-1 upon excitation.**58**Giese, K.; Petkovic, M.; Naundorf, H.; Kühn, O. Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bonds.*Phys. Rep.*2006,*430*, 211– 276, DOI: 10.1016/j.physrep.2006.04.005[Crossref], [CAS], Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmsVGiu78%253D&md5=5879c72836446ce346c8fc7b9803bd38Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bondsGiese, K.; Petkovic, M.; Naundorf, H.; Kuehn, O.Physics Reports (2006), 430 (4), 211-276CODEN: PRPLCM; ISSN:0370-1573. (Elsevier B.V.)A review. Hydrogen bonds are of outstanding importance for many processes in Chem., Biol., and Physics. From the theor. perspective the small mass of the proton in a hydrogen bond makes it the primary quantum nucleus and the phenomena one expects to surface in a particular clear way are, for instance, zero-point energy effects, quantum tunneling, or coherent wave packet dynamics. While this is well established in the limit of one-dimensional motion, the details of the multidimensional aspects of the dynamics of hydrogen bonds are just becoming accessible to expts. and numerical simulations. In this review we discuss the theor. treatment of multidimensional quantum dynamics of hydrogen-bonded systems in the context of IR spectroscopy. Here, the multidimensionality is reflected in the complex shape of linear IR absorption spectra which is related to combination transitions and resonances, but also to mode-selective tunneling splittings. The dynamics underlying these spectra can be unravelled by means of time-resolved nonlinear IR spectroscopy. As a fundamental theor. ingredient we outline the generation of potential energy surfaces for gas and condensed phase nonreactive and reactive systems. For nonreactive anharmonic vibrational dynamics in the vicinity of a min. geometry, expansions in terms of normal mode coordinates often provide a reasonable description. For reactive dynamics one can resort to reaction surface ideas, i.e., a combination of large amplitude motion of the reactive coordinates and orthogonal harmonic motion of the remaining coordinates. For isolated systems, dynamics and spectroscopy follow from the time-dependent Schroedinger equation. Here, the multiconfiguration time-dependent Hartree method is shown to allow for describing the correlated dynamics of many degrees of freedom. Classical trajectory based methods are also discussed as an alternative to quantum dynamics. Their merits and shortcomings are scrutinized in the context of incorporating tunneling effects in the calcn. of spectra. For the condensed phase, reduced d. operator based approaches such as the quantum master equation are introduced to properly account for the energy and phase relaxation processes due to the interaction of the hydrogen bond with its surroundings.**59**Wang, Y.; Bowman, J. M. One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal mode.*J. Chem. Phys.*2008,*129*, 121103, DOI: 10.1063/1.2978230[Crossref], [PubMed], [CAS], Google Scholar59https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXht1WnsLzF&md5=ce945fff02748db28261a2360be2e932One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal modeWang, Yimin; Bowman, Joel M.Journal of Chemical Physics (2008), 129 (12), 121103/1-121103/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors present tunneling calcns. using the reaction path Hamiltonian in the zero-curvature approxn. and a 1-dimensional Hamiltonian in the imaginary-frequency, rectilinear normal mode of a saddle point, neglecting the vibrational angular momentum terms. This latter Hamiltonian was recently introduced and applied to the tunneling splitting in full-dimensional malonaldehyde. The results using the latter method are much more accurate than those using the former one for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H2 reaction in three dimensions for zero total angular momentum. (c) 2008 American Institute of Physics.**60**Wang, Y.; Bowman, J. M. Mode-specific tunneling using the*Q*_{im}path: Theory and an application to full-dimensional malonaldehyde.*J. Chem. Phys.*2013,*139*, 154303, DOI: 10.1063/1.4824713[Crossref], [PubMed], [CAS], Google Scholar60https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1Wit73P&md5=07e482216ece63c4981fe93e78fb87d7Mode-specific tunneling using the Qim path: Theory and an application to full-dimensional malonaldehydeWang, Yimin; Bowman, Joel M.Journal of Chemical Physics (2013), 139 (15), 154303/1-154303/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a theory of mode-specific tunneling that makes use of the general tunneling path along the imaginary-frequency normal mode of the saddle point, Qim, and the assocd. relaxed potential, V(Qim). The novel aspect of the theory is the projection of the normal modes of a min. onto the Qim path and the detn. of turning points on V(Qim). From that projection, the change in tunneling upon mode excitation can be calcd. If the projection is zero, no enhancement of tunneling is predicted. In that case vibrationally adiabatic (VA) theory could apply. However, if the projection is large then VA theory is not applicable. The approach is applied to mode-specific tunneling in full-dimensional malonaldehyde, using an accurate full-dimensional potential energy surface. Results are in semi-quant. agreement with expt. for modes that show large enhancement of the tunneling, relative to the ground state tunneling splitting. For the six out-of-plane modes, which have zero projection on the planar Qim path, VA theory does apply, and results from that theory agree qual. and even semi-quant. with expt. We also verify the failure of simple VA theory for modes that show large enhancement of tunneling. (c) 2013 American Institute of Physics.**61**Collins, M. A.; Bettens, R. P. A. Energy-based molecular fragmentation methods.*Chem. Rev.*2015,*115*, 5607– 5642, DOI: 10.1021/cr500455b[ACS Full Text ], [CAS], Google Scholar61https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtVajsbY%253D&md5=a83ac50604af530b6d89c94f1a6b6df6Energy-Based Molecular Fragmentation MethodsCollins, Michael A.; Bettens, Ryan P. A.Chemical Reviews (Washington, DC, United States) (2015), 115 (12), 5607-5642CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review including the following topics: methods and principles, applications and examples, and speculations and future developments etc.**62**Gadre, S. R.; Shirsat, R. N.; Limaye, A. C. Molecular tailoring approach for simulation of electrostatic properties.*J. Phys. Chem.*1994,*98*, 9165– 9169, DOI: 10.1021/j100088a013[ACS Full Text ], [CAS], Google Scholar62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXls1Cgtb0%253D&md5=8cc186eed0f00621147f1aea9732fa87Molecular Tailoring Approach for Simulation of Electrostatic PropertiesGadre, Shridhar R.; Shirsat, Rajendra N.; Limaye, Ajay C.Journal of Physical Chemistry (1994), 98 (37), 9165-9CODEN: JPCHAX; ISSN:0022-3654.A method for synthesizing ab initio mol. electrostatic potential (MESP) and field (MEF) by "stitching" together suitably tailored smaller fragments is presented. The procedure is assessed for its ability to mimic the ab initio MESP and its topog. for the model cases of zeolite silicon pentamer (Si5O16H12) and decamer (Si10O10H20) and has been found fairly reliable. A further application to di- and tripeptides is shown to simulate well the ab initio MESP and MEF with the resp. MESP min. reproduced to within 1% or less. This reliability, coupled with bypassing of the SCF computation of the tailored mol., makes the approach an attractive one for exploring one-electron properties of large mol. systems.**63**Ganesh, V.; Dongare, R. K.; Balanarayan, P.; Gadre, S. R. Molecular tailoring approach for geometry optimization of large molecules: Energy evaluation and parallelization strategies.*J. Chem. Phys.*2006,*125*, 104109, DOI: 10.1063/1.2339019[Crossref], [PubMed], [CAS], Google Scholar63https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XpvV2hsrw%253D&md5=1b61a9df6829c4d08d3426c4efc921d4Molecular tailoring approach for geometry optimization of large molecules: Energy evaluation and parallelization strategiesGanesh, V.; Dongare, Rameshwar K.; Balanarayan, P.; Gadre, Shridhar R.Journal of Chemical Physics (2006), 125 (10), 104109/1-104109/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A linear-scaling scheme for estg. the electronic energy, gradients, and Hessian of a large mol. at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided mol. tailoring approach (CG-MTA) for ab initio geometry optimization of large mols. is implemented. The method employs energy gradients extd. from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for d.-functional-theory-based geometry optimization of a variety of mols. including α-tocopherol, taxol, γ-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient ests. obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large mols.**64**Rahalkar, A. P.; Katouda, M.; Gadre, S. R.; Nagase, S. Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: A comparison with fragment molecular orbital method.*J. Comput. Chem.*2010,*31*, 2405– 2418, DOI: 10.1002/jcc.21533[Crossref], [PubMed], [CAS], Google Scholar64https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXptFOltbs%253D&md5=1a08953eeb1b2cf2f6266c8b65d50b44Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: a comparison with fragment molecular orbital methodRahalkar, Anuja P.; Katouda, Michio; Gadre, Shridhar R.; Nagase, ShigeruJournal of Computational Chemistry (2010), 31 (13), 2405-2418CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)Many Divide-and-Conquer based approaches are being developed to overcome the high scaling problem of the ab initio methods. In this work, one such method, Mol. Tailoring Approach (MTA) has been interfaced with recently developed efficient Moller-Plesset second order perturbation theory (MP2) codes viz. IMS-MP2 and RI-MP2 to reap the advantage of both. An external driver script is developed for implementing MTA at the front-end and the MP2 codes at the back-end. The present version of the driver script is written only for a single point energy evaluation of a mol. system at a fixed geometry. The performance of these newly developed MTA-IMS-MP2 and MTA-RI-MP2 codes is extensively benchmarked for a variety of mol. systems vis-a-vis the corresponding actual runs. In addn. to this, the performance of these programs is also critically compared with Fragment MO (FMO), another popular fragment-based method. It is obsd. that FMO2/2 is superior to FMO3/2 and MTA with respect to time advantage; however, the errors of FMO2 are much beyond chem. accuracy. However, FMO3/2 is a highly accurate method for biol. systems but is unsuccessful in case of water clusters. MTA produces ests. with errors within 1 kcal/mol uniformly for all systems with reasonable time advantage. Anal. carried out employing various basis sets shows that FMO gives its optimum performance only for basis sets, which does not include diffuse functions. On the contrary, MTA performance is found to be similar for any basis set used. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010.**65**Furtado, J. P.; Rahalkar, A. P.; Shanker, S.; Bandyopadhyay, P.; Gadre, S. R. Facilitating minima search for large water clusters at the MP2 level via molecular tailoring.*J. Phys. Chem. Lett.*2012,*3*, 2253– 2258, DOI: 10.1021/jz300663u[ACS Full Text ], [CAS], Google Scholar65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFWhsrrE&md5=a4f5783ee90ea5e32d262a4127f31875Facilitating Minima Search for Large Water Clusters at the MP2 Level via Molecular TailoringFurtado, Jonathan P.; Rahalkar, Anuja P.; Shanker, Sudhanshu; Bandyopadhyay, Pradipta; Gadre, Shridhar R.Journal of Physical Chemistry Letters (2012), 3 (16), 2253-2258CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Water clusters (H2O)20 and (H2O)25 are explored at the Moller-Plesset second-order perturbation (MP2) level of theory. Geometry optimization is carried out on favorable structures, initially generated by the temp. basin paving (TBP) method, utilizing the fragment-based mol. tailoring approach (MTA). MTA-based stabilization energies at the complete basis set limit are accurately estd. by grafting the energy correction using a smaller basis set. For prototypical cases, the min. are established via MTA-based vibrational frequency calcns. at the MP2/aug-cc-pVDZ level. The potential of MTA in tackling large clusters is further demonstrated by performing geometry optimization at MP2/aug-cc-pVDZ starting with the global min. of (H2O)30 reported by Monte Carlo (MC) and mol. dynamics (MD) investigations. The present study brings out the efficacy of MTA in performing computationally expensive ab initio calcns. with minimal off-the-shelf hardware without significant loss of accuracy.**66**Sahu, N.; Gadre, S. R. Molecular tailoring approach: A route for*ab initio*rreatment of large clusters.*Acc. Chem. Res.*2014,*47*, 2739– 2747, DOI: 10.1021/ar500079b[ACS Full Text ], [CAS], Google Scholar66https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXnsVehsbo%253D&md5=f8e37a08a65e23f60ec8f0350c1411f4Molecular Tailoring Approach: A Route for ab Initio Treatment of Large ClustersSahu, Nityananda; Gadre, Shridhar R.Accounts of Chemical Research (2014), 47 (9), 2739-2747CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)A review. Chem. on the scale of mol. clusters may be dramatically different from that in the macroscopic bulk. Greater understanding of chem. in this size regime could greatly influence fields such as materials science and atm. and environmental chem. Recent advances in exptl. techniques and computational resources have led to accurate investigations of the energies and spectral properties of weakly bonded mol. clusters. These have enabled researchers to learn how the physicochem. properties evolve from individual mols. to bulk materials and to understand the growth patterns of clusters. Exptl. techniques such as IR, microwave, and photoelectron spectroscopy are the most popular and powerful tools for probing mol. clusters. In general, these exptl. techniques do not directly reveal the atomistic details of the clusters but provide data from which the structural details need to be unearthed. Furthermore, the resoln. of the spectral properties of energetically close cluster conformers can be prohibitively difficult. Thus, these investigations of mol. aggregates require a combination of expts. and theory. On the theor. front, researchers have been actively engaged in quantum chem. ab initio calcns. as well as simulation-based studies for the last few decades. To obtain reliable results, there is a need to use correlated methods such as Moller-Plesset second order method, coupled cluster theory, or dispersion cor. d. functional theory. However, due to nonlinear scaling of these methods, optimizing the geometry of large clusters still remains a formidable quantum chem. challenge. Fragment-based methods, such as divide-and-conquer, mol. tailoring approach (MTA), fragment MOs, and generalized energy-based fragmentation approach, provide alternatives for overcoming the scaling problem for spatially extended mol. systems. Within MTA, a large system is broken down into two or more subsystems that can be readily treated computationally. Finally, the properties of the large system are obtained by patching the corresponding properties of all the subsystems. Due to these approxns., the resulting MTA-based energies carry some error in comparison with calcns. based on the full system. An approach for correcting these errors has been attempted by grafting the error at a lower basis set onto a higher basis set. Furthermore, investigating the growth patterns and nucleation processes in clusters is necessary for understanding the structural transitions and the phenomena of magic nos. in cluster chem. Therefore, systematic building-up or the introduction of stochastics for generating mol. assemblies is the most crucial step for studying large clusters. In this Account, we discuss the working principle of MTA for probing mol. clusters at ab initio level followed by a brief summary of an automated and electrostatics-guided algorithm for building mol. assemblies. The mol. aggregates presented here as test cases are generated based on either an electrostatic criterion or the basin hopping method. At MP2 level computation, the errors in MTA-based grafted energies are typically reduced to a submillihartree level, reflecting the potential of finding accurate energies of mol. clusters much more quickly. In summary, MTA provides a platform for effectively studying large mol. clusters at ab initio level of theory using minimal computer hardware.**67**Khire, S. S.; Gurav, N. D.; Nandi, A.; Gadre, S. R. Enabling rapid and accurate construction of CCSD(T)-level potential energy surface of large molecules using molecular tailoring approach.*J. Phys. Chem. A*2022,*126*, 1458– 1464, DOI: 10.1021/acs.jpca.2c00025[ACS Full Text ], [CAS], Google Scholar67https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjslWgt7k%253D&md5=3ad6d07296b3f36833c7d283a97b3fd2Enabling Rapid and Accurate Construction of CCSD(T)-Level Potential Energy Surface of Large Molecules Using Molecular Tailoring ApproachKhire, Subodh S.; Gurav, Nalini D.; Nandi, Apurba; Gadre, Shridhar R.Journal of Physical Chemistry A (2022), 126 (8), 1458-1464CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The construction of a potential energy surface (PES) of even a medium-sized mol. employing correlated theory, such as CCSD(T), is arduous due to the high computational cost involved. The present study reports the possibility of efficiently constructing such a PES of mols. contg. up to 15 atoms and 550 basis functions by employing the fragment-based mol. tailoring approach (MTA) on off-the-shelf hardware. The MTA energies at the CCSD(T)/aug-cc-pVTZ level for several geometries of three test mols., viz., acetylacetone, N-methylacetamide, and tropolone, are reported. These energies are in excellent agreement with their full calcn. counterparts with a time advantage factor of 3-5. The energy barrier from the ground to transition state is also accurately captured. Further, we demonstrate the accuracy and efficiency of MTA for estg. the energy gradients at the CCSD(T) level. As a further application of our MTA methodol., the energies of acetylacetone at ∼ 430 geometries are computed at the CCSD(T)/aug-cc-pVTZ level and used for generating a Δ-machine learning (Δ-ML) PES. This leads to the H-transfer barrier of 3.02 kcal/mol, well in agreement with the benchmarked barrier of 3.19 kcal/mol. The fidelity of this Δ-ML PES is examd. by geometry optimization and normal mode frequency calcns. of global min. and saddle point geometries. We trust that the present work is a major development for the rapid and accurate construction of PES at the CCSD(T) level for mols. contg. up to 20 atoms and 600 basis functions using off-the-shelf hardware.**68**McDaniel, J. G.; Schmidt, J. Next-generation force fields from symmetry-adapted perturbation theory.*Annu. Rev. Phys. Chem.*2016,*67*, 467– 488, DOI: 10.1146/annurev-physchem-040215-112047[Crossref], [PubMed], [CAS], Google Scholar68https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmtVamtrg%253D&md5=9a252853aac46abd18c82fb5db9e00e6Next-Generation Force Fields from Symmetry-Adapted Perturbation TheoryMcDaniel, Jesse G.; Schmidt, J. R.Annual Review of Physical Chemistry (2016), 67 (), 467-488CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free est. of mol. interaction energies, a phys. intuitive energy decompn., and a seamless transition to an asymptotic picture of intermol. interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical mol. dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calcns. It also highlights a no. of applications of SAPT-based force fields for chem. systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.**69**Jing, Z.; Liu, C.; Cheng, S. Y.; Qi, R.; Walker, B. D.; Piquemal, J.-P.; Ren, P. Polarizable force fields for biomolecular simulations: Recent advances and applications.*Annu. Rev. Biophys.*2019,*48*, 371– 394, DOI: 10.1146/annurev-biophys-070317-033349[Crossref], [PubMed], [CAS], Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXmtVGnu7s%253D&md5=87b2bbf40c3e1977cd0e55e90b314d45Polarizable Force Fields for Biomolecular Simulations: Recent Advances and ApplicationsJing, Zhifeng; Liu, Chengwen; Cheng, Sara Y.; Qi, Rui; Walker, Brandon D.; Piquemal, Jean-Philip; Ren, PengyuAnnual Review of Biophysics (2019), 48 (), 371-394CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)A review. Realistic modeling of biomol. systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in phys. models, simulation algorithms, and computing hardware, biomol. simulations with advanced force fields at biol. relevant timescales are becoming increasingly promising. These advancements have not only led to new biophys. insights but also afforded opportunities to advance our understanding of fundamental intermol. forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomol. simulations.**70**Inakollu, V. S.; Geerke, D. P.; Rowley, C. N.; Yu, H. Polarisable force fields: what do they add in biomolecular simulations?.*Curr. Opin. Struct. Biol.*2020,*61*, 182– 190, DOI: 10.1016/j.sbi.2019.12.012[Crossref], [PubMed], [CAS], Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitFehurc%253D&md5=505957eb301190f636028eec3fdddb04Polarisable force fields: what do they add in biomolecular simulationsInakollu, V. S. Sandeep; Geerke, Daan P.; Rowley, Christopher N.; Yu, HaiboCurrent Opinion in Structural Biology (2020), 61 (), 182-190CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)A review. The quality of biomol. simulations critically depends on the accuracy of the force field used to calc. the potential energy of the mol. configurations. Currently, most simulations employ non-polarisable force fields, which describe electrostatic interactions as the sum of Coulombic interactions between fixed at. charges. Polarisation of these charge distributions is incorporated only in a mean-field manner. In the past decade, extensive efforts have been devoted to developing simple, efficient, and yet generally applicable polarisable force fields for biomol. simulations. In this review, we summarise the latest developments in accounting for key biomol. interactions with polarisable force fields and applications to address challenging biol. questions. In the end, we provide an outlook for future development in polarisable force fields.**71**Partridge, H.; Schwenke, D. W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio Calculations and Experimental Data.*J. Chem. Phys.*1997,*106*, 4618, DOI: 10.1063/1.473987[Crossref], [CAS], Google Scholar71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXhvVyiuro%253D&md5=b5dd1c238894f2288fd0b70942bd7865The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental dataPartridge, Harry; Schwenke, David W.Journal of Chemical Physics (1997), 106 (11), 4618-4639CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report on the detn. of a high quality ab initio potential energy surface (PES) and dipole moment function for water. This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J ≤ 5 for H216O. The changes in the PES are small, nonetheless including an est. of core (oxygen 1s) electron correlation greatly improves the agreement with the expt. Using this adjusted PES, we can match 30 092 of the 30 117 transitions in the HITRAN 96 data base for H216O with theor. lines. The 10, 25, 50, 75, and 90 percentiles of the difference between the calcd. and tabulated line positions are -0.11, -0.04, -0.01, 0.02, and 0.07 cm-1. Nonadiabatic effects are not explicitly included. About 3% of the tabulated line positions appear to be incorrect. Similar agreement using this adjusted PES is obtained for the 17O and 18O isotopes. For HD16O, the agreement is not as good, with a root-mean-square error of 0.25 cm-1 for lines with J ≤ 5. This error is reduced to 0.02 cm-1 by including a small asym. correction to the PES, which is parameterized by simultaneously fitting to HD16O and D216O data. Scaling this correction by mass factors yields good results for T2O and HTO. The intensities summed over vibrational bands are usually in good agreement between the calcns. and the tabulated results, but individual line strengths can differ greatly. A high-temp. list consisting of 307 721 352 lines is generated for H216O using our PES and dipole moment function.**72**Yu, Q.; Qu, C.; Houston, P. L.; Conte, R.; Nandi, A.; Bowman, J. M. q-AQUA: A many-body CCSD(T) water potential, including 4-body interactions, demonstrates the quantum nature of water from clusters to the liquid phase.*J. Phys. Chem. Lett.*2022,*13*, 5068– 5074, DOI: 10.1021/acs.jpclett.2c00966[ACS Full Text ], [CAS], Google Scholar72https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsVWmu7jO&md5=0454787c7c4d803194b5ad2b36f1de03q-AQUA: A Many-Body CCSD(T) Water Potential, Including Four-Body Interactions, Demonstrates the Quantum Nature of Water from Clusters to the Liquid PhaseYu, Qi; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Nandi, Apurba; Bowman, Joel M.Journal of Physical Chemistry Letters (2022), 13 (22), 5068-5074CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Many model potential energy surfaces (PESs) have been reported for water; however, none are strictly from "first-principles". Here we report such a potential, based on a many-body representation at the CCSD(T) level of theory up to the four-body interaction. The new PES is benchmarked for the isomers of the water hexamer for dissocn. energies, harmonic frequencies, and unrestricted diffusion Monte Carlo (DMC) calcns. of the zero-point energies of the Prism, Book, and Cage isomers. Dissocn. energies of several isomers of the 20-mer agree well with recent benchmark energies. Exploratory DMC calcns. on this cluster verify the robustness of the new PES for quantum simulations. The accuracy and speed of the new PES are demonstrated for std. condensed phase properties, i.e., the radial distribution function and the self-diffusion const. Quantum effects are shown to be substantial for these observables and also needed to bring theory into excellent agreement with expt.**73**Heindel, J. P.; Xantheas, S. S. The many-body expansion for aqueous systems revisited: I. water–water interactions.*J. Chem. Theory Comput.*2020,*16*, 6843– 6855, DOI: 10.1021/acs.jctc.9b00749[ACS Full Text ], [CAS], Google Scholar73https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitVyku7bL&md5=5d6f0287f24676a3da2c9d1fb2178d25The Many-Body Expansion for Aqueous Systems Revisited: I. Water-Water InteractionsHeindel, Joseph P.; Xantheas, Sotiris S.Journal of Chemical Theory and Computation (2020), 16 (11), 6843-6855CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We revisit the many-body expansion (MBE) for water-water interactions by examg. the effects of the basis set, including those resulting from the basis set superposition error (BSSE) correction, and electron correlation on the various terms for selected sizes of water clusters up to n = 21. The anal. is performed at the second-order Moller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality (aug-cc-pVxZ, x = D, T, Q, 5) for the (H2O)n, n = 7, 10, 13, 16, and 21, clusters for which we report either the complete MBE (for n = 7, 10) or the ones through the 6-body (for n = 13) and the 5-body terms (for n = 16, 21). For the n = 3 and 7 clusters, we also report the anal. at the coupled cluster with single, double, and perturbative triple replacements in order to assess the effects of a higher correlation on the magnitude and percentage of the various MBE terms. Our results suggest that the oscillatory behavior around zero found for the 5-body and larger terms is solely an artifact of the (small) size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero upon increasing the size of the basis set toward the complete basis set (CBS) limit. In that respect, the BSSE-cor. 5-body and above terms do not exhibit the oscillatory behavior on either side of zero with the basis set obsd. for the BSSE-uncorrected terms. In addn., the magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSE-cor.) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small so that neglecting the correlation contribution in all terms above the 3-body results in an error of the order of 0.1%. The BSSE correction to the largest 2-body term in the MBE was accurately estd. from the function a[1 + erf( - b·R)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are sepd. by R with the consts. a and b fitted to the calcd. BSSE corrections for the individual 2-body terms of the clusters with each basis set and R is the distance between oxygen atoms. Our results demonstrate that the MBE for water-water interactions converges by the 4-body term since any finite terms above the 4-body are artifacts of the size of the basis set. The MBE can thus be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the smaller aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate ab initio based many-body mol. dynamics simulations for aq. systems.**74**Nandi, A.; Qu, C.; Houston, P. L.; Conte, R.; Yu, Q.; Bowman, J. M. A CCSD(T)-based 4-body potential for water.*J. Phys. Chem. Lett.*2021,*12*, 10318– 10324, DOI: 10.1021/acs.jpclett.1c03152[ACS Full Text ], [CAS], Google Scholar74https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1Cqtr3O&md5=5e33ce3c2c2c22d11b680b7a35afd5e9A CCSD(T)-Based 4-Body Potential for WaterNandi, Apurba; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Yu, Qi; Bowman, Joel M.Journal of Physical Chemistry Letters (2021), 12 (42), 10318-10324CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)High-level, ab initio calcns. find that the 4-body (4-b) interaction is needed to account for near-100% of the total interaction energy for water clusters as large as the 21-mer. Motivated by this, we report a permutationally invariant polynomial potential energy surface (PES) for the 4-body interaction. This machine-learned PES is a fit to 2119 symmetry-unique, CCSD(T)-F12a/haTZ 4-b interaction energies. Configurations for these come from tetramer direct-dynamics calcns., fragments from an MD water simulation at 300 K, and tetramer fragments in a variety of water clusters. The PIP basis is purified to ensure that the PES goes rigorously to zero in monomer + trimer and dimer + dimer dissocns. The 4-b energies of isomers of the hexamer calcd. with the new PES are shown to be in better agreement with benchmark CCSD(T) results than those from the MB-pol potential. Tests on larger clusters further validate the high-fidelity of the PES. The PES is shown to be fast to evaluate, taking 2.4 s for 105 evaluations on a single core of 2.4 GHz Intel Xeon processor, and significantly faster using a parallel version of the PES.**75**Conte, R.; Qu, C.; Bowman, J. M. Permutationally invariant fitting of many-body, non-covalent interactions with application to three-body methane–water–water.*J. Chem. Theory Comput.*2015,*11*, 1631, DOI: 10.1021/acs.jctc.5b00091[ACS Full Text ], [CAS], Google Scholar75https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXjvVOhsrs%253D&md5=5a08d4fa1f8c5b521d4fe52e796c4013Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane-Water-WaterConte, Riccardo; Qu, Chen; Bowman, Joel M.Journal of Chemical Theory and Computation (2015), 11 (4), 1631-1638CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A modified, computationally efficient method to provide permutationally invariant polynomial bases for mol. energy surface fitting via monomial symmetrization (Xie Z.; Bowman J. M. J. Chem. Theory Comput.2010, 6, 26-34) is reported for applications to complex systems, characterized by many-body, non-covalent interactions. Two approaches, each able to ensure the asymptotic zero-interaction limit of intrinsic potentials, are presented. They are both based on the tailored selection of a subset of the polynomials of the original basis. A computationally efficient approach exploits reduced permutational invariance and provides a compact fitting basis dependent only on intermol. distances. We apply the original and new techniques to obtain a no. of full-dimensional potentials for the intrinsic three-body methane-water-water interaction by fitting a database made of 22,592 ab initio energies calcd. at the MP2-F12 level of theory with haTZ (aug-cc-pVTZ for C and O, cc-pVTZ for H) basis set. An investigation of the effects of permutational symmetry on fitting accuracy and computational costs is reported. Several of the fitted potentials are then employed to evaluate with high accuracy the three-body contribution to the CH4-H2O-H2O binding energy and the three-body energy of three conformers of the [email protected](H2O)20 cluster.**76**Liu, K.; Brown, M.; Carter, C.; Saykally, R.; Gregory, J.; Clary, D. Characterization of a cage form of the water hexamer.*Nature*1996,*381*, 501– 503, DOI: 10.1038/381501a0[Crossref], [CAS], Google Scholar76https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XjsVWisLs%253D&md5=b7f94d0867748c08052407744e0f3ad0Characterization of a cage form of the water hexamerLiu, K.; Brown, M. G.; Carter, C.; Saykally, R. J.; Gregory, J. K.; Clary, D. C.Nature (London) (1996), 381 (6582), 501-503CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)Water has been studied more extensively than any other liq., yet its microscopic properties remain poorly understood. The difficulty in obtaining a rigorous mol.-scale description of water structure is largely a consequence of the extended, dynamic hydrogen-bonded network that exists throughout the liq. Studies of the structure and dynamics of isolated small clusters of water mols. provide a means of quantifying the intermol. forces and hydrogen-bond rearrangements that occur in condensed phases. Expts. and theory strongly suggest that the water trimer, tetramer and pentamer have cyclic min. energy structures. Larger water clusters are expected to have three-dimensional geometries, with the hexamer representing the transition from cyclic to such three-dimensional structures. Here we report investigations by terahertz laser vibration-rotation tunneling spectroscopy of the structure of the water hexamer. A comparison of our results with quantum Monte Carlo simulations of this species suggests that the most stable form of (H2O)6 is indeed a cage-like structure, held together by eight hydrogen bonds.**77**Lambros, E.; Paesani, F. How good are polarizable and flexible models for water: Insights from a many-body perspective.*J. Chem. Phys.*2020,*153*, 060901, DOI: 10.1063/5.0017590[Crossref], [PubMed], [CAS], Google Scholar77https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFyhtL%252FN&md5=c1c047fd27facf1b9fcf9abaf76a0f6bHow good are polarizable and flexible models for water: Insights from a many-body perspectiveLambros, Eleftherios; Paesani, FrancescoJournal of Chemical Physics (2020), 153 (6), 060901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a systematic anal. of state-of-the-art polarizable and flexible water models from a many-body perspective, with a specific focus on their ability to represent the Born-Oppenheimer potential energy surface of water from the gas to the liq. phase. Using coupled cluster data in the complete basis set limit as a ref., we examine the accuracy of the polarizable models in reproducing individual many-body contributions to interaction energies and harmonic frequencies of water clusters and compare their performance with that of MB-pol, an explicit many-body model that has been shown to correctly predict the properties of water across the entire phase diagram. Based on these comparisons, we use MB-pol as a ref. to analyze the ability of the polarizable models to reproduce the energy landscape of liq. water under ambient conditions. We find that, while correctly reproducing the energetics of min.-energy structures, the polarizable models examd. in this study suffer from inadequate representations of many-body effects for distorted configurations. To investigate the role played by geometry-dependent representations of 1-body charge distributions in reproducing coupled cluster data for both interaction and many-body energies, we introduce a simplified version of MB-pol that adopts fixed at. charges and demonstrate that the new model retains the same accuracy as the original MB-pol model. Based on the analyses presented in this study, we believe that future developments of both polarizable and explicit many-body models should continue in parallel and would benefit from synergistic efforts aimed at integrating the best aspects of the two theor./computational frameworks. (c) 2020 American Institute of Physics.**78**Reddy, S. K.; Straight, S. C.; Bajaj, P.; Huy Pham, C.; Riera, M.; Moberg, D. R.; Morales, M. A.; Knight, C.; Götz, A. W.; Paesani, F. On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice.*J. Chem. Phys.*2016,*145*, 194504, DOI: 10.1063/1.4967719[Crossref], [PubMed], [CAS], Google Scholar78https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhvVynt7nF&md5=d3e342ad6c8a263b199b46bf4e050cceOn the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and iceReddy, Sandeep K.; Straight, Shelby C.; Bajaj, Pushp; Huy Pham, C.; Riera, Marc; Moberg, Daniel R.; Morales, Miguel A.; Knight, Chris; Gotz, Andreas W.; Paesani, FrancescoJournal of Chemical Physics (2016), 145 (19), 194504/1-194504/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The MB-pol many-body potential has recently emerged as an accurate mol. model for water simulations from the gas to the condensed phase. In this study, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with exptl. data and high-level ab initio calcns. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calcd. with MB-pol are in excellent agreement with ref. data obtained at the coupled cluster level. Several structural, thermodn., and dynamical properties of the liq. phase at atm. pressure are investigated through classical mol. dynamics simulations as a function of temp. The structural properties of the liq. phase are in nearly quant. agreement with X-ray diffraction data available over the temp. range from 268 to 368 K. The anal. of other thermodn. and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, esp. at low temp., for a phys. correct description of the properties of liq. water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water. (c) 2016 American Institute of Physics.**79**Heindel, J. P.; Herman, K. M.; Aprà, E.; Xantheas, S. S. Guest–host interactions in clathrate hydrates: Benchmark MP2 and CCSD(T)/CBS binding energies of CH_{4}, CO_{2}, and H_{2}S in (H_{2}O)_{20}Cages.*J. Phys. Chem. Lett.*2021,*12*, 7574– 7582, DOI: 10.1021/acs.jpclett.1c01884[ACS Full Text ], [CAS], Google Scholar79https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhs12msrjP&md5=5155e919f843943682570de41e792e31Guest-Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2, and H2S in (H2O)20 CagesHeindel, Joseph P.; Herman, Kristina M.; Apra, Edoardo; Xantheas, Sotiris S.Journal of Physical Chemistry Letters (2021), 12 (31), 7574-7582CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)We present benchmark binding energies of naturally occurring gas mols. CH4, CO2, and H2S in the small cage, namely, the pentagonal dodecahedron (512) (H2O)20, which is one of the constituent cages of the 3 major lattices (structures I, II, and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with an increasing basis set to the complete basis set (CBS) limit, necessitating the use of large basis sets up to the aug-cc-pV5Z and subsequent correction for basis set superposition error (BSSE). For the host hollow (H2O)20 cages, we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Addnl., we report converged second order Moller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H2O)20 cage of -4.3 ± 0.1 for [email protected](H2O)20, -6.6 ± 0.1 for [email protected](H2O)20, and -8.5 ± 0.1 kcal/mol for [email protected](H2O)20, resp. For [email protected](H2O)20, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS est. of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calcn. for [email protected](H2O)20 is the largest one reported to date (168 valence electrons, 1978 basis functions, and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350 208 cores) of the "Cori" supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 min (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermol. interactions in complex systems. They also provide a path toward parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as d. functional theory (DFT) and MP2 including its spin-biased variants.**80**Bates, D. M.; Tschumper, G. S. CCSD(T) complete basis set limit relative energies for low-lying water hexamer structures.*J. Phys. Chem. A*2009,*113*, 3555– 3559, DOI: 10.1021/jp8105919[ACS Full Text ], [CAS], Google Scholar80https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXisVCjurw%253D&md5=659c73ab1e07c66601cfd8345ecb6d3eCCSD(T) Complete Basis Set Limit Relative Energies for Low-Lying Water Hexamer StructuresBates, Desiree M.; Tschumper, Gregory S.Journal of Physical Chemistry A (2009), 113 (15), 3555-3559CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)MP2 and CCSD(T) complete basis set (CBS) limit relative electronic energies (ΔEe) have been detd. for eight low-lying structures of the water hexamer by combining explicitly correlated MP2-R12 computations with higher-order correlation corrections from CCSD(T) calcns. Higher-order correlation effects are quite substantial and increase ΔEe by at least +0.19 kcal mol-1 and as much as +0.59 kcal mol-1. The effects from zero-point vibrational energy (ZPVE) have been assessed from unscaled harmonic vibrational frequencies computed at the MP2 level with a correlation consistent triple-ζ basis set (cc-pVTZ for H and aug-cc-pVTZ for O). ZPVE effects are even more significant than higher-order correlation effects and are uniformly neg., decreasing the relative energies by -0.16 kcal mol-1 to -1.61 kcal mol-1. Although it has been widely accepted that the cage becomes the lowest-energy structure after ZPVE effects are included, the prism is consistently the most stable structure in this work, lying 0.06 kcal mol-1 below the nearly isoenergetic cage isomer at the electronic MP2 CBS limit, 0.25 kcal mol-1 below at the electronic CCSD(T) CBS limit, and 0.09 kcal mol-1 below at the harmonic ZPVE cor. CCSD(T) CBS limit. Moreover, application of any uniform scaling factor less than unity to correct for anharmonicity further stabilizes the prism and increases the relative energies of the other structures.**81**Zhu, J.; Vuong, V. Q.; Sumpter, B. G.; Irle, S. Artificial neural network correction for density-functional tight-binding molecular dynamics simulations.*MRS Commun.*2019,*9*, 867– 873, DOI: 10.1557/mrc.2019.80[Crossref], [CAS], Google Scholar81https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvVKisrvK&md5=17b123e38564eb369fdfc4ba3a8296e7Artificial neural network correction for density-functional tight-binding molecular dynamics simulationsZhu, Junmian; Vuong, Van Quan; Sumpter, Bobby G.; Irle, StephanMRS Communications (2019), 9 (3), 867-873CODEN: MCROF8; ISSN:2159-6867. (Cambridge University Press)The authors developed a Behler-Parrinello-type neural network (NN) to improve the d.-functional tight-binding (DFTB) energy and force prediction. The Δ-machine learning approach was adopted and the NN was designed to predict the energy differences between the d. functional theory (DFT) quantum chem. potential and DFTB for a given mol. structure. Most notably, the DFTB-NN method is capable of improving the energetics of intramol. hydrogen bonds and torsional potentials without modifying the framework of DFTB itself. This improvement enables considerably larger simulations of complex chem. systems that currently could not easily been accomplished using DFT or higher level ab initio quantum chem. methods alone.**82**Qu, C.; Conte, R.; Houston, P. L.; Bowman, J. M. Full-dimensional Potential Energy Surface for Acetylacetone and Tunneling Splittings.*Phys. Chem. Chem. Phys.*2021,*23*, 7758– 7767, DOI: 10.1039/D0CP04221H[Crossref], [PubMed], [CAS], Google Scholar82https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvVGgs7rK&md5=fde99d4eba58249eba57685bef99d1a4Full-dimensional potential energy surface for acetylacetone and tunneling splittingsQu, Chen; Conte, Riccardo; Houston, Paul L.; Bowman, Joel M.Physical Chemistry Chemical Physics (2021), 23 (13), 7758-7767CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)We present a full-dimensional potential energy surface for acetylacetone (AcAc) using full and fragmented permutationally invariant polynomial approaches. Previously reported MP2/aVTZ energies and gradients are augmented by addnl. calcns. at this level of theory for the fits. Numerous stationary points are reported as are the usual metrics to assess the precision of the fit. The electronic barrier height for the H-atom transfer is roughly 2.2 kcal mol-1. Diffusion Monte Carlo (DMC) calcns. are used to calc. the ground state wavefunction and zero-point energy of acetylacetone. These together with fixed-node DMC calcns. for the first excited-state provide the predicted tunneling splitting due to the barrier to H-transfer sepg. two equiv. wells. Simpler 1d calcns. of this splitting are also reported for varying barrier heights including the CCSD(T) barrier height of 3.2 kcal mol-1. Based on those results the DMC splitting of 160 cm-1 with a statistical uncertainty of roughly 21 cm-1, calcd. using the MP2-based PES, is estd. to decrease to 100 cm-1 for a barrier of 3.2 kcal mol-1. The fragmented surface is shown to be fast to evaluate.**83**Shank, A.; Wang, Y.; Kaledin, A.; Braams, B. J.; Bowman, J. M. Accurate*ab initio*and “hybrid” potential energy surfaces, intramolecular vibrational energies, and classical ir spectrum of the water dimer.*J. Chem. Phys.*2009,*130*, 144314, DOI: 10.1063/1.3112403[Crossref], [PubMed], [CAS], Google Scholar83https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkslaqtLc%253D&md5=fb83e37c1cb24fa292957b2557b981e7Accurate ab initio and "hybrid" potential energy surfaces, intramolecular vibrational energies, and classical IR spectrum of the water dimerShank, Alex; Wang, Yimin; Kaledin, Alexey; Braams, Bastiaan J.; Bowman, Joel M.Journal of Chemical Physics (2009), 130 (14), 144314/1-144314/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors report 3 modifications to recent ab initio, full-dimensional potential energy surfaces (PESs) for the H2O dimer. The 1st modification is a refit of ab initio electronic energies to produce an accurate dissocn. energy De. The 2nd modification adds replacing the H2O monomer component of the PES with a spectroscopically accurate 1 and the 3rd modification produces a hybrid potential that goes smoothly in the asymptotic region to the flexible, Thole-type model potential, version 3 dimer potential (denoted TTM3-F). The rigorous D0 for these PESs, obtained using diffusion Monte Carlo calcns. of the dimer zero-point energy, and an accurate zero-point energy of the monomer, range from 12.5 to 13.2 kJ/mol (2.99-3.15 kcal/mol), with the latter being the suggested benchmark value. For TTM3-F D0 is 16.1 kJ/mol. Vibrational calcns. of monomer fundamental energies using the code MULTIMODE are reported for these PESs and the TTM3-F PES and compared to expt. A classical mol. dynamics simulation of the IR spectra of the H2O dimer and D2O dimer at 300 K are also reported using the ab initio dipole moment surface reported previously. (c) 2009 American Institute of Physics.**84**Mallory, J. D.; Mandelshtam, V. A. Diffusion monte carlo studies of MB-pol (H_{2}O)_{2–6}and (D_{2}O)_{2–6}clusters: structures and binding energies.*J. Chem. Phys.*2016,*145*, 064308, DOI: 10.1063/1.4960610[Crossref], [CAS], Google Scholar84https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xhtlalu7zK&md5=dc5ea1aadd9a6cae0bbdb9932d6a5b65Diffusion Monte Carlo studies of MB-pol (H2O)2-6 and (D2O)2-6 clusters: Structures and binding energiesMallory, Joel D.; Mandelshtam, Vladimir A.Journal of Chemical Physics (2016), 145 (6), 064308/1-064308/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We employ the diffusion Monte Carlo (DMC) method in conjunction with the recently developed, ab initio-based MB-pol potential energy surface to characterize the ground states of small (H2O)2-6 clusters and their deuterated isotopomers. Observables, other than the ground state energies, are computed using the descendant weighting approach. Among those are various spatial correlation functions and relative isomer fractions. Interestingly, the ground states of all clusters considered in this study, except for the dimer, are delocalized over at least two conformations that differ by the orientation of one or more water monomers with the relative isomer populations being sensitive to the isotope substitution. Most remarkably, the ground state of the (H2O)6 hexamer is represented by four distinct cage structures, while that of (D2O)6 is dominated by the prism, i.e., the global min. geometry, with a very small contribution from a prism-book geometry. In addn., for (H2O)6 and (D2O)6, we performed DMC calcns. to compute the ground states constrained to the cage and prism geometries. These calcns. compared results for three different potentials, MB-pol, TTM3/F, and q-TIP4P/F. (c) 2016 American Institute of Physics.**85**Wang, X.-G.; Carrington, T. Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer.*J. Chem. Phys.*2018,*148*, 074108, DOI: 10.1063/1.5020426[Crossref], [PubMed], [CAS], Google Scholar85https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjtF2rtrk%253D&md5=f1e3c2b701f58f1003b7d49f3b066792Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimerWang, Xiao-Gang; Carrington, TuckerJournal of Chemical Physics (2018), 148 (7), 074108/1-074108/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors compute numerically exact rovibrational levels of H2O dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305(2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calcn., it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calc. the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions the authors use are products of monomer vibrational wavefunctions and std. rigid-monomer basis functions (which involve products of 3 Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom mols. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calcn. of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, good agreement for the intermol. levels and larger differences for the intramol. H2O bend levels were found. (c) 2018 American Institute of Physics.**86**Leforestier, C.; Szalewicz, K.; van der Avoird, A. Spectra of water dimer from a new*ab initio*potential with flexible Monomers.*J. Chem. Phys.*2012,*137*, 014305, DOI: 10.1063/1.4722338[Crossref], [PubMed], [CAS], Google Scholar86https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XpvVOmt78%253D&md5=4a037eeb53e13892153e9b6c8f35d624Spectra of water dimer from a new ab initio potential with flexible monomersLeforestier, Claude; Szalewicz, Krzysztof; van der Avoird, AdJournal of Chemical Physics (2012), 137 (1), 014305/1-014305/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report the definition and testing of a new ab initio 12-dimensional potential for the water dimer with flexible monomers. Using our recent accurate CCpol-8s rigid water pair potential as a ref. for the undistorted monomers' geometries, a distortion correction was added, which was taken from a former flexible-monomer ab initio potential. This correction allows us to retrieve the correct binding energy De=21.0 kJ mol-1, and leads to an equil. geometry in close agreement with the one obtained from benchmark calcns. The kinetic energy operator describing the flexible-monomer water dimer was expressed in terms of Radau coordinates for each monomer and a recent general cluster polyspherical formulation describing their relative motions. Within this formulation, an adiabatic scheme was invoked to decouple fast (intramol.) modes and slow (intermol.) ones. Different levels of approxn. were tested, which differ in the way in which the residual potential coupling between the intramol. modes located on different monomers and the dependence of the monomer rotational consts. on the dimer geometry are handled. Accurate calcns. of the vibration-rotation-tunneling levels of (H2O)2 and (D2O)2 were performed, which show the best agreement with expts. achieved so far for any water potential. Intramol. excitations of the two monomers were calcd. within two limiting cases, to account for the lack of non-adiabatic coupling between intramol. modes due to the intermol. motion. In the first model, the excitation was assumed to stay either on the donor or the acceptor mol., and to hop between the two moieties upon donor-acceptor interchange. In the second model, the excitation remains on the same mol. whatever is the dimer geometry. Marginal frequency differences, less than 2 cm-1, were obtained for all modes, and the resulting IR shifts are in good agreement with expts. (c) 2012 American Institute of Physics.**87**Wang, Y.; Bowman, J. M. Communication: Rigorous calculation of dissociation energies (*D*_{0}) of the water trimer (H_{2}O)_{3}and (D_{2}O)_{3}.*J. Chem. Phys.*2011,*135*, 131101, DOI: 10.1063/1.3647584[Crossref], [PubMed], [CAS], Google Scholar87https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXht1Gms7vN&md5=6c545d5a9f2df0b5d286b5ed2495fc10Communication: Rigorous calculation of dissociation energies (D0) of the water trimer, (H2O)3 and (D2O)3Wang, Yi-Min; Bowman, Joel M.Journal of Chemical Physics (2011), 135 (13), 131101/1-131101/3CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Using a recent, full-dimensional, ab initio potential energy surface together with rigorous diffusion Monte Carlo calcns. of the zero-point energy of the water trimer, we report dissocn. energies, D0, to form one monomer plus the water dimer and three monomers. The calcns. make use of essentially exact zero-point energies for the water trimer, dimer, and monomer, and benchmark values of the electronic dissocn. energies, De, of the water trimer. The D0 results are 3855 and 2726 cm-1 for the 3H2O and H2O + (H2O)2 dissocn. channels, resp., and 4206 and 2947 cm-1 for 3D2O and D2O + (D2O)2 dissocn. channels, resp. The results have estd. uncertainties of 20 and 30 cm-1 for the monomer plus dimer and three monomer of dissocn. channels, resp. (c) 2011 American Institute of Physics.**88**Rocher-Casterline, B. E.; Ch’ng, L. C.; Mollner, A. K.; Reisler, H. Communication: Determination of the bond dissociation energy (*D*_{0}) of the water dimer, (H_{2}O)_{2}, by velocity map imaging.*J. Chem. Phys.*2011,*134*, 211101, DOI: 10.1063/1.3598339[Crossref], [PubMed], [CAS], Google Scholar88https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmvFaiurk%253D&md5=4a6f332ae44ae8c668135c5b68d4910dCommunication: Determination of the bond dissociation energy (D0) of the water dimer, (H2O)2, by velocity map imagingRocher-Casterline, Blithe E.; Ch'ng, Lee C.; Mollner, Andrew K.; Reisler, HannaJournal of Chemical Physics (2011), 134 (21), 211101/1-211101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The bond dissocn. energy (D0) of the water dimer is detd. by using state-to-state vibrational predissocn. measurements following excitation of the bound OH stretch fundamental of the donor unit of the dimer. Velocity map imaging and resonance-enhanced multiphoton ionization (REMPI) are used to det. pair-correlated product velocity and translational energy distributions. H2O fragments are detected in the ground vibrational (000) and the first excited bending (010) states by 2 + 1 REMPI via the ~C 1B1 (000) ← ~ X 1A1 (000 and 010) transitions. The fragments' velocity and center-of-mass translational energy distributions are detd. from images of selected rovibrational levels of H2O. An accurate value for D0 is obtained by fitting both the structure in the images and the max. velocity of the fragments. This value, D0 = 1105 ± 10 cm-1 (13.2 ± 0.12 kJ/mol), is in excellent agreement with the recent theor. value of D0 = 1103 ± 4 cm-1 (13.2 ± 0.05 kJ/mol) suggested as a benchmark by Shank et al. [J. Chem. Phys. 130, 144314 (2009)]. (c) 2011 American Institute of Physics.**89**Ch’ng, L. C.; Samanta, A. K.; Wang, Y.; Bowman, J. M.; Reisler, H. Experimental and theoretical investigations of the dissociation energy (*D*_{0}) and dynamics of the water trimer, (H_{2}O)_{3}.*J. Phys. Chem. A*2013,*117*, 7207– 7216, DOI: 10.1021/jp401155v[ACS Full Text ], [CAS], Google Scholar89https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXkslWgu7g%253D&md5=131dfa295086beee90759190d9f84b71Experimental and Theoretical Investigations of the Dissociation Energy (D0) and Dynamics of the Water Trimer, (H2O)3Ch'ng, Lee C.; Samanta, Amit K.; Wang, Yimin; Bowman, Joel M.; Reisler, HannaJournal of Physical Chemistry A (2013), 117 (32), 7207-7216CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)We report a joint exptl.-theor. study of the predissocn. dynamics of the water trimer following excitation of the hydrogen bonded OH-stretch fundamental. The bond dissocn. energy (D0) for the (H2O)3 → H2O + (H2O)2 dissocn. channel is detd. from fitting the speed distributions of selected rovibrational states of the water monomer fragment using velocity map imaging. The exptl. value, D0 = 2650 ± 150 cm-1, is in good agreement with the previously detd. theor. value, 2726 ± 30 cm-1, obtained using an ab initio full-dimensional potential energy surface (PES) together with Diffusion Monte Carlo calcns. Comparing this value to D0 of the dimer places the contribution of nonpairwise additivity to the hydrogen bonding at 450-500 cm-1. Quasiclassical trajectory (QCT) calcns. using this PES help elucidate the reaction mechanism. The trajectories show that most often one hydrogen bond breaks first, followed by breaking and re-forming of hydrogen bonds (often with different hydrogen bonds breaking) until, after many picoseconds, a water monomer is finally released. The translational energy distributions calcd. by QCT for selected rotational levels of the monomer fragment agree with the exptl. observations. The product translational and rotational energy distributions calcd. by QCT also agree with statistical predictions. The availability of low-lying intermol. vibrational levels in the dimer fragment is likely to facilitate energy transfer before dissocn. occurs, leading to statistical-like product state distributions.**90**Pérez, C.; Muckle, M. T.; Zaleski, D. P.; Seifert, N. A.; Temelso, B.; Shields, G. C.; Kisiel, Z.; Pate, B. H. Structures of cage, prism, and book isomers of water hexamer from broadband rotational spectroscopy.*Science*2012,*336*, 897– 901, DOI: 10.1126/science.1220574[Crossref], [PubMed], [CAS], Google Scholar90https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XmvFens7g%253D&md5=1e138ca90bb27d88488982766b326cd7Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational SpectroscopyPerez, Cristobal; Muckle, Matt T.; Zaleski, Daniel P.; Seifert, Nathan A.; Temelso, Berhane; Shields, George C.; Kisiel, Zbigniew; Pate, Brooks H.Science (Washington, DC, United States) (2012), 336 (6083), 897-901CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Theory predicts the water hexamer to be the smallest water cluster with a three-dimensional hydrogen-bonding network as its min. energy structure. There are several possible low-energy isomers, and calcns. with different methods and basis sets assign them different relative stabilities. Previous exptl. work has provided evidence for the cage, book, and cyclic isomers, but no expt. has identified multiple coexisting structures. Here, we report that broadband rotational spectroscopy in a pulsed supersonic expansion unambiguously identifies all three isomers; we detd. their oxygen framework structures by means of oxygen-18-substituted water (H218O). Relative isomer populations at different expansion conditions establish that the cage isomer is the min. energy structure. Rotational spectra consistent with predicted heptamer and nonamer structures have also been identified.**91**Nauta, K.; Miller, R. Formation of cyclic water hexamer in liquid helium: The smallest piece of ice.*Science*2000,*287*, 293– 295, DOI: 10.1126/science.287.5451.293[Crossref], [PubMed], [CAS], Google Scholar91https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXlvVWksA%253D%253D&md5=dd7ae25d4a0886726f3429bbf07d5cd6Formation of cyclic water hexamer in liquid helium: the smallest piece of iceNauta, K.; Miller, R. E.Science (Washington, D. C.) (2000), 287 (5451), 293-295CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)The cyclic water hexamer, a higher energy isomer than the cage structure previously characterized in the gas phase, was formed in liq. helium droplets and studied with IR spectroscopy. This isomer is formed selectively as a result of unique cluster growth processes in liq. helium. The exptl. results indicate that the cyclic hexamer is formed by insertion of water mols. into smaller preformed cyclic complexes and that the rapid quenching provided by the liq. helium inhibits its rearrangement to the more stable cage structure.**92**Burnham, C. J.; Xantheas, S. S.; Miller, M. A.; Applegate, B. E.; Miller, R. E. The formation of cyclic water complexes by sequential ring insertion: Experiment and theory.*J. Chem. Phys.*2002,*117*, 1109– 1122, DOI: 10.1063/1.1483259[Crossref], [CAS], Google Scholar92https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XltVOhtrs%253D&md5=b001f004eafe2ec973415fa9822e43ddThe formation of cyclic water complexes by sequential ring insertion: Experiment and theoryBurnham, Christian J.; Xantheas, Sotiris S.; Miller, Mark A.; Applegate, Brian E.; Miller, Roger E.Journal of Chemical Physics (2002), 117 (3), 1109-1122CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The growth of water clusters in liq. helium droplets results in the formation of cyclic structures up to and including the hexamer. In view of the sequential nature of the mol. pick-up process, the formation of water rings involves the insertion of water monomers into preformed cyclic water clusters. The implication of this observation is that the barriers to the ring insertion process are low enough to be overcome during the expt. This paper presents a combined exptl. and theor. effort to explore the insertion process in detail. Our results provide important new insights into the dynamics of hydrogen-bonded networks. We map out the cluster potential energy surfaces and visualize them using disconnectivity graphs. Nonequil. walks on these surfaces show that ring water clusters can be formed during sequential addn. of water mols. by surmounting small barriers that are thermally accessible even at the low temp. of the expt. The effects of zero-point energy are significant in making these processes feasible.**93**Steinbach, C.; Andersson, P.; Melzer, M.; Kazimirski, J. K.; Buck, U.; Buch, V. Detection of the book isomer from the OH-stretch spectroscopy of size selected water hexamers.*Phys. Chem. Chem. Phys.*2004,*6*, 3320– 3324, DOI: 10.1039/b400664j[Crossref], [CAS], Google Scholar93https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXlsVaksrk%253D&md5=8594ccfaf5a6eecb0559bdcf76a690a7Detection of the book isomer from the OH-stretch spectroscopy of size selected water hexamersSteinbach, C.; Andersson, P.; Melzer, M.; Kazimirski, J. K.; Buck, U.; Buch, V.Physical Chemistry Chemical Physics (2004), 6 (13), 3320-3324CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The vibrational OH-stretch spectrum of size selected H2O hexamer clusters was measured for cluster temps. between 40 and 60 K By comparison with temp. dependent calcns. the spectra were identified to be those of the book isomer. This result is in good agreement with recent predictions of the equil. isomer distributions in this temp. range.**94**Diken, E. G.; Robertson, W. H.; Johnson, M. A. The Vibrational spectrum of the neutral (H_{2}O)_{6}precursor to the “magic” (H_{2}O)_{6}^{–}cluster anion by argon-mediated, population-modulated electron attachment spectroscopy.*J. Phys. Chem. A*2004,*108*, 64– 68, DOI: 10.1021/jp0309973[ACS Full Text ], [CAS], Google Scholar94https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXps1Gmu7s%253D&md5=afe127063864a3477e954fe68414a2d0The Vibrational Spectrum of the Neutral (H2O)6 Precursor to the "Magic" (H2O)6- Cluster Anion by Argon-Mediated, Population-Modulated Electron Attachment SpectroscopyDiken, Eric G.; Robertson, William H.; Johnson, Mark A.Journal of Physical Chemistry A (2004), 108 (1), 64-68CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)A new technique is introduced for the acquisition of size-selected neutral cluster spectra on the basis of argon-mediated, population-modulated electron attachment. This method is demonstrated and used to obtain the vibrational spectrum of the neutral water hexamer precursor to the (H2O)6- cluster ion. The mid-IR spectrum of the neutral species is dominated by four intense features above 3400 cm-1, clearly indicating that significant structural rearrangements occur upon slow electron attachment to form the "magic" hexamer cluster anion. Comparison with previous spectroscopic reports and theor. predictions indicates that the low-energy "book" isomer is most consistent with the obsd. band pattern and is suggested to be the species that captures a low-energy electron to form the hexamer anion.**95**Wang, Y. M.; Bowman, J. M. IR spectra of the water hexamer: Theory, with inclusion of the monomer bend overtone, and experiment are in agreement.*J. Phys. Chem. Lett.*2013,*4*, 1104, DOI: 10.1021/jz400414a[ACS Full Text ], [CAS], Google Scholar95https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXktF2lsrY%253D&md5=08a758bb7a18d4905195d503914dd390IR Spectra of the Water Hexamer: Theory, with Inclusion of the Monomer Bend Overtone, and Experiment Are in AgreementWang, Yimin; Bowman, Joel M.Journal of Physical Chemistry Letters (2013), 4 (7), 1104-1108CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Signature IR spectra of isomers of the H2O hexamer in the spectral range 3000-3800 cm-1 were reported by experimentalists, but crucial theor. interpretation has still not been definitive. Using ab initio potential and dipole moment surfaces and a fully coupled quantum treatment of the intramol. modes, the ring and book are assigned to spectra obtained in the He nanodroplet and Ar tagging expts., resp. The overtone of the intramol. bend at ∼3200 cm-1 is a new calcd. feature that completes an important missing piece in previous exptl. and theor. comparisons and leads to a consistent assignment of these 2 exptl. spectra. Calcd. IR spectra for the lowest energy forms of the H2O heptamer and octomer are also presented and compared to expt. In all the calcd. spectra, the bend overtone is a noticeable feature, and this is 1 important conclusion from the work. Also, the danger in using scaled double-harmonic spectra to assign spectra is demonstrated.**96**Liu, H. C.; Wang, Y. M.; Bowman, J. M. Local-monomer calculations of the intramolecular IR spectra of the cage and prism isomers of HOD(D_{2}O)_{5}and HOD and D_{2}O ice lh.*J. Phys. Chem. B*2014,*118*, 14124, DOI: 10.1021/jp5061182[ACS Full Text ], [CAS], Google Scholar96https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFChtbfJ&md5=00bce8735a6f773fc1937f34a9bd0155Local-Monomer Calculations of the Intramolecular IR Spectra of the Cage and Prism Isomers of HOD(D2O)5 and HOD and D2O Ice IhLiu, Hanchao; Wang, Yimin; Bowman, Joel M.Journal of Physical Chemistry B (2014), 118 (49), 14124-14131CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)Dil. mixts. of HOD in pure H2O and D2O ices and liq. were used by experimentalists to focus on the spectrum and vibrational dynamics of the local OH and OD stretches and bend of HOD in these complex and highly heterogeneous environments. The hexamer version of the mixt. is HOD(D2O)5. The cage isomer of this cluster was recently studied and analyzed theor. using local-mode calcns. of the IR spectrum by Skinner and co-workers. This and the further possibility of exptl. study of this cluster have stimulated one to study HOD(D2O)5 using the 3-mode, local-monomer model, with the ab initio WHBB dipole moment and potential energy surfaces. Both the cage and prism isomers of this cluster are considered. In addn. to providing addnl. insight into the HOD portion of the spectrum, the spectral signatures of each D2O are also presented at 1000-4000 cm-1. The OH stretch bands of both the prism and cage isotopomers exhibit rich structures at 3100-3700 cm-1 that are indicative of the position of the HOD in these hexamers. A preliminary study of the site preference of the HOD is also reported for both cage and prism HOD(D2O)5 using an harmonic zero-point energy anal. of the entire cluster. The energies of free-OH sites are lower than the ones of H-bonded OH sites. Finally, following earlier work on the IR spectra of H2O ice models, the authors present IR spectra of pure D2O and HOD.**97**Douberly, G. Private communication, 2013.Google ScholarThere is no corresponding record for this reference.**98**Adjoua, O.; Lagardère, L.; Jolly, L.-H.; Durocher, A.; Very, T.; Dupays, I.; Wang, Z.; Inizan, T. J.; Célerse, F.; Ren, P.; Ponder, J. W.; Piquemal, J.-P. Tinker-HP: Accelerating molecular dynamics simulations of large complex systems with advanced point dipole polarizable force fields using GPUs and multi-GPU systems.*J. Chem. Theory Comput.*2021,*17*, 2034– 2053, DOI: 10.1021/acs.jctc.0c01164[ACS Full Text ], [CAS], Google Scholar98https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXmvFarsbs%253D&md5=cbbdb13c07fdac87e37d698e1f1dc6f5Tinker-HP: Accelerating molecular dynamics simulations of large complex systems with advanced point dipole polarizable force fields using GPUs and multi-GPU systemsAdjoua, Olivier; Lagardere, Louis; Jolly, Luc-Henri; Durocher, Arnaud; Very, Thibaut; Dupays, Isabelle; Wang, Zhi; Inizan, Theo Jaffrelot; Celerse, Frederic; Ren, Pengyu; Ponder, Jay W.; Piquemal, Jean-PhilipJournal of Chemical Theory and Computation (2021), 17 (4), 2034-2053CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We present the extension of the Tinker-HP package (Lagarde´re et al., Chem. Sci., 2018,9, 956-972) to the use of Graphics Processing Unit (GPU) cards to accelerate mol. dynamics simulations using polarizable many-body force fields. The new high-performance module allows for an efficient use of single- and multi-GPUs architectures ranging from research labs. to modern supercomputer centers. After detailing an anal. of our general scalable strategy that relies on OPENACC and CUDA, we discuss the various capabilities of the package. Among them, the multiprecision possibilities of the code are discussed. If an efficient double precision implementation is provided to preserve the possibility of fast ref. computations, we show that a lower precision arithmetic is preferred providing a similar accuracy for mol. dynamics while exhibiting superior performances. As Tinker-HP is mainly dedicated to accelerate simulations using new generation point dipole polarizable force field, we focus our study on the implementation of the AMOEBA model. Testing various NVIDIA platforms including 2080Ti, 3090, V100 and A100 cards, we provide illustrative benchmarks of the code for single- and multicards simulations on large biosystems encompassing up to millions of atoms. The new code strongly reduces time to soln. and offers the best performances to date obtained using the AMOEBA polarizable force field. Perspectives toward the strong-scaling performance of our multinode massive parallelization strategy, unsupervised adaptive sampling and large scale applicability of the Tinker-HP code in biophysics are discussed. The present software has been released in phase advance on GitHub in link with the High Performance Computing community COVID-19 research efforts and is free for Academics (see https://github.com/TinkerTools/tinker-hp).**99**Liu, Y.; Li, J. Permutation-invariant-polynomial neural-network-based Δ-machine learning approach: A case for the HO_{2}self-reaction and its dynamics study.*J. Phys. Chem. Lett.*2022,*13*, 4729– 4738, DOI: 10.1021/acs.jpclett.2c01064[ACS Full Text ], [CAS], Google Scholar99https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhtlGqtbfE&md5=ab5481f4756ed5689898b2080ef2a1f4Permutation-Invariant-Polynomial Neural-Network-Based Δ-Machine Learning Approach: A Case for the HO2 Self-Reaction and Its Dynamics StudyLiu, Yang; Li, JunJournal of Physical Chemistry Letters (2022), 13 (21), 4729-4738CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Δ-Machine learning, or the hierarchical construction scheme, is a highly cost-effective method, as only a small no. of high-level ab initio energies are required to improve a potential energy surface (PES) fit to a large no. of low-level points. However, there is no efficient and systematic way to select as few points as possible from the low-level data set. We here propose a permutation-invariant-polynomial neural-network (PIP-NN)-based Δ-machine learning approach to construct full-dimensional accurate PESs of complicated reactions efficiently. Particularly, the high flexibility of the NN is exploited to efficiently sample points from the low-level data set. This approach is applied to the challenging case of a HO2 self-reaction with a large configuration space. Only 14% of the DFT data set is used to successfully bring a newly fitted DFT PES to the UCCSD(T)-F12a/AVTZ quality. Then, the quasiclassical trajectory (QCT) calcns. are performed to study its dynamics, particularly the mode specificity.**100**Gazdy, B.; Bowman, J. M. An adjusted global potential surface for HCN based on rigorous vibrational calculations.*J. Chem. Phys.*1991,*95*, 6309– 6316, DOI: 10.1063/1.461551[Crossref], [CAS], Google Scholar100https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXms1ertLs%253D&md5=ccec9c7633f72eb19af972fbe3dbda70An adjusted global potential surface for hydrogen cyanide based on rigorous vibrational calculationsGazdy, Bela; Bowman, Joel M.Journal of Chemical Physics (1991), 95 (9), 6309-16CODEN: JCPSA6; ISSN:0021-9606.Extensive trial and error modifications were made of the Murrell-Carter-Jalonen potential surface for HCN to improve agreement with expts. on highly excited stretching and bending states. The vibrational calcns. make use of an exact Hamiltonian for nonrotating HCN and use an exact formalism to obtain energies. Two exptl. data bases are used to compare against the calcns. One is for highly excited stretch states, but with no bend excitation, and the other is for highly excited bed and CN stretch states, but with no CH stretch excitation. The combined data base consists of 58 vibrational energies for nonrotating HCN. The modifications applied are angular and stretch coordinate scaling and an angular-dependent potential scaling.**101**Meuwly, M.; Hutson, J. M. Morphing ab initio potentials: A systematic study of Ne–HF.*J. Chem. Phys.*1999,*110*, 8338– 8347, DOI: 10.1063/1.478744[Crossref], [CAS], Google Scholar101https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXisFCgsr8%253D&md5=35f4dfb8f9632df57187ee2caa71c8f6Morphing ab initio potentials: a systematic study of Ne-HFMeuwly, Markus; Hutson, Jeremy M.Journal of Chemical Physics (1999), 110 (17), 8338-8347CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A procedure for "morphing" an ab initio potential energy surface to obtain agreement with exptl. data is presented. The method involves scaling functions for both the energy and the intermol. distance. In the present work, the scaling functions are parameterized and detd. by least-squares fitting to the exptl. data. The method is tested on the system Ne-HF, for which high-resoln. IR spectra are available. It is shown to work well even with relatively low-level ab initio calcns. Several basis sets are investigated at the CCSD(T) correlation level, including various aug-cc-pVnZ basis sets and the specially-tailored Ne-HF basis set of ONeil, et al. All give good results after morphing, but the changes needed to match expt. are much smaller for the ONeil basis set. The use of MP2 calcns. is also investigated: again, the MP2 potential is quite satisfactory after morphing, but requires much more modification than the CCSD(T) potential.**102**Wang, Y. M.; Bowman, J. M.*Ab initio*potential and dipole moment surfaces for water. II. Local-monomer calculations of the infrared spectra of water clusters.*J. Chem. Phys.*2011,*134*, 154510, DOI: 10.1063/1.3579995[Crossref], [PubMed], [CAS], Google Scholar102https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXkvFGgtbw%253D&md5=47480545a99421319dd189056e086993Ab initio potential and dipole moment surfaces for water. II. Local-monomer calculations of the infrared spectra of water clustersWang, Yimin; Bowman, Joel M.Journal of Chemical Physics (2011), 134 (15), 154510/1-154510/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We employ recent flexible ab initio potential energy and dipole surfaces to the calcn. of IR spectra of the intramol. modes of water clusters. We use a quantum approach that begins with a partitioned normal-mode anal. of perturbed monomers, and then obtains solns. of the corresponding Schrodinger equations for the fully coupled intramol. modes of each perturbed monomer. For water clusters, these modes are the two stretches and the bend. This approach is tested against benchmark calcns. for the water dimer and trimer and then applied to the water clusters (H2O)n for n = 6-10 and n = 20. Comparisons of the spectra are made with previous ab initio harmonic and empirical potential calcns. and available expts. (c) 2011 American Institute of Physics.**103**Fanourgakis, G. S.; Xantheas, S. S. Development of transferable interaction potentials for water. V. extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid Water.*J. Chem. Phys.*2008,*128*, 074506, DOI: 10.1063/1.2837299[Crossref], [PubMed], [CAS], Google Scholar103https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXislKgu7o%253D&md5=8f515a7326e184fa0ea7a12d516fdf21Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid waterFanourgakis, George S.; Xantheas, Sotiris S.Journal of Chemical Physics (2008), 128 (7), 074506/1-074506/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors present a new parametrization of the flexible, polarizable Thole-type model for H2O, with emphasis in describing the vibrational spectra of both H2O clusters and liq. H2O. The new model is able to produce results of similar quality with the previous versions for the structures and energetics of H2O clusters as well as structural and thermodn. properties of liq. H2O evaluated with classical and converged quantum statistical mech. atomistic simulations. At the same time it yields accurate red-shifts for the OH vibrational stretches of both H2O clusters and liq. H2O. (c) 2008 American Institute of Physics.**104**Babin, V.; Medders, G. R.; Paesani, F. Development of a “First Principles” Water Potential with Flexible Monomers. II: Trimer Potential Energy Surface, Third Virial Coefficient, and Small Clusters.*J. Chem. Theory Comput.*2014,*10*, 1599– 1607, DOI: 10.1021/ct500079y[ACS Full Text ], [CAS], Google Scholar104https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXktFeisbo%253D&md5=54f68422445298bdb87fdf8864894f7eDevelopment of a "First Principles" Water Potential with Flexible Monomers. II: Trimer Potential Energy Surface, Third Virial Coefficient, and Small ClustersBabin, Volodymyr; Medders, Gregory R.; Paesani, FrancescoJournal of Chemical Theory and Computation (2014), 10 (4), 1599-1607CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A full-dimensional potential energy function (MB-pol) for simulations of water from the dimer to bulk phases is developed entirely from "first principles" by building upon the many-body expansion of the interaction energy. Specifically, the MB-pol potential is constructed by combining a highly accurate dimer potential energy surface with explicit three-body and many-body polarization terms. The three-body contribution, expressed as a combination of permutationally invariant polynomials and classical polarizability, is derived from a fit to more than 12000 three-body energies calcd. at the CCSD(T)/aug-cc-pVTZ level of theory, imposing the correct asymptotic behavior as predicted from "first principles". Here, the accuracy of MB-pol is demonstrated through comparison of the calcd. third virial coeff. with the corresponding exptl. data as well as through anal. of the relative energy differences of small clusters.**105**Burnham, C. J.; Anick, D. J.; Mankoo, P. K.; Reiter, G. F. The vibrational proton potential in bulk liquid water and ice.*J. Chem. Phys.*2008,*128*, 154519, DOI: 10.1063/1.2895750[Crossref], [PubMed], [CAS], Google Scholar105https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXltFyls7g%253D&md5=4fe9a32d86a14bf6b575edc281f115d1The vibrational proton potential in bulk liquid water and iceBurnham, C. J.; Anick, D. J.; Mankoo, P. K.; Reiter, G. F.Journal of Chemical Physics (2008), 128 (15), 154519/1-154519/20CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors present an empirical flexible and polarizable H2O model which gives an improved description of the position, momentum, and dynamical (spectroscopic) distributions of H nuclei in H2O. The authors use path integral mol. dynamics techniques to obtain momentum and position distributions and an approx. soln. to the Schrodinger equation to obtain the IR spectrum. When the calcd. distributions are compared to expt. the existing empirical models tend to overestimate the stiffness of the H nuclei involved in H bonds. Also, these models vastly underestimate the enormous increase in the integrated IR intensity obsd. in the bulk over the gas-phase value. The over-rigidity of the OH stretch and the underestimation of intensity are connected to the failure of existing models to reproduce the correct monomer polarizability surface. A new model, TTM4-F, is parametrized against electronic structure results to better reproduce the polarizability surface. TTM4-F gives a superior description of the obsd. spectroscopy, showing both the correct red shift and a much improved intensity. TTM4-F also has a somewhat improved dielec. const. and OH distribution function. It also gives an improved match to the exptl. momentum distribution, although some discrepancies remain. (c) 2008 American Institute of Physics.**106**Townsend, J.; Vogiatzis, K. D. Data-driven acceleration of the coupled-cluster singles and doubles iterative solver.*J. Phys. Chem. Lett.*2019,*10*, 4129– 4135, DOI: 10.1021/acs.jpclett.9b01442[ACS Full Text ], [CAS], Google Scholar106https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXht1eksrnJ&md5=54449f17bc091cb9ca8759073b58e643Data-Driven Acceleration of the Coupled-Cluster Singles and Doubles Iterative SolverTownsend, Jacob; Vogiatzis, Konstantinos D.Journal of Physical Chemistry Letters (2019), 10 (14), 4129-4135CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Solving the coupled-cluster (CC) equations is a cost-prohibitive process that exhibits poor scaling with system size. These equations are solved by detg. the set of amplitudes (t) that minimize the system energy with respect to the coupled-cluster equations at the selected level of truncation. Here, a novel approach to predict the converged coupled-cluster singles and doubles (CCSD) amplitudes, thus the coupled-cluster wave function, is explored by using machine learning and electronic structure properties inherent to the MP2 level. Features are collected from quantum chem. data, such as orbital energies, one-electron Hamiltonian, Coulomb, and exchange terms. The data-driven CCSD (DDCCSD) is not an alchem. method because the actual iterative coupled-cluster equations are solved. However, accurate energetics can also be obtained by bypassing solving the CC equations entirely. Our preliminary data show that it is possible to achieve remarkable speedups in solving the CCSD equations, esp. when the correct physics are encoded and used for training of machine learning models.**107**Dick, S.; Fernandez-Serra, M. Machine learning accurate exchange and correlation functionals of the electronic density.*Nat. Commun.*2020,*11*, 3509, DOI: 10.1038/s41467-020-17265-7[Crossref], [PubMed], [CAS], Google Scholar107https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsVSmtrvM&md5=ed10c269bb81fe1b9cddd53f4f5ebce0Machine learning accurate exchange and correlation functionals of the electronic densityDick, Sebastian; Fernandez-Serra, MariviNature Communications (2020), 11 (1), 3509CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Abstr.: D. functional theory (DFT) is the std. formalism to study the electronic structure of matter at the at. scale. In Kohn-Sham DFT simulations, the balance between accuracy and computational cost depends on the choice of exchange and correlation functional, which only exists in approx. form. Here, we propose a framework to create d. functionals using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the phys. information contained in the training data, making them transferable across systems. A NeuralXC functional optimized for water outperforms other methods characterizing bond breaking and excels when comparing against exptl. results. This work demonstrates that NeuralXC is a first step towards the design of a universal, highly accurate functional valid for both mols. and solids.**108**Qiao, Z.; Welborn, M.; Anandkumar, A.; Manby, F. R.; Miller, T. F. OrbNet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital features.*J. Chem. Phys.*2020,*153*, 124111, DOI: 10.1063/5.0021955[Crossref], [PubMed], [CAS], Google Scholar108https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvFyqs7fK&md5=031f87ddd1536195dc5662b7fc7e9e23OrbNet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital featuresQiao, Zhuoran; Welborn, Matthew; Anandkumar, Animashree; Manby, Frederick R.; Miller, Thomas F.Journal of Chemical Physics (2020), 153 (12), 124111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We introduce a machine learning method in which energy solns. from the Schroedinger equation are predicted using symmetry adapted AO features and a graph neural-network architecture. OrbNet is shown to outperform existing methods in terms of learning efficiency and transferability for the prediction of d. functional theory results while employing low-cost features that are obtained from semi-empirical electronic structure calcns. For applications to datasets of drug-like mols., including QM7b-T, QM9, GDB-13-T, DrugBank, and the conformer benchmark dataset of Folmsbee and Hutchison [Int. J. Quantum Chem. (published online) (2020)], OrbNet predicts energies within chem. accuracy of d. functional theory at a computational cost that is 1000-fold or more reduced. (c) 2020 American Institute of Physics.**109**Ikabata, Y.; Fujisawa, R.; Seino, J.; Yoshikawa, T.; Nakai, H. Machine-learned electron correlation model based on frozen core approximation.*J. Chem. Phys.*2020,*153*, 184108, DOI: 10.1063/5.0021281[Crossref], [PubMed], [CAS], Google Scholar109https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitleltbnJ&md5=804e54d5a4803e2497e940009b79f05bMachine-learned electron correlation model based on frozen core approximationIkabata, Yasuhiro; Fujisawa, Ryo; Seino, Junji; Yoshikawa, Takeshi; Nakai, HiromiJournal of Chemical Physics (2020), 153 (18), 184108CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The machine-learned electron correlation (ML-EC) model is a regression model in the form of a d. functional that reproduces the correlation energy d. based on wavefunction theory. In a previous study [T. Nudejima et al., J. Chem. Phys. 151, 024104 (2019)], the ML-EC model was constructed using the correlation energy d. from all-electron calcns. with basis sets including core polarization functions. In this study, we applied the frozen core approxn. (FCA) to the correlation energy d. to reduce the computational cost of the response variable used in machine learning. The coupled cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy d. obtained from a grid-based energy d. anal. was analyzed within FCA and correlation-consistent basis sets without core polarization functions. The complete basis set (CBS) limit of the correlation energy d. was obtained using the extrapolation and composite schemes. The CCSD(T)/CBS correlation energy densities based on these schemes showed reasonable behavior, indicating its appropriateness as a response variable. As expected, the computational time was significantly reduced, esp. for systems contg. elements with a large no. of inner-shell electrons. Based on the d.-to-d. relationship, a large no. of data (5 662 500 points), which were accumulated from 30 mols., were sufficient to construct the ML-EC model. The valence-electron correlation energies and reaction energies calcd. using the constructed model were in good agreement with the ref. values, the latter of which were superior in accuracy to d. functional calcns. using 71 exchange-correlation functionals. The numerical results indicate that the FCA is useful for constructing a versatile model. (c) 2020 American Institute of Physics.**110**Ruth, M.; Gerbig, D.; Schreiner, P. R. Machine learning of coupled cluster (T)-energy corrections via delta (Δ)-Learning.*J. Chem. Theory Comput.*2022,*18*, 4846– 4855, DOI: 10.1021/acs.jctc.2c00501[ACS Full Text ], [CAS], Google Scholar110https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhslCrt7%252FI&md5=9a2576c37d27e2940c0e9e5cac796d47Machine Learning of Coupled Cluster (T)-Energy Corrections via Delta (Δ)-LearningRuth, Marcel; Gerbig, Dennis; Schreiner, Peter R.Journal of Chemical Theory and Computation (2022), 18 (8), 4846-4855CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Accurate thermochem. is essential in many chem. disciplines, such as astro-, atm., or combustion chem. These areas often involve fleetingly existent intermediates whose thermochem. is difficult to assess. Whenever direct calorimetric expts. are infeasible, accurate computational ests. of relative mol. energies are required. However, high-level computations, often using coupled cluster theory, are generally resource-intensive. To expedite the process using machine learning techniques, we generated a database of energies for small org. mols. at the CCSD(T)/cc-pVDZ, CCSD(T)/aug-cc-pVDZ, and CCSD(T)/cc-pVTZ levels of theory. Leveraging the power of deep learning by employing graph neural networks, we are able to predict the effect of perturbatively included triples (T), i.e., the difference between CCSD and CCSD(T) energies, with a mean abs. error of 0.25, 0.25, and 0.28 kcal mol-1 (R2 of 0.998, 0.997, and 0.998) with the cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets, resp. Our models were further validated by application to three validation sets taken from the S22 Database as well as to a selection of known theor. challenging cases.**111**Dral, P. O.; Zubatiuk, T.; Xue, B.-X. Learning from multiple quantum chemical methods: Δ-learning, transfer learning, co-kriging, and beyond. In*Quantum Chemistry in the Age of Machine Learning*; Dral, P. O., Ed.; Elsevier, 2023; pp 491– 507.

## Cited By

This article is cited by 1 publications.

- Michael S. Chen, Joonho Lee, Hong-Zhou Ye, Timothy C. Berkelbach, David R. Reichman, Thomas E. Markland. Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy. Journal of Chemical Theory and Computation
**2023**, Article ASAP.

## References

ARTICLE SECTIONSThis article references 111 other publications.

**1**Pinheiro, M.; Ge, F.; Ferré, N.; Dral, P. O.; Barbatti, M. Choosing the right molecular machine learning potential.*Chem. Sci.*2021,*12*, 14396– 14413, DOI: 10.1039/D1SC03564A[Crossref], [PubMed], [CAS], Google Scholar1https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitVanur7I&md5=22cd3cb82edeac237781df45e99ff126Choosing the right molecular machine learning potentialPinheiro, Max; Ge, Fuchun; Ferre, Nicolas; Dral, Pavlo O.; Barbatti, MarioChemical Science (2021), 12 (43), 14396-14413CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)A review. Quantum-chem. simulations based on potential energy surfaces of mols. provide invaluable insight into the physicochem. processes at the atomistic level and yield such important observables as reaction rates and spectra. Machine learning potentials promise to significantly reduce the computational cost and hence enable otherwise unfeasible simulations. However, the surging no. of such potentials begs the question of which one to choose or whether we still need to develop yet another one. Here, we address this question by evaluating the performance of popular machine learning potentials in terms of accuracy and computational cost. In addn., we deliver structured information for non-specialists in machine learning to guide them through the maze of acronyms, recognize each potential's main features, and judge what they could expect from each one.**2**Houston, P. L.; Qu, C.; Nandi, A.; Conte, R.; Yu, Q.; Bowman, J. M. Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods.*J. Chem. Phys.*2022,*156*, 044120, DOI: 10.1063/5.0080506[Crossref], [PubMed], [CAS], Google Scholar2https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XisFKisrY%253D&md5=2109ba8195704092c1f422cc6e88c85dPermutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methodsHouston, Paul L.; Qu, Chen; Nandi, Apurba; Conte, Riccardo; Yu, Qi; Bowman, Joel M.Journal of Chemical Physics (2022), 156 (4), 044120CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Permutationally invariant polynomial (PIP) regression has been used to obtain machine-learned potential energy surfaces, including anal. gradients, for many mols. and chem. reactions. Recently, the approach has been extended to moderate size mols. with up to 15 atoms. The algorithm, including "purifn. of the basis," is computationally efficient for energies; however, we found that the recent extension to obtain anal. gradients, despite being a remarkable advance over previous methods, could be further improved. Here, we report developments to further compact a purified basis and, more significantly, to use the reverse differentiation approach to greatly speed up gradient evaluation. We demonstrate this for our recent four-body water interaction potential. Comparisons of training and testing precision on the MD17 database of energies and gradients (forces) for ethanol against numerous machine-learning methods, which were recently assessed by Dral and co-workers, are given. The PIP fits are as precise as those using these methods, but the PIP computation time for energy and force evaluation is shown to be 10-1000 times faster. Finally, a new PIP potential energy surface (PES) is reported for ethanol based on a more extensive dataset of energies and gradients than in the MD17 database. Diffusion Monte Carlo calcns. that fail on MD17-based PESs are successful using the new PES. (c) 2022 American Institute of Physics.**3**Chmiela, S.; Tkatchenko, A.; Sauceda, H. E.; Poltavsky, I.; Schütt, K. T.; Müller, K.-R. Machine learning of accurate energy-conserving molecular force fields.*Sci. Adv.*2017,*3*, e1603015, DOI: 10.1126/sciadv.1603015[Crossref], [PubMed], [CAS], Google Scholar3https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXkvVGjsrg%253D&md5=f26ef9dd87735d5d8fdbf5cc1ab9ae7cMachine learning of accurate energy-conserving molecular force fieldsChmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schuett, Kristof T.; Mueller, Klaus-RobertScience Advances (2017), 3 (5), e1603015/1-e1603015/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)Using conservation of energy-a fundamental property of closed classical and quantum mech. systems-we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate mol. force fields using a restricted no. of samples from ab initio mol. dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized mols. with an accuracy of 0.3 kcal mol-1 for energies and 1 kcal mol-1 Å-1 for at. forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of mols., including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quant. mol. dynamics simulations for mols. at a fraction of cost of explicit AIMD calcns., thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.**4**Qu, C.; Yu, Q.; Bowman, J. M. Permutationally invariant potential energy surfaces.*Annu. Rev. Phys. Chem.*2018,*69*, 151– 175, DOI: 10.1146/annurev-physchem-050317-021139[Crossref], [PubMed], [CAS], Google Scholar4https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlWmsLo%253D&md5=684145e7db426713476bc1322ab96b64Permutationally Invariant Potential Energy SurfacesQu, Chen; Yu, Qi; Bowman, Joel M.Annual Review of Physical Chemistry (2018), 69 (), 151-175CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)A review. Over the past decade, about 50 potential energy surfaces (PESs) for polyatomics with 4-11 atoms and for clusters have been calcd. using the permutationally invariant polynomial method. This is a general, mainly linear least-squares method for precise math. fitting of tens of thousands of electronic energies for reactive and nonreactive systems. A brief tutorial of the methodol. is given, including several recent improvements. Recent applications to the formic acid dimer (the current record holder in size for a reactive system), the H2-H2O complex, and four protonated water clusters [H+(H2O)n=2,3,4,6] are given. The last application also illustrates extension to large clusters using the many-body representation.**5**Qu, C.; Bowman, J. M. An*ab initio*potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1–4-mode subspaces.*Phys. Chem. Chem. Phys.*2016,*18*, 24835– 24840, DOI: 10.1039/C6CP03073D[Crossref], [PubMed], [CAS], Google Scholar5https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xhtleit7bE&md5=c001c74dac883174800b374b90f2b06cAn ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1-4-mode subspacesQu, Chen; Bowman, Joel M.Physical Chemistry Chemical Physics (2016), 18 (36), 24835-24840CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The authors report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer. This PES is a least-squares fit to 13475 CCSD(T)-F12a/haTZ (VTZ for H and aVTZ for C and O) energies. The energy-weighted, root-mean-square fitting error is 11 cm-1 and the barrier for the double-proton transfer on the PES is 2848 cm-1, in good agreement with the directly-calcd. ab initio value of 2853 cm-1. The zero-point vibrational energy of 15,337 ± 7 cm-1 is obtained from diffusion Monte Carlo calcns. Energies of fundamentals of fifteen modes are calcd. using the vibrational SCF and virtual-state CI method. The ground-state tunneling splitting is computed using a reduced-dimensional Hamiltonian with relaxed potentials. The highest-level, four-mode coupled calcn. gives a tunneling splitting of 0.037 cm-1, which is roughly twice the exptl. value. The tunneling splittings of (DCOOH)2 and (DCOOD)2 from one to three mode calcns. are, as expected, smaller than that for (HCOOH)2 and consistent with expt.**6**Meyer, J.; Tajti, V.; Carrascosa, E.; Györi, T.; Stei, M.; Michaelsen, T.; Bastian, B.; Czakó, G.; Wester, R. Atomistic dynamics of elimination and nucleophilic substitution disentangled for the F^{–}+ CH_{3}CH_{2}Cl reaction.*Nat. Chem.*2021,*13*, 977– 981, DOI: 10.1038/s41557-021-00753-8[Crossref], [PubMed], [CAS], Google Scholar6https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhslKgu7zK&md5=cc796e0b2602550fc8ca9a87fb766082Atomistic dynamics of elimination and nucleophilic substitution disentangled for the F- + CH3CH2Cl reactionMeyer, Jennifer; Tajti, Viktor; Carrascosa, Eduardo; Gyori, Tibor; Stei, Martin; Michaelsen, Tim; Bastian, Bjoern; Czako, Gabor; Wester, RolandNature Chemistry (2021), 13 (10), 977-981CODEN: NCAHBB; ISSN:1755-4330. (Nature Portfolio)Chem. reaction dynamics are studied to monitor and understand the concerted motion of several atoms while they rearrange from reactants to products. When the no. of atoms involved increases, the no. of pathways, transition states and product channels also increases and rapidly presents a challenge to expt. and theory. Here we disentangle the dynamics of the competition between bimol. nucleophilic substitution (SN2) and base-induced elimination (E2) in the polyat. reaction F- + CH3CH2Cl. We find quant. agreement for the energy- and angle-differential reactive scattering cross-sections between ion-imaging expts. and quasi-classical trajectory simulations on a 21-dimensional potential energy hypersurface. The anti-E2 pathway is most important, but the SN2 pathway becomes more relevant as the collision energy is increased. In both cases the reaction is dominated by direct dynamics. Our study presents at.-level dynamics of a major benchmark reaction in phys. org. chem., thereby pushing the no. of atoms for detailed reaction dynamics studies to a size that allows applications in many areas of complex chem. networks and environments.**7**Tajti, V.; Czako, G. Vibrational mode-specific dynamics of the F + CH_{3}CH_{2}Cl multi-channel reaction.*Phys. Chem. Chem. Phys.*2022,*24*, 8166– 8181, DOI: 10.1039/D2CP00685E[Crossref], [PubMed], [CAS], Google Scholar7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XotV2jsbw%253D&md5=1771cdee870c90aa3bb4d5e7ca43fb3bVibrational mode-specific dynamics of the F- + CH3CH2Cl multi-channel reactionTajti, Viktor; Czako, GaborPhysical Chemistry Chemical Physics (2022), 24 (14), 8166-8181CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)We investigate the mode-specific dynamics of the ground-state, C-Cl stretching (v10), CH2 wagging (v7), sym-CH2 stretching (v1), and sym-CH3 stretching (v3) excited F- + CH3CH2Cl(vk = 0, 1) [k = 10, 7, 1, 3] → Cl- + CH3CH2F (SN2), HF + CH3CHCl-, FH···Cl- + C2H4, and Cl- + HF + C2H4 (E2) reactions using a full-dimensional high-level anal. global potential energy surface and the quasi-classical trajectory method. Excitation of the C-Cl stretching, CH2 stretching, and CH2/CH3 stretching modes enhances the SN2, proton abstraction, and FH···Cl- and E2 channels, resp. Anti-E2 dominates over syn-E2 (kinetic anti-E2 preference) and the thermodynamically-favored SN2 (wider reactive anti-E2 attack angle range). The direct (a) SN2, (b) proton abstraction, (c) FH···Cl- + C2H4, (d) syn-E2, and (e) anti-E2 channels proceed with (a) back-side/backward, (b) isotropic/forward, (c) side-on/forward, (d) front-side/forward, and (e) back-side/forward attack/scattering, resp. The HF products are vibrationally cold, esp. for proton abstraction, and their rotational excitation increases for proton abstraction, anti-E2, and syn-E2, in order. Product internal-energy and mode-specific vibrational distributions show that CH3CH2F is internally hot with significant C-F stretching and CH2 wagging excitations, whereas C2H4 is colder. One-dimensional Gaussian binning technique is proved to solve the normal mode anal. failure caused by Me internal rotation.**8**Yin, C.; Tajti, V.; Czakó, G. Full-dimensional potential energy surface development and dynamics for the HBr + C_{2}H_{5}→ Br(^{2}P_{3/2}) + C_{2}H_{6}reaction.*Phys. Chem. Chem. Phys.*2022,*24*, 24784– 24792, DOI: 10.1039/D2CP03580D[Crossref], [PubMed], [CAS], Google Scholar8https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XisFygu7jK&md5=486b837cb4d3deecce2b14d31cfb81f8Full-dimensional potential energy surface development and dynamics for hydrogen bromide + ethyl radical to bromine + ethane reactionYin, Cangtao; Tajti, Viktor; Czako, GaborPhysical Chemistry Chemical Physics (2022), 24 (40), 24784-24792CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)We report a full-dimensional spin-orbit-cor. anal. potential energy surface (PES) for the HBr + C2H5 → Br + C2H6 reaction and a quasi-classical dynamics study on the new PES. For the PES development, the ROBOSURFER program package is applied and the ManyHF-based UCCSD(T)-F12a/cc-pVDZ-F12(-PP) energy points are fitted using the permutationally-invariant monomial symmetrization approach. The spin-orbit coupling at the level of MRCI-F12+Q(5,3)/cc-pVDZ-F12(-PP) is taken into account, since it has a significant effect in the exit channel of this reaction. Our simulations show that in the 1-40 kcal mol-1 collision energy (Ecoll) range the b = 0 reaction probability increases first and then decreases with increasing Ecoll, reaching around 15% at the medium Ecoll. No significant Ecoll dependence is obsd. in the range of 5-20 kcal mol-1. The reaction probabilities decrease monotonically with increasing b and the max. b where reactivity vanishes is smaller and smaller as Ecoll increases. Unlike in the case of HBr + CH3, the integral cross-section decays sharply as Ecoll changes from 5 to 1 kcal mol-1. Scattering angle distributions usually show forward scattering preference, indicating the dominance of the direct stripping mechanism. The reaction clearly favors H-side attack over side-on HBr and the least-preferred Br-side approach, and favors side-on CH3CH2 attack over the CH2-side and the least-preferred CH3-side approach. The initial translational energy turns out to convert mostly into product recoil, whereas the reaction energy excites the C2H6 vibration. The vibrational and rotational distributions of the C2H6 product slightly blue-shift as Ecoll increases, and very few reactive trajectories violate zero-point energy.**9**Braams, B. J.; Bowman, J. M. Permutationally invariant potential energy surfaces in high dimensionality.*Int. Rev. Phys. Chem.*2009,*28*, 577– 606, DOI: 10.1080/01442350903234923[Crossref], [CAS], Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhsF2hu7bF&md5=50bbc9c85ace405edcb390865d98ccd2Permutationally invariant potential energy surfaces in high dimensionalityBraams, Bastiaan J.; Bowman, Joel M.International Reviews in Physical Chemistry (2009), 28 (4), 577-606CODEN: IRPCDL; ISSN:0144-235X. (Taylor & Francis Ltd.)We review recent progress in developing potential energy and dipole moment surfaces for polyat. systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of thousands of scattered ab initio energies using a special, compact fitting basis of permutationally invariant polynomials in Morse-type variables of all the internuclear distances. The computational mathematics underlying this approach is reviewed first, followed by a review of the practical approaches used to obtain the data for the fits. A straightforward symmetrization approach is also given, mainly for pedagogical purposes. The methods are illustrated for potential energy surfaces for CH+5, (H2O)2 and CH3CHO. The relationship of this approach to other approaches is also briefly reviewed.**10***MSA Software with Gradients*, 2019. https://github.com/szquchen/MSA-2.0 (accessed 2019-01-20).Google ScholarThere is no corresponding record for this reference.**11**Györi, T.; Czakó, G. Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program System.*J. Chem. Theory Comput.*2020,*16*, 51– 66, DOI: 10.1021/acs.jctc.9b01006[ACS Full Text ], [CAS], Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MbhsFCmtQ%253D%253D&md5=b7817b4b8f54e3372c069db735ca7a91Automating the Development of High-Dimensional Reactive Potential Energy Surfaces with the robosurfer Program SystemGyori Tibor; Czako GaborJournal of chemical theory and computation (2020), 16 (1), 51-66 ISSN:.The construction of high-dimensional global potential energy surfaces (PESs) from ab initio data has been a major challenge for decades. Advances in computer hardware, electronic structure theory, and PES fitting methods have greatly alleviated many challenges in PES construction, but building fitting sets has remained a bottleneck so far. We present the robosurfer program system that completely automates the generation of new geometries, performs ab initio computations, and iteratively improves the PES under development. Unlike previous efforts to automate PES development, robosurfer does not require any uncertainty estimate from the PES fitting method and thus it is compatible with the permutationally invariant polynomial (PIP) method. As a demonstration we have developed five related but different global reactive PIP PESs for the CH3Br + F(-) system and used them to perform quasiclassical trajectory (QCT) reaction dynamics simulations over a wide range of collision energies. The automatically developed PESs show good to excellent accuracy at known stationary points without any manual sampling, and QCT results indicate the lack of unphysical minima on the fitted surfaces. We also present evidence suggesting that the breakdown of single reference electronic structure theory may contribute significantly to the fitting errors of global reactive PESs.**12**Czakó, G.; Györi, T.; Papp, D.; Tajti, V.; Tasi, D. A. First-Principles reaction dynamics beyond six-atom systems.*J. Phys. Chem. A*2021,*125*, 2385– 2393, DOI: 10.1021/acs.jpca.0c11531[ACS Full Text ], [CAS], Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXkvFyisLc%253D&md5=08815ec095c5dc58b793084d6cd0e829First-Principles Reaction Dynamics beyond Six-Atom SystemsCzako, Gabor; Gyori, Tibor; Papp, Dora; Tajti, Viktor; Tasi, Domonkos A.Journal of Physical Chemistry A (2021), 125 (12), 2385-2393CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)A review. Moving beyond the six-at. benchmark systems, we discuss the new age and future of first-principles reaction dynamics which investigates complex, multichannel chem. reactions. We describe the methodol. starting from the benchmark ab initio characterization of the stationary points, followed by full-dimensional potential energy surface (PES) developments and reaction dynamics computations. We highlight our composite ab initio approach providing benchmark stationary-point properties with subchem. accuracy, the ROBOSURFRER program system enabling automatic PES development, and applications for the Cl + C2H6, F + C2H6, and OH- + CH3I reactions focusing on ab initio issues and their solns. as well as showing the excellent agreement between theory and expt.**13**Lambros, E.; Dasgupta, S.; Palos, E.; Swee, S.; Hu, J.; Paesani, F. General many-body framework for data-driven potentials with arbitrary quantum mechanical accuracy: water as a case study.*J. Chem. Theory Comput.*2021,*17*, 5635– 5650, DOI: 10.1021/acs.jctc.1c00541[ACS Full Text ], [CAS], Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhslahsLzO&md5=b06f7e098c2de001b980bc51c6a08a96General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case StudyLambros, Eleftherios; Dasgupta, Saswata; Palos, Etienne; Swee, Steven; Hu, Jie; Paesani, FrancescoJournal of Chemical Theory and Computation (2021), 17 (9), 5635-5650CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small mols. at an arbitrary quantum-mech. (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from d. functionals belonging to different rungs across Jacob's ladder of approxns. within d. functional theory (MB-DFT) and from Moller-Plesset perturbation theory (MB-MP2). Through a systematic anal. of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calcns., with the exception of those derived from d. functionals within the generalized gradient approxn. (GGA). The differences between the DFT and MB-DFT results are traced back to d.-driven errors that prevent GGA functionals from accurately representing the underlying mol. interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using d.-cor. functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.**14**Moberg, D. R.; Jasper, A. W. Permutationally invariant polynomial expansions with unrestricted complexity.*J. Chem. Theory Comput.*2021,*17*, 5440– 5455, DOI: 10.1021/acs.jctc.1c00352[ACS Full Text ], [CAS], Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvFWmsbzN&md5=d16d508a3685baa08aa5f706e846aac8Permutationally Invariant Polynomial Expansions with Unrestricted ComplexityMoberg, Daniel R.; Jasper, Ahren W.Journal of Chemical Theory and Computation (2021), 17 (9), 5440-5455CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chem. systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atm. chem., and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the no. of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphys. unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.**15**Moberg, D. R.; Jasper, A. W.; Davis, M. J. Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy Selection.*J. Phys. Chem. Lett.*2021,*12*, 9169– 9174, DOI: 10.1021/acs.jpclett.1c02721[ACS Full Text ], [CAS], Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitVaku77L&md5=a7948ec2233918e1617979880381ff63Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy SelectionMoberg, Daniel R.; Jasper, Ahren W.; Davis, Michael J.Journal of Physical Chemistry Letters (2021), 12 (37), 9169-9174CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Potential energy surfaces fit with basis set expansions have been shown to provide accurate representations of electronic energies and have enabled a variety of high-accuracy dynamics, kinetics, and spectroscopy applications. The no. of terms in these expansions scales poorly with system size, a drawback that challenges their use for systems with more than ~ 10 atoms. A soln. is presented here using dictionary learning. Subsets of the full set of conventional basis functions are optimized using a newly developed multipass greedy regression method inspired by forward and backward selection methods from the statistics, signal processing, and machine learning literatures. The optimized representations have accuracies comparable to the full set but are 1 or more orders of magnitude smaller, and notably, the no. of terms in the optimized multipass greedy expansions scales approx. linearly with the no. of atoms.**16**Qu, C.; Bowman, J. M. Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?.*Phys. Chem. Chem. Phys.*2019,*21*, 3397– 3413, DOI: 10.1039/C8CP04990D[Crossref], [PubMed], [CAS], Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitVWjurbL&md5=e5758610af64d91ef76cfa1cc9f465c7Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?Qu, Chen; Bowman, Joel M.Physical Chemistry Chemical Physics (2019), 21 (7), 3397-3413CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)A review. The subject of this Perspective is quantum approaches, beyond the harmonic approxn., to vibrational dynamics and IR spectroscopy. We begin with a pedagogical, unifying review of the most widely used quantum approaches. Some of the key details that lead to steep computational scaling of these approaches are reviewed, as well as some effective strategies to overcome or at least mitigate them. Considering in particular the application to IR spectroscopy, we stress the strength and weakness of each approach for spectral features that evolve from "simple" to "complex". We use the 10-atom formic acid dimer as an ideal example of this evolution. The IR spectrum of this dimer and two isotopologs has been obtained computationally using our software, MULTIMODE, and approaches to obtain accurate, ab initio, full-dimensional potential energy and dipole moment surfaces, also developed by our group. The IR spectra obtained with the widely used "ab initio mol. dynamics" approach are also presented and assessed. The extension of quantum approaches to mol. clusters and even condensed phase applications, where mol. dynamics approaches are typically used, is discussed mainly in the context of the local monomer model. This approach is illustrated for a methane clathrate hydrate, where vibrational energies of the sym. and asym. stretches of methane are given for a no. of water cages and compared to expt. The question about interpretation is also addressed throughout the Perspective.**17**Conte, R.; Qu, C.; Houston, P. L.; Bowman, J. M. Efficient generation of permutationally invariant potential energy surfaces for large molecules.*J. Chem. Theory Comput.*2020,*16*, 3264– 3272, DOI: 10.1021/acs.jctc.0c00001[ACS Full Text ], [CAS], Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXls12hu70%253D&md5=51e9d22fbd49e36d8fc216018c665340Efficient Generation of Permutationally Invariant Potential Energy Surfaces for Large MoleculesConte, Riccardo; Qu, Chen; Houston, Paul L.; Bowman, Joel M.Journal of Chemical Theory and Computation (2020), 16 (5), 3264-3272CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)An efficient method is described for generating a fragmented, permutationally invariant polynomial basis to fit electronic energies and, if available, gradients for large mols. The method presented rests on the fragmentation of a large mol. into any no. of fragments while maintaining the permutational invariance and uniqueness of the polynomials. The new approach improves on a previous one reported by Qu and Bowman by avoiding repetition of polynomials in the fitting basis set and speeding up gradient evaluations while keeping the accuracy of the PES. The method is demonstrated for CH3-NH-CO-CH3 (N-methylacetamide) and NH2-CH2-COOH (glycine).**18**Houston, P. L.; Conte, R.; Qu, C.; Bowman, J. M. Permutationally invariant polynomial potential energy surfaces for tropolone and H and D atom Tunneling Dynamics.*J. Chem. Phys.*2020,*153*, 024107, DOI: 10.1063/5.0011973[Crossref], [PubMed], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtlKqu7nP&md5=b1ae8cf76e76f44231a6524a74c22ffaPermutationally invariant polynomial potential energy surfaces for tropolone and H and D atom tunneling dynamicsHouston, Paul; Conte, Riccardo; Qu, Chen; Bowman, Joel M.Journal of Chemical Physics (2020), 153 (2), 024107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report permutationally invariant polynomial (PIP) fits to energies and gradients for 15-atom tropolone. These include std., augmented, and fragmented PIP bases. Approx., 6600 energies and their assocd. gradients are obtained from direct-dynamics calcns. using DFT/B3LYP/6-31+G(d) supplemented by grid calcns. spanning an energy range up to roughly 35 000 cm-1. Three fragmentation schemes are investigated with respect to efficiency and fit precision. In addn., several fits are done with reduced wt. for gradient data relative to energies. These do result in more precision for the H-transfer barrier height. The properties of the fits such as stationary points, harmonic frequencies, and the barrier to H-atom transfer are reported and compared to direct calcns. A previous 1D model is used to obtain the tunneling splitting for the ground vibrational state and qual. predictions for excited vibrational states. This model is applied to numerous fits with different barrier heights and then used to extrapolate the H and D atom tunneling splittings to values at the CCSD(T)-F12 barrier. The extrapolated values are 2.3 and 0.14 cm-1, resp. for H and D. These are about a factor of two larger than expt., but within the expected level of agreement with expt. for the 1D method used and the level of the electronic structure theory. (c) 2020 American Institute of Physics.**19**McCoy, A. B.; Braams, B. J.; Brown, A.; Huang, X.; Jin, Z.; Bowman, J. M.*Ab initio*diffusion monte carlo calculations of the quantum behavior of CH_{5}^{+}in full dimensionality.*J. Phys. Chem. A*2004,*108*, 4991– 4994, DOI: 10.1021/jp0487096[ACS Full Text ], [CAS], Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjvVCksbo%253D&md5=ca3ca54006f02e11af63f4042e5f3340Ab Initio Diffusion Monte Carlo Calculations of the Quantum Behavior of CH5+ in Full DimensionalityMcCoy, Anne B.; Braams, Bastiaan J.; Brown, Alex; Huang, Xinchuan; Jin, Zhong; Bowman, Joel M.Journal of Physical Chemistry A (2004), 108 (23), 4991-4994CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)We report an ab initio calcn. of the potential surface, quantum structures, and zero-point energies of CH5+ and CH2D3+ in full dimensionality. This potential energy surface is a very precise fit to 20 633 ab initio energies and an even larger data set of potential gradients, obtained at the MP2/cc-pVTZ level of theory/basis. The potential, which exactly obeys the permutational symmetry of the five hydrogen atoms, is used in diffusion Monte Carlo (DMC) calcns. of the fully anharmonic zero-point energies and ground-state wave functions of CH5+ and CH2D3+. Bond length distributions are obtained from the DMC ground state and are compared to those resulting from classical mol. dynamics simulations, which are performed at the quantum zero-point energy for roughly 300 ps.**20**McCoy, A. B.; Huang, X.; Carter, S.; Landeweer, M. Y.; Bowman, J. M. Full-dimensional vibrational calculations for H_{5}O_{2}^{+}using an*ab initio*potential energy surface.*J. Chem. Phys.*2005,*122*, 061101, DOI: 10.1063/1.1857472[Crossref], [PubMed], [CAS], Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtlWrtr0%253D&md5=654dcd1d4c39944a6f2d55037198f4bdFull-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surfaceMcCoy, Anne B.; Huang, Xinchuan; Carter, Stuart; Landeweer, Marc Y.; Bowman, Joel M.Journal of Chemical Physics (2005), 122 (6), 061101/1-061101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report quantum diffusion Monte Carlo (DMC) and variational calcns. in full dimensionality for selected vibrational states of H5O2+ using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calcns. OH-stretch fundamentals are also calcd. using "fixed-node" DMC calcns. and variationally using two versions of the code MULTIMODE. These results are compared with IR multiphoton dissocn. measurements of L. I. Yeh et al. (1989). Some preliminary results for the energies of several modes of the shared hydrogen are also reported.**21**McCoy, A. B. Diffusion monte carlo approaches for investigating the structure and vibrational spectra of fluxional systems.*Int. Rev. Phys. Chem.*2006,*25*, 77– 107, DOI: 10.1080/01442350600679347[Crossref], [CAS], Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmtV2mt70%253D&md5=4e17d880afb8e5c3b3ee09b1465463edDiffusion Monte Carlo approaches for investigating the structure and vibrational spectra of fluxional systemsMcCoy, Anne B.International Reviews in Physical Chemistry (2006), 25 (1-2), 77-107CODEN: IRPCDL; ISSN:0144-235X. (Taylor & Francis Ltd.)A review. Recent advances in diffusion Monte Carlo (DMC) are reviewed within the context of the vibrational motions of systems that undergo large amplitude motions. A review. Specifically, the authors describe the DMC approach for obtaining the ground state were function and zero-point energy (ZPE) of the system of interest, as well as extensions to the method for evaluating probability amplitudes, rotational consts., vibrationally excited states and methods for obtaining vibrational spectra. The discussion is framed in terms of the properties of several systems of current exptl. and theor. interest, specifically complexes of neon atoms with OH or SH, H3O-2, H5O+2, and CH+5. The results of the DMC simulations provide the information necessary to characterize the extent of delocalization of the probability amplitudes, even in the ground vibrational states. Methods for evaluating expectation values and vibrationally excited states are explored, and, when possible, the results are compared with those from other approaches. Finally, the methods for evaluating intensities are described and existing and future challenges for the approach are reviewed.**22**Wang, Y. M.; Babin, V.; Bowman, J. M.; Paesani, F. The water hexamer: cage, prism, or both. Full dimensional quantum simulations say both.*J. Am. Chem. Soc.*2012,*134*, 11116, DOI: 10.1021/ja304528m[ACS Full Text ], [CAS], Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XptF2gsL0%253D&md5=65e5ba6199bbd78f0ca7cb64f53ddd70The Water Hexamer: Cage, Prism, or Both. Full Dimensional Quantum Simulations Say BothWang, Yimin; Babin, Volodymyr; Bowman, Joel M.; Paesani, FrancescoJournal of the American Chemical Society (2012), 134 (27), 11116-11119CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)State-of-the-art quantum simulations on a full-dimensional ab initio potential energy surface are used to characterize the properties of the water hexamer. The relative populations of the different isomers are detd. over a wide range of temps. While the prism isomer is identified as the global min.-energy structure, the quantum simulations, which explicitly include zero-point energy and quantum thermal motion, predict that both the cage and prism isomers are present at low temp. down to almost 0 K. This is largely consistent with the available exptl. data and, in particular, with recent measurements of broadband rotational spectra of the water hexamer recorded in supersonic expansions.**23**Bowman, J. M.; Czakó, G.; Fu, B. High-dimensional ab initio potential energy surfaces for reaction dynamics calculations.*Phys. Chem. Chem. Phys.*2011,*13*, 8094– 8111, DOI: 10.1039/c0cp02722g[Crossref], [PubMed], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXkvFakurs%253D&md5=fd50abf6ba72080b0220aecc71574e87High-dimensional ab initio potential energy surfaces for reaction dynamics calculationsBowman, Joel M.; Czako, Gabor; Fu, BinaPhysical Chemistry Chemical Physics (2011), 13 (18), 8094-8111CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)A review. There has been great progress in the development of potential energy surfaces (PESs) for reaction dynamics that are fits to ab initio energies. The fitting techniques described here explicitly represent the invariance of the PES with respect to all permutations of like atoms. A review of a subset of dynamics calcns. using such PESs (currently 16 such PESs exist) is then given. Bimol. reactions of current interest to the community, namely, H + CH4 and F + CH4, are focused on. Unimol. reactions are then reviewed, with a focus on the photodissocn. dynamics of H2CO and CH3CHO, where so-called "roaming" pathways have been discovered. The challenges for electronically nonadiabatic reactions, and assocd. PESs, are presented with a focus on the OH* + H2 reaction. Finally, some thoughts on future directions and challenges are given.**24**Czakó, G.; Bowman, J. M. Reaction dynamics of methane with F, O, Cl, and Br on*ab initio*potential energy surfaces.*J. Phys. Chem. A*2014,*118*, 2839– 2864, DOI: 10.1021/jp500085h[ACS Full Text ], [CAS], Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXjsFOlu7w%253D&md5=ef3cf173be46dd476c74a025d372705aReaction Dynamics of Methane with F, O, Cl, and Br on ab Initio Potential Energy SurfacesCzako, Gabor; Bowman, Joel M.Journal of Physical Chemistry A (2014), 118 (16), 2839-2864CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)A review. The bimol. hydrogen abstraction reactions of methane with atoms have become benchmark systems to test and extend our knowledge of polyat. chem. reactivity. We review the state-of-the-art methodologies for reaction dynamics computations of X + methane [X = F, O(3P), Cl, Br] reactions, which consist of two key steps: (1) potential energy surface (PES) developments and (2) reaction dynamics computations on the PES using either classical or quantum methods. We briefly describe the permutationally invariant polynomial approach for step 1 and the quasiclassical trajectory method, focusing on the mode-specific polyat. product anal. and the Gaussian binning (1GB) techniques, and reduced-dimensional quantum models for step 2. High-quality full-dimensional ab initio PESs and dynamical studies of the X + CH4 and CHD3 reactions are reviewed. The computed integral cross-sections, angular, vibrational, and rotational product distributions are compared with available expts. Both exptl. and theor. findings shed light on the rules of mode-selective polyat. reactivity.**25**Bowman, J. M.; Qu, C.; Conte, R.; Nandi, A.; Houston, P. L.; Yu, Q. The MD17 datasets from the perspective of datasets for gas-phase “small” molecule potentials.*J. Chem. Phys.*2022,*156*, 240901, DOI: 10.1063/5.0089200[Crossref], [PubMed], [CAS], Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFOnurnJ&md5=6c228a4aec39325136eaf734f35a2e16The MD17 datasets from the perspective of datasets for gas-phase "small" molecule potentialsBowman, Joel M.; Qu, Chen; Conte, Riccardo; Nandi, Apurba; Houston, Paul L.; Yu, QiJournal of Chemical Physics (2022), 156 (24), 240901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each mol. in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three "small" mols., ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the potential energy surfaces (PESs) in mind: a rigorous calcn. of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde, and, in the case of glycine, a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-mol. but complex chem. reactions. Finally, we introduce a new database, "QM-22," which contains datasets of mols. ranging from 4 to 15 atoms that extend to high energies and a large span of configurations. (c) 2022 American Institute of Physics.**26**Nandi, A.; Qu, C.; Houston, P. L.; Conte, R.; Bowman, J. M. Δ-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theory.*J. Chem. Phys.*2021,*154*, 051102, DOI: 10.1063/5.0038301[Crossref], [PubMed], [CAS], Google Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXjsVGlsb8%253D&md5=bfe9137fc71598377f305232c3f58047Δ-machine learning for potential energy surfaces: A PIP approach to bring a DFT-based PES to CCSD(T) level of theoryNandi, Apurba; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Bowman, Joel M.Journal of Chemical Physics (2021), 154 (5), 051102CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)"Δ-Machine learning" refers to a machine learning approach to bring a property such as a potential energy surface (PES) based on low-level (LL) d. functional theory (DFT) energies and gradients close to a coupled cluster (CC) level of accuracy. Here, we present such an approach that uses the permutationally invariant polynomial (PIP) method to fit high-dimensional PESs. The approach is represented by a simple equation, in obvious notation VLL→CC = VLL + ΔVCC-LL, and demonstrated for CH4, H3O+, and trans and cis-N-Me acetamide (NMA), CH3CONHCH3. For these mols., the LL PES, VLL, is a PIP fit to DFT/B3LYP/6-31+G(d) energies and gradients and ΔVCC-LL is a precise PIP fit obtained using a low-order PIP basis set and based on a relatively small no. of CCSD(T) energies. For CH4, these are new calcns. adopting an aug-cc-pVDZ basis, for H3O+, previous CCSD(T)-F12/aug-cc-pVQZ energies are used, while for NMA, new CCSD(T)-F12/aug-cc-pVDZ calcns. are performed. With as few as 200 CCSD(T) energies, the new PESs are in excellent agreement with benchmark CCSD(T) results for the small mols., and for 12-atom NMA, training is done with 4696 CCSD(T) energies. (c) 2021 American Institute of Physics.**27**Ramakrishnan, R.; Dral, P. O.; Rupp, M.; von Lilienfeld, O. A. Big data meets quantum chemistry approximations: The Δ-machine learning approach.*J. Chem. Theory Comput.*2015,*11*, 2087– 2096, DOI: 10.1021/acs.jctc.5b00099[ACS Full Text ], [CAS], Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtlams7Y%253D&md5=a59b33f51a9dd6dbad95290f2642c306Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning ApproachRamakrishnan, Raghunathan; Dral, Pavlo O.; Rupp, Matthias; von Lilienfeld, O. AnatoleJournal of Chemical Theory and Computation (2015), 11 (5), 2087-2096CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Chem. accurate and comprehensive studies of the virtual space of all possible mols. are severely limited by the computational cost of quantum chem. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approx. legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger mol. sets than used for training. For thermochem. properties of up to 16k isomers of C7H10O2 we present numerical evidence that chem. accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qual. relationship between mol. entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chem. and machine learning models trained on 1 and 10% of 134k org. mols., to reproduce enthalpies of all remaining mols. at d. functional theory level of accuracy.**28**Dral, P. O.; Owens, A.; Dral, A.; Csányi, G. Hierarchical machine learning of potential energy surfaces.*J. Chem. Phys.*2020,*152*, 204110, DOI: 10.1063/5.0006498[Crossref], [PubMed], [CAS], Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVGgsrrE&md5=4b6eb648c3879342f52bc8c000ac94f6Hierarchical machine learning of potential energy surfacesDral, Pavlo O.; Owens, Alec; Dral, Alexey; Csanyi, GaborJournal of Chemical Physics (2020), 152 (20), 204110CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present hierarchical machine learning (hML) of highly accurate potential energy surfaces (PESs). Our scheme is based on adding predictions of multiple Δ-machine learning models trained on energies and energy corrections calcd. with a hierarchy of quantum chem. methods. Our (semi-)automatic procedure dets. the optimal training set size and compn. of each constituent machine learning model, simultaneously minimizing the computational effort necessary to achieve the required accuracy of the hML PES. Machine learning models are built using kernel ridge regression, and training points are selected with structure-based sampling. As an illustrative example, hML is applied to a high-level ab initio CH3Cl PES and is shown to significantly reduce the computational cost of generating the PES by a factor of 100 while retaining similar levels of accuracy (errors of ∼1 cm-1). (c) 2020 American Institute of Physics.**29**Nguyen, K. A.; Rossi, I.; Truhlar, D. G. A dual-level Shepard interpolation method for generating potential energy surfaces for dynamics calculations.*J. Chem. Phys.*1995,*103*, 5522– 5530, DOI: 10.1063/1.470536**30**Fu, B.; Xu, X.; Zhang, D. H. A hierarchical construction scheme for accurate potential energy surface generation: An application to the F + H_{2}reaction.*J. Chem. Phys.*2008,*129*, 011103, DOI: 10.1063/1.2955729[Crossref], [PubMed], [CAS], Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXosVyhtrg%253D&md5=5f12304ac43c1ededad519c07bbf3c99A hierarchical construction scheme for accurate potential energy surface generation: An application to the F+H2 reactionFu, Bina; Xu, Xin; Zhang, Dong H.Journal of Chemical Physics (2008), 129 (1), 011103/1-011103/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a hierarchical construction scheme for accurate ab initio potential energy surface generation. The scheme is based on the observation that when mol. configuration changes, the variation in the potential energy difference between different ab initio methods is much smaller than the variation for potential energy itself. This means that it is easier to numerically represent energy difference to achieve a desired accuracy. Because the computational cost for ab initio calcns. increases very rapidly with the accuracy, one can gain substantial saving in computational time by constructing a high accurate potential energy surface as a sum of a low accurate surface based on extensive ab initio data points and an energy difference surface for high and low accuracy ab initio methods based on much fewer data points. The new scheme was applied to construct an accurate ground potential energy surface for the FH2 system using the coupled-cluster method and a very large basis set. The constructed potential energy surface is found to be more accurate on describing the resonance states in the FH2 and FHD systems than the existing surfaces. (c) 2008 American Institute of Physics.**31**Yu, Q.; Bowman, J. M.*Ab initio*potential for H_{3}O^{+}→ H^{+}+ H_{2}O: A step to a many-body representation of the hydrated proton?.*J. Chem. Theory Comput.*2016,*12*, 5284– 5292, DOI: 10.1021/acs.jctc.6b00765[ACS Full Text ], [CAS], Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFOktrzP&md5=480982a0ce8c433d2c9ed48861c52ff2Ab Initio Potential for H3O+ → H+ + H2O: A Step to a Many-Body Representation of the Hydrated Proton?Yu, Qi; Bowman, Joel M.Journal of Chemical Theory and Computation (2016), 12 (11), 5284-5292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We report a new potential energy surface (PES) for hydronium that dissocs. to H+ + H2O. The PES is a permutationally invariant fit to a data set of nearly 100,000 electronic energies, of which most are CCSD(T)-F12/aug-cc-pVQZ, plus a small set of MRCI-aug-cc-pVTZ diabatic energies in the region where the CCSD(T) method fails. The long-range part of the PES is described accurately by a classical Coulomb interaction between the proton and H2O using partial charges obtained from an accurate, full-dimensional dipole moment surface. A switching function connects the fitted PES to this long-range interaction. The fidelity of this global PES is detd. by a combination of std. geometry and harmonic analyses at the min. and inversion saddle point. In addn., VSCF/VCI calcns. of the fundamentals and tunneling splittings are reported; all of these are within 3 cm-1 or less of exptl. values. A diffusion Monte Carlo calcn. is also reported for the zero-point state. The PES is used in a two-body representation of the interaction of the proton with two water mols., including a 2-body H2O-H2O interaction, and is shown to give a realistic description of the Zundel cation H5O2+. This demonstrates that the PES may be usable as a component in a many-body potential describing the hydrated proton, esp. for vibrational calcns. of protonated water clusters.**32**Cisneros, G. A.; Wikfeldt, K. T.; Ojamäe, L.; Lu, J.; Xu, Y.; Torabifard, H.; Bartók, A. P.; Csányi, G.; Molinero, V.; Paesani, F. Modeling molecular interactions in water: From pairwise to many-body potential energy functions.*Chem. Rev.*2016,*116*, 7501– 7528, DOI: 10.1021/acs.chemrev.5b00644[ACS Full Text ], [CAS], Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XnvFeqs7w%253D&md5=69e5c66d2b4a029a4ca90b940366194aModeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy FunctionsCisneros, Gerardo Andres; Wikfeldt, Kjartan Thor; Ojamae, Lars; Lu, Jibao; Xu, Yao; Torabifard, Hedieh; Bartok, Albert P.; Csanyi, Gabor; Molinero, Valeria; Paesani, FrancescoChemical Reviews (Washington, DC, United States) (2016), 116 (13), 7501-7528CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. Almost 50 years have passed from the first computer simulations of water, and a large no. of mol. models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of anal. potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approxns. and on their ability to accurately reproduce ref. data obtained from state-of-the-art electronic structure calcns. and exptl. measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a phys. correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.**33**Qu, C.; Yu, Q.; Conte, R.; Houston, P. L.; Nandi, A.; Bowman, J. M. A Δ-machine learning approach for force fields, illustrated by a CCSD(T) 4-body correction to the MB-pol water potential.*Digital Discovery*2022,*1*, 658– 664, DOI: 10.1039/D2DD00057A**34**Fanourgakis, G. S.; Xantheas, S. S. The flexible, polarizable, Thole-type interaction potential for water (TTM2-F) revisited.*J. Phys. Chem. A*2006,*110*, 4100– 4106, DOI: 10.1021/jp056477k[ACS Full Text ], [CAS], Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhvVKlsbs%253D&md5=d088b728272fae6e49733fc1f862a5efThe Flexible, Polarizable, Thole-Type Interaction Potential for Water (TTM2-F) RevisitedFanourgakis, George S.; Xantheas, Sotiris S.Journal of Physical Chemistry A (2006), 110 (11), 4100-4106CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)We present a revision of the flexible, polarizable, Thole-type interaction potential for water [J. Chem. Phys. 2002, 116, 5115], which allows for condensed-phase simulations. The revised version (TTM2.1-F) of the potential correctly describes the individual water mol. dipole moment and alleviates problems arising at short intermol. sepns. that can be sampled in the course of mol. dynamics and Monte Carlo simulations of condensed environments. Furthermore, its parallel implementation under periodic boundary conditions enables the efficient calcn. of the macroscopic structural and thermodn. properties of liq. water, as its performance scales superlinearly with up to a no. of 64 processors for a simulation box of 512 mols. We report the radial distribution functions, av. energy, internal geometry, and dipole moment in the liq. as well as the d., dielec. const., and self-diffusion coeff. at T = 300 K from (NVT) and (NPT) classical mol. dynamics simulations by using the revised version of the potential.**35**Qu, C.; Bowman, J. M. Communication: A fragmented, permutationally invariant polynomial approach for potential energy surfaces of large molecules: Application to*N*-methyl acetamide.*J. Chem. Phys.*2019,*150*, 141101, DOI: 10.1063/1.5092794[Crossref], [PubMed], [CAS], Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXmvFWgtrw%253D&md5=5beda36666eda7f3a1c0b94b46a48225A fragmented, permutationally invariant polynomial approach for potential energy surfaces of large molecules: Application to N-methyl acetamideQu, Chen; Bowman, Joel M.Journal of Chemical Physics (2019), 150 (14), 141101/1-141101/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We describe and apply a method to extend permutationally invariant polynomial (PIP) potential energy surface (PES) fitting to mols. with more than 10 atoms. The method creates a compact basis of PIPs as the union of PIPs obtained from fragments of the mol. An application is reported for trans-N-Me acetamide, where B3LYP/cc-pVDZ electronic energies and gradients are used to develop a full-dimensional potential for this prototype peptide mol. The performance of several fragmented bases is verified against a benchmark PES using all (66) Morse variables. The method appears feasible for much larger mols. (c) 2019 American Institute of Physics.**36**Nandi, A.; Qu, C.; Bowman, J. M. Full and fragmented permutationally invariant polynomial potential energy surfaces for*trans*and*cis N*-methyl Acetamide and isomerization saddle points.*J. Chem. Phys.*2019,*151*, 084306, DOI: 10.1063/1.5119348[Crossref], [PubMed], [CAS], Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhs12jtLjN&md5=ca33c1749defcb985c9a613ce9b1140aFull and fragmented permutationally invariant polynomial potential energy surfaces for trans and cis N-methyl acetamide and isomerization saddle pointsNandi, Apurba; Qu, Chen; Bowman, Joel M.Journal of Chemical Physics (2019), 151 (8), 084306/1-084306/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report full and fragmented potential energy surfaces (PESs) for N-Me acetamide that contain the cis and trans isomers and the saddle points sepg. them. The full PES uses Permutationally Invariant Polynomials (PIPs) in reduced symmetry which describe the three-fold symmetry of each Me rotor. A more efficient PES is an extension of the fragmented PIP approach we reported recently. In this approach, the set of Morse variables is partitioned and the fragmented PIP basis is the union of the PIP basis for each set of variables. This approach is general and can be used with neural network fits. The fits are done using roughly 250 000 electronic energies and gradients obtained from direct dynamics, using the B3LYP/cc-pVDZ level of theory. The full PIP basis in 66 Morse variables, with a max. polynomial order of 3, contains 8040 linear coeffs. The fragmented PIP basis, also with a max. polynomial order of 3, contains 6121 coeffs. The root-mean-square errors of both PESs are roughly 100 cm-1 for energies and 15 cm-1/bohr per atom for gradients, for energies up to roughly 45 000 cm-1, relative to the trans min. Energies and normal mode frequencies of the cis and trans isomers for the full and fragmented PESs agree well with direct calcns. The energies of the two saddle points sepg. these min. are precisely given by both PESs. Diffusion Monte Carlo calcns. of the zero-point energies of the two isomers are also reported. (c) 2019 American Institute of Physics.**37**Suenram, R.; Golubiatnikov, G.; Leonov, I.; Hougen, J.; Ortigoso, J.; Kleiner, I.; Fraser, G. Reinvestigation of the microwave spectrum of acetamide.*J. Mol. Spectrosc.*2001,*208*, 188– 193, DOI: 10.1006/jmsp.2001.8377[Crossref], [CAS], Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXmsF2mu7c%253D&md5=5d22c08e93ce8af1602bb4c8f4c416caReinvestigation of the Microwave Spectrum of AcetamideSuenram, R. D.; Golubiatnikov, G. Yu.; Leonov, I. I.; Hougen, J. T.; Ortigoso, J.; Kleiner, I.; Fraser, G. T.Journal of Molecular Spectroscopy (2001), 208 (2), 188-193CODEN: JMOSA3; ISSN:0022-2852. (Academic Press)About 50 jet-cooled Fourier transform lines for acetamide were recorded using a new version of spectrometer, which was upgraded with a heated nozzle and an expanded automatic scanning range. Nuclear quadrupole hyperfine structure arising from the N atom was removed theor. to yield hyperfine-free center frequencies. In addn., ∼30 mm measurements were carried out. When hyperfine structure was obsd. for these lines, it was also removed theor. A set of 115 A-species and E-species rotational transitions in the torsional ground state, obtained by combining new measurements with the literature data, were fit to a model involving 28 torsion, rotation, and torsion-rotation interaction parameters to near exptl. uncertainty (i.e., to a weighted unitless std. deviation of 1.5), significantly improving on previous fits. Various theor. problems assocd. with K labels for E-species levels in this very low barrier mol. are briefly discussed and used to justify a variant of the signed Ka labels frequently used for internal-rotor E states. (c) 2001 Academic Press.**38**Nandi, A.; Conte, R.; Qu, C.; Houston, P. L.; Yu, Q.; Bowman, J. M. Quantum calculations on a new CCSD(T) machine-learned potential energy surface reveal the leaky nature of gas-phase*trans*and*gauche*ethanol conformers.*J. Chem. Theory Comput.*2022,*18*, 5527– 5538, DOI: 10.1021/acs.jctc.2c00760[ACS Full Text ], [CAS], Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitV2jtL3N&md5=4eb3d99f030720b57d1d9eb69e22fb4eQuantum Calculations on a New CCSD(T) Machine-Learned Potential Energy Surface Reveal the Leaky Nature of Gas-Phase Trans and Gauche Ethanol ConformersNandi, Apurba; Conte, Riccardo; Qu, Chen; Houston, Paul L.; Yu, Qi; Bowman, Joel M.Journal of Chemical Theory and Computation (2022), 18 (9), 5527-5538CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Ethanol is a mol. of fundamental interest in combustion, astrochem., and condensed phase as a solvent. It is characterized by two Me rotors and trans (anti) and gauche conformers, which are known to be very close in energy. Here we show that based on rigorous quantum calcns. of the vibrational zero-point state, using a new ab initio potential energy surface (PES), the ground state resembles the trans conformer, but substantial delocalization to the gauche conformer is present. This explains exptl. issues about identification and isolation of the two conformers. This "leak" effect is partially quenched when deuterating the OH group, which further demonstrates the need for a quantum mech. approach. Diffusion Monte Carlo and full-dimensional semiclassical dynamics calcns. are employed. The new PES is obtained by means of a Δ-machine learning approach starting from a pre-existing low level d. functional theory surface. This surface is brought to the CCSD(T) level of theory using a relatively small no. of ab initio CCSD(T) energies. Agreement between the cor. PES and direct ab initio results for std. tests is excellent. One- and two-dimensional discrete variable representation calcns. focusing on the trans-gauche torsional motion are also reported, in reasonable agreement with expt.**39**Durig, J.; Larsen, R. Torsional vibrations and barriers to internal rotation for ethanol and 2,2,2-trifluoroethanol.*J. Mol. Struct.*1990,*238*, 195– 222, DOI: 10.1016/0022-2860(90)85015-B[Crossref], [CAS], Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXhtVSqtrw%253D&md5=169af24806d8b4da302d68bcff4861b1Torsional vibrations and barriers to internal rotation for ethanol and 2,2,2-trifluoroethanolDurig, J. R.; Larsen, R. A.Journal of Molecular Structure (1990), 238 (), 195-222CODEN: JMOSB4; ISSN:0022-2860.The far-IR (370-50 cm-1) spectra of gaseous ethanol, EtOH, and the O-d compd. were recorded at a resoln. of 0.10 cm-1. Similar far-IR spectra were collected for 2,2,2-trifluoroethanol, CF3CH2OH, and the O-d, C-d2 and -d3 isotopic species. In addn., the Raman (4000-50 cm-1) and the mid-IR (5000-400 cm-1) spectra were collected for CF3CH2OH and the isotopic compds. in the vapor phase. A detailed examn. of the torsional modes was carried out and potential functions for the hindered internal rotation of the O-H and O-D groups and the CH3 and CF3 rotors were calcd. For ethanol, the fundamental O-H torsion for the trans conformer is obsd. at 202.6 cm-1 whereas for the gauche conformation, the 1-←0+ transition is found at 243.1 cm-1 and the 1+←0- transition is 195.8 cm-1. An asym. potential function utilizing these transitions gives values of 403 cm-1 (1.15 kcal mol-1) for the trans/gauche barrier and 399 cm-1 (1.14 kcal mol-1) for the gauche/gauche barrier with the trans conformer more stable by 42 cm-1 (120 cal mol-1) than the gauche conformer. Potential functions for the hydroxy torsions are also calcd. for the ethanol-O-d compd. and the four 2,2,2-trifluoroethanol isotopic mols. The CH3 torsional transitions of trans ethanol give a V3 barrier of 1185 ± 16 cm-1 (3.39 ± 0.05 kcal mol-1) and the corresponding barrier for the gauche conformer is 1251 ± 2 cm-1 (3.58 ± 0.01 kcal mol-1). Similarly, a series of CF3 torsional transitions was obsd. for the trans and gauche conformations of the CF3CH2OH mol. as well as for some of the isotopic species. In addn. to the examn. of the far-IR spectra, a series of sum and difference bands assocd. with the O-H and O-D stretching fundamentals is found in the mid-IR spectra for the 2,2,2-trifluoroethanol compds. and a possible explanation for these modes is given.**40**Wang, Y.; Braams, B. J.; Bowman, J. M.; Carter, S.; Tew, D. P. Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface.*J. Chem. Phys.*2008,*128*, 224314, DOI: 10.1063/1.2937732[Crossref], [PubMed], [CAS], Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXntFyns7c%253D&md5=bb210d3fb84a1cb7f545f6c16c72247eFull-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surfaceWang, Yimin; Braams, Bastiaan J.; Bowman, Joel M.; Carter, Stuart; Tew, David P.Journal of Chemical Physics (2008), 128 (22), 224314/1-224314/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Quantum calcns. of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcal/mol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calcns. of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calcd. using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm-1 in Cartesian coordinates and 22.6 cm-1 in normal coordinates, with an uncertainty of 2-3 cm-1. This splitting is also calcd. based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calcn. gives a tunneling splitting of 21-22 cm-1. The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm-1. These calcd. tunneling splittings agree with each other to within less than the std. uncertainties obtained with the DMC method used, which are between 2 and 3 cm-1, and agree well with the exptl. values of 21.6 and 2.9 cm-1 for the H and D transfer, resp. (c) 2008 American Institute of Physics.**41**Qu, C.; Conte, R.; Houston, P. L.; Bowman, J. M. Full-dimensional potential energy surface for acetylacetone and tunneling splittings.*Phys. Chem. Chem. Phys.*2021,*23*, 7758– 7767, DOI: 10.1039/D0CP04221H[Crossref], [PubMed], [CAS], Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvVGgs7rK&md5=fde99d4eba58249eba57685bef99d1a4Full-dimensional potential energy surface for acetylacetone and tunneling splittingsQu, Chen; Conte, Riccardo; Houston, Paul L.; Bowman, Joel M.Physical Chemistry Chemical Physics (2021), 23 (13), 7758-7767CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)We present a full-dimensional potential energy surface for acetylacetone (AcAc) using full and fragmented permutationally invariant polynomial approaches. Previously reported MP2/aVTZ energies and gradients are augmented by addnl. calcns. at this level of theory for the fits. Numerous stationary points are reported as are the usual metrics to assess the precision of the fit. The electronic barrier height for the H-atom transfer is roughly 2.2 kcal mol-1. Diffusion Monte Carlo (DMC) calcns. are used to calc. the ground state wavefunction and zero-point energy of acetylacetone. These together with fixed-node DMC calcns. for the first excited-state provide the predicted tunneling splitting due to the barrier to H-transfer sepg. two equiv. wells. Simpler 1d calcns. of this splitting are also reported for varying barrier heights including the CCSD(T) barrier height of 3.2 kcal mol-1. Based on those results the DMC splitting of 160 cm-1 with a statistical uncertainty of roughly 21 cm-1, calcd. using the MP2-based PES, is estd. to decrease to 100 cm-1 for a barrier of 3.2 kcal mol-1. The fragmented surface is shown to be fast to evaluate.**42**Meuwly, M. Atomistic simulations for reactions and vibrational spectroscopy in the era of machine learning─*quo vadis?*.*J. Phys. Chem. B*2022,*126*, 2155– 2167, DOI: 10.1021/acs.jpcb.2c00212[ACS Full Text ], [CAS], Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XmvV2hsr8%253D&md5=1adeb410ff1794f8fe5abaec37066868Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning-Quo Vadis?Meuwly, MarkusJournal of Physical Chemistry B (2022), 126 (11), 2155-2167CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)A review. Atomistic simulations using accurate energy functions can provide mol.-level insight into functional motions of mols. in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the IR spectroscopy of mols. in soln. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose mol. simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.**43**Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.*MOLPRO, a package of ab initio programs*, ver. 2015.1, 2015; http://www.molpro.net.Google ScholarThere is no corresponding record for this reference.**44**Qu, C.; Houston, P. L.; Conte, R.; Nandi, A.; Bowman, J. M. Breaking the coupled cluster barrier for machine-learned potentials of large molecules: The case of 15-Atom acetylacetone.*J. Phys. Chem. Lett.*2021,*12*, 4902– 4909, DOI: 10.1021/acs.jpclett.1c01142[ACS Full Text ], [CAS], Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhtFSitb%252FL&md5=cf8ef9d6a8f3da518260f003408922bcBreaking the Coupled Cluster Barrier for Machine-Learned Potentials of Large Molecules: The Case of 15-Atom AcetylacetoneQu, Chen; Houston, Paul L.; Conte, Riccardo; Nandi, Apurba; Bowman, Joel M.Journal of Physical Chemistry Letters (2021), 12 (20), 4902-4909CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Machine-learned potential energy surfaces (PESs) for mols. with more than 10 atoms are typically forced to use lower-level electronic structure methods such as d. functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2). While these are efficient and realistic, they fall short of the accuracy of the "gold std." coupled-cluster method, esp. with respect to reaction and isomerization barriers. We report a major step forward in applying a Δ-machine learning method to the challenging case of acetylacetone, whose MP2 barrier height for H-atom transfer is low by roughly 1.1 kcal/mol relative to the benchmark CCSD(T) barrier of 3.2 kcal/mol. From a database of 2151 local CCSD(T) energies and training with as few as 430 energies, we obtain a new PES with a barrier of 3.5 kcal/mol in agreement with the LCCSD(T) barrier of 3.5 kcal/mol and close to the benchmark value. Tunneling splittings due to H-atom transfer are calcd. using this new PES, providing improved ests. over previous ones obtained using an MP2-based PES.**45**Redington, R. L. H atom and heavy atom tunneling process in tropolone.*J. Chem. Phys.*2000,*113*, 2319– 2335, DOI: 10.1063/1.482046[Crossref], [CAS], Google Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXltFygt74%253D&md5=bbb86ee39b2783206169d815a3e26e8cH atom and heavy atom tunneling processes in tropoloneRedington, Richard L.Journal of Chemical Physics (2000), 113 (6), 2319-2335CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The min. energy pathway leading between the tautomers of tropolone was calcd. using MO methods. This, with various 1D and 2D cuts of the potential energy surface (PES) topog., reveals the {tunneling skeleton}/{tunneling H atom} mechanism for tautomerization. In the zero-point states the H atom is localized to one of the O atoms until the tropolone skeleton becomes sufficiently vibrationally displaced towards C2v configurations that near-equal double-min. potential energy functions (PEFs) arise for the H atom vibration. The resulting delocalization of the H atom between the two O atom sites allows the skeletal displacement to proceed through the barrier and the tautomerization process to be completed. The v1 (OH stretching) energies in quantum states N1 are strongly dependent on the skeletal geometry and, adiabatically sepd. from the slow v22 vibration, they contribute to markedly different 1D effective potential energy functions V22eff[N1] for v22. V22eff[N1=0] is a normal equal double min. PEF while V22eff[N1≠0] have more complex shapes. Expressed as a function of the v22 skeletal displacement ΔS, the v1 states show a nonadiabatic curve crossing E1(1) E1(2) contributing to the V22eff[N1=1 2] effective PEF for v22 vibration in the lowest excited OH stretching state. This function, rather than V22eff[N1=1], is strongly supported by the IR observations on v1. The computed effective energy barriers on the "model" tunneling path for the zero point states are 4.97 kcal/mol for the skeletal motion, and 3.22 kcal/mol for the H atom vibration at C2v skeletal geometry. Overall, the independent computational model predicts the major spectroscopic features obsd. for S0 tropolone(OH) and tropolone(OD): (a) similar IR tunneling doublets with ∼10 cm-1 splittings for the v22 skeletal vibration; (b) weak v1 IR absorbance with 20 and 5 cm-1 tunneling doublet sepns. for the isotopomers; (c) small tunneling splittings of the zero point states; and (d) unresolved vibrational state-specific IR tunneling doublets for all other fundamentals.**46**Redington, R. L.; Redington, T. E.; Montgomery, J. M. IR spectra of tropolone(OH) and tropolone(OD).*J. Chem. Phys.*2000,*113*, 2304– 2318, DOI: 10.1063/1.482045[Crossref], [CAS], Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXltFygtrc%253D&md5=1428f2b1fb3055eeef608283373e4340IR spectra of tropolone(OH) and tropolone(OD)Redington, Richard L.; Redington, Theresa E.; Montgomery, Jason M.Journal of Chemical Physics (2000), 113 (6), 2304-2318CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)IR spectra of tropolone(OH) and tropolone(OD) obtained from vapor phase, solvated, and rare gas matrix-isolated samples, and from fluorescence dip IR spectroscopy expts. by Frost et al. on jet-cooled samples, are analyzed with the guidance of high level ab initio MO computations. The anharmonicity of the double min. global potential energy surface of S0 tropolone is manifested by multistate local resonance networks coupling fundamental vibrations to nearby overtone and combination states. These resonance networks pervade the IR spectrum of tropolone >500 cm-1, and the absorbances are much more strongly perturbed from harmonic level predictions than the frequencies. Some of the IR absorbances are also sensitive to intermol. interactions. At max. spectral resolns. reaching ∼0.2 cm-1 only the v1 and v22 (OH stretching and nascent skeletal tunneling) vibrations show resolved vibrational state-specific tunneling doublets. The tunneling behavior of tropolone is analyzed in the accompanying article.**47**Redington, R. L.; Sams, R. L. N_{2}pressure broadened Q branch spikes and vibration–contortion–rotation effects in the high resolution FTIR spectrum of tropolone.*Chem. Phys.*2002,*283*, 135– 151, DOI: 10.1016/S0301-0104(02)00614-6[Crossref], [CAS], Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XntVWksLw%253D&md5=539d3e1fc2d22037d5e683953ec53043N2 pressure broadened Q branch spikes and vibration-contortion-rotation effects in the high resolution FTIR spectrum of tropoloneRedington, Richard L.; Sams, Robert L.Chemical Physics (2002), 283 (1-2), 135-151CODEN: CMPHC2; ISSN:0301-0104. (Elsevier Science B.V.)N pressure broadening effects are obsd. on the high resoln. (0.0025 cm-1) FTIR spectrum of gaseous tropolone at 298 K and 32 m of path length. Broadening observations on narrow absorption spikes contribute to understanding of the spectroscopy and dynamics of tropolone in several ways. First, they help to establish a remarkable progression of sharp peaks near 752 cm-1 as a part of the Q branch of the anharmonic ν22 (COH torsion) fundamental. The subband spacings of ∼0.005-0.010 cm-1 are too large to be detd. by harmonic vibrational differences in the rotational consts. alone and are attributed to vibration-contortion-rotation perturbations of the upper state (ν22) energy levels of this anharmonic and relatively large amplitude vibration. Second, the isolated and sharp Q branch spikes near 915 cm-1 allow 1st ests. to be made for effective composite pressure broadening coeffs. of tropolone-N2 collisions. The coeffs. for transitions within the Ncon=0 and Ncon=1 contortion states differ from each other. They are relatively small due to the preponderance of high rotational states in their compn. Third, N2 broadening effects on substructure in the Q branch doublet near 754 cm-1 help support the assignment of this doublet to tunneling structure of the ν37 fundamental (contortion or incipient skeletal tunneling). The obsd. doublet components appear as perturbatively IR enhanced 3 and 5 peak fragments of weak longer progressions. The parallel spectroscopic behaviors of the perturbed anharmonic ν22 and ν37 vibrations differ markedly from behavior obsd. for the quasiharmonic vibrations.**48**Redington, R. L.; Sams, R. L. State-specific spectral doublets in the FTIR spectrum of gaseous tropolone.*J. Phys. Chem. A*2002,*106*, 7494– 7511, DOI: 10.1021/jp0122631[ACS Full Text ], [CAS], Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXosFahu7c%253D&md5=06b6d6ba5edfc9e28001449114483accState-Specific Spectral Doublets in the FTIR Spectrum of Gaseous TropoloneRedington, Richard L.; Sams, Robert L.Journal of Physical Chemistry A (2002), 106 (33), 7494-7511CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The IR absorption spectrum of tropolone vapor at 25 °C, ∼0.01 Torr, and 32 m path length has been recorded from 960 to about 700 cm-1 at a resoln. of 0.0025 cm-1. Twenty-nine cold band and hot band spectral tunneling doublets marked by sharp type A or type C Q branch apexes protruding from the congested vibration-contortion-rotation absorption profiles are assigned. Twenty-six vibration-contortion state-specific splittings are estd. for tropolone in its ground electronic state. This no. is currently unprecedented in the literature for any sizable mol. About half of these quasiharmonic vibrational states show an appreciable quenching of tunneling due to increased effective barriers and/or path lengths and, in the case of the nominal COH torsion, the tunneling is reduced to 0.07 of the zero-point (ZP) value of 0.974 cm-1. The anal. is guided by predictions of the independent {tunneling skeleton}{tunneling H atom} tautomerization model that was previously applied to the vibrational spectrum and tautomerization mechanism of tropolone. The increase of effective tunneling path length by a few percent over the ZP path length is attributed to dynamical complexity arising from an atom-to-atom exchange of unequal vibrational displacements as a part of the tautomerization process. This aspect of tunneling quenching behavior can arise for quasiharmonic vibrations lacking direct contact to the OH···O group. For the case of tropolone, the tautomerization model advocates heavy atom tunneling as equal in importance to H atom tunneling. Heavy atom tunneling is supported by the observation of a (perturbed) spectral tunneling doublet at 754 cm-1 with the sepn. 0.80 cm-1. This doubling of the high frequency component of the previously obsd. 11 cm-1 doublet obsd. using Ne matrix-isolation sampling provides evidence for the "doublet of doublet" quartet structure predicted for the ν37 nascent skeletal tunneling (contortion) vibration. The compilation of numerous vibrational state-specific tunneling doublings for a 15-atom nonrigid mol. invites further exptl. and theor. research aimed at advancing the understanding of multidimensional intramol. tunneling dynamics, vibrational energy redistribution, and unimol. reaction kinetics. Several strong parallels are seen between the vibrational interactions arising in our studies of the tautomerization of tropolone and those appearing in recent articles discussing possible behaviors in the active sites of enzymic H transfer reactions.**49**Redington, R. L.; Redington, T. E.; Blake, T. A.; Sams, R. L.; Johnson, T. J. O18 Effects on the infrared spectrum and skeletal tunneling of tropolone.*J. Chem. Phys.*2005,*122*, 224311, DOI: 10.1063/1.1897367[Crossref], [PubMed], [CAS], Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXlsFGlsbk%253D&md5=c8442542c7d6a616260726eddcea4b3e18O effects on the infrared spectrum and skeletal tunneling of tropoloneRedington, Richard L.; Redington, Theresa E.; Blake, Thomas A.; Sams, Robert L.; Johnson, Timothy J.Journal of Chemical Physics (2005), 122 (22), 224311/1-224311/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)IR-absorption profiles obsd. for vibrational transitions of gaseous tropolone often show sharp Q branch peaks, some of them ultranarrow spikes, indicative of the band origins for vibrational state-specific spectral tunneling doublets. O isotope effects for 2 CH wagging fundamentals, the COH torsion fundamental, and the skeletal contortion fundamental are reported. They allow considerations to be given: (1) O isotope effects on the vibrational frequencies and state-specific tunneling splittings; (2) the asymmetry offset of the potential-energy min. for 16O and 18O tropolone; and (3) addnl. details concerning previously proposed high J rotation-contortion resonances in the contortional fundamental. The new results help to characterize the skeletal contortion fundamental and support the joint participation of skeletal tunneling with H tunneling in the vibrational state-specific tautomerization processes of tropolone in its ground electronic state.**50**Redington, R. L.; Redington, T. E.; Sams, R. L. Quantum tunneling in the midrange vibrational fundamentals of tropolone.*J. Phys. Chem. A*2006,*110*, 9633– 9641, DOI: 10.1021/jp062068s[ACS Full Text ], [CAS], Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmvFWhsbw%253D&md5=2cbdaf0496264daa12c7be6a49d013c1Quantum Tunneling in the Midrange Vibrational Fundamentals of TropoloneRedington, Richard L.; Redington, Theresa E.; Sams, Robert L.Journal of Physical Chemistry A (2006), 110 (31), 9633-9642CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The Fourier transform IR spectrum of tropolone(OH) vapor in the 1175-1700 cm-1 region is reported at 0.0025 and 0.10 cm-1 spectral resolns. The 12 vibrational fundamentals in this region of rapidly rising vibrational state d. are dominated by mixts. of the CC, CO, CCH, and COH internal coordinates. Ests. based on the measurement of sharp Q branch peaks are reported for 11 of the spectral doublet component sepns. DSν = |Δν ± Δ0|. Δ0 = 0.974 Cm-1 is the known zero-point splitting, and three a1 modes show tunneling splittings Δν ≈ Δ0, four b2 modes show splittings Δν ≈ 0.90Δ0, and the remaining four modes show splittings Δνv falling 5-14% from Δ0. Significantly, the splitting for the nominal COH bending mode ν8 (a1) is small, i.e., 10% from Δ0. Many of the vibrational excited states demonstrate strong anharmonic behavior, but there are only mild perturbations on the tautomerization mechanism driving Δ0. The data suggest, esp. for the higher frequency a1 fundamentals, the onset of selective intramol. vibrational energy redistribution processes that are fast on the time scale of the tautomerization process. These appear to delocalize and smooth out the topog. modifications of the zero-point potential energy surface that are anticipated to follow absorption of the νν photon. Further, the spectra show the propensity for the Δν splittings of b2 and other complex vibrations to be damped relative to Δ0.**51**Redington, R. L.; Redington, T. E.; Sams, R. L. Infrared absorption spectra in the hydroxyl stretching regions of gaseous tropolone OHO Isotopomers.*Z. Phys. Chem.*2008,*222*, 1197– 1211, DOI: 10.1524/zpch.2008.5383[Crossref], [CAS], Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhsV2js7jN&md5=69470b2468135b4a3a0feba0c8723d69Infrared absorption spectra in the hydroxyl stretching regions of gaseous tropolone OHO isotopomersRedington, Richard L.; Redington, Theresa E.; Sams, Robert L.Zeitschrift fuer Physikalische Chemie (Muenchen, Germany) (2008), 222 (8-9), 1197-1211CODEN: ZPCFAX; ISSN:0942-9352. (Oldenbourg Wissenschaftsverlag GmbH)Fourier transform IR (FTIR) absorption spectra in the 2000 to 3500 cm-1 range are reported for the gaseous 16O, 16O-, and 18O, 18O-isotopomers of tropolone[OH(OD)] at 25°. The spectral doublet component sepns. are near 20 and 19 cm-1 for 16O, 16O-, and 18O, 18O-Tp(OH), resp., and near 7 and 6.5 cm-1 for 16O, 16O-, and 18O, 18O-Tp(OD). The spectra suggest the tautomerization tunneling mechanisms in these states are complex multidimensional processes including the participation of IVR. In general, the OHO isotope effects demonstrate a mixing of O atom displacement coordinates into the intramol. dynamics for most of the vibrational states obsd. in the fundamental CH/OH(OD) stretching regions.**52**Redington, R. L.; Redington, T. E.; Sams, R. L. Tunneling splittings for “O···O stretching” and other vibrations of tropolone isotopomers observed in the infrared spectrum below 800 cm^{–1}.*J. Phys. Chem. A*2008,*112*, 1480– 1492, DOI: 10.1021/jp0757255[ACS Full Text ], [CAS], Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXps1Kjsg%253D%253D&md5=5998090839f0024081ba1a2028089b78Tunneling Splittings for "O···O Stretching" and Other Vibrations of Tropolone Isotopomers Observed in the Infrared Spectrum Below 800 cm-1Redington, Richard L.; Redington, Theresa E.; Sams, Robert L.Journal of Physical Chemistry A (2008), 112 (7), 1480-1492CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)Fourier transform IR absorption spectra contg. evidence for about two dozen spectral tunneling doublets are reported for gaseous tropolone(OH), tropolone (OD), and 18O,18O-tropolone(OH) in the 800 to 300 cm-1 spectral range. No FTIR absorption was detected in the 300-150 cm-1 range. The known zero-point (ZP) tunneling splitting values Δ0 = 0.974 cm-1 for tropolone(OH) (Tanaka et al.) and 0.051 cm-1 for tropolone(OD) (Keske et al.) allow vibrational state-specific tunneling splittings Δv to be estd. for fundamentals including three with strong O···O stretching displacements [cf. for tropolone(OH) ν13(a1) = 435.22 cm-1 with HΔ13 = 1.71 cm-1 = 1.76 HΔ0, and for tropolone(OD) ν13(a1) = 429.65 cm-1 with DΔ13 = 0.32 cm-1 = 6.27 DΔ0]. The majority of Δv splittings in the sub-800 cm-1 range are dilated relative to the isotopomer Δ0 values. The FTIR spectra demonstrate the presence of dynamic couplings and potential function anharmonicity in addn. to revealing Δv splittings and many OH/D and 18O/16O isotope effects. Approx. values are obtained for the ZP splittings 88Δ0 and 86Δ0 of the doubly and singly 18O-labeled isotopomers of tropolone(OH). The diverse values of the obsd. Δv/Δ0 splitting ratios underscore the inherent multidimensionality and corner-cutting activities entering the state-specific tunneling processes of the tropolone tautomerization reaction.**53**Frost, R. K.; Hagemeister, F. C.; Arrington, C. A.; Zwier, T. S.; Jordan, K. D. Fluorescence-dip infrared spectroscopy of tropolone and tropolone-OD.*J. Chem. Phys.*1996,*105*, 2595– 1604, DOI: 10.1063/1.472119[Crossref], [CAS], Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XltVGjtLs%253D&md5=7ea43463fa5db131e9db28f82746f114Fluorescence-dip infrared spectroscopy of tropolone and tropolone-ODFrost, Rex K.; Hagemeister, C.; Arrington, Caleb A.; Zwier, Timothy S.; Jordan, Kenneth D.Journal of Chemical Physics (1996), 105 (7), 2595-2604CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Fluorescence-dip IR spectroscopy (FDIRS) is employed to record the IR spectra of the isolated, jet-cooled tropolone mol. (TrOH) and its singly deuterated isotopomer TrOD in the O-H and C-H stretch regions. The ability of the method to monitor a single ground-state level enables the acquisition of spectra out of the lower and upper levels of the zero-point tunneling doublet free from interference from one another. The high power of the optical parametric oscillator used for IR generation produces FDIR spectra with good signal-to-noise despite the weak intensity of the C-H and O-H stretch transitions in tropolone. The expectation that both spectra will exhibit two OH stretch transitions sepd. by OH(ν = 1) tunneling splitting is only partially verified in the present study. The spectra of TrOH are compared with those form deuterated tropolone (TrOD) to assign transitions due to C-H and O-H, which are in close proximity in TrOH. The appearance of the spectra out of lower (a1 symmetry) and upper (b2 symmetry) tunneling levels are surprisingly similar. Two sharp transitions at 3134.9 cm-1 (out of the a1 tunneling level) and 3133.9 cm-1 (out of the b2 tunneling level) are sepd. by the ground-state tunneling splitting (0.99 cm-1), and thereby terminate in the same upper state tunneling level. Their similar intensities relative to the C-H stretch transitions indicate that the y- and z-polarized transitions are of comparable intensity, as predicted by ab initio calcns. The corresponding transitions to the other member of the upper state tunneling doublet are not assigned by the present study, but the broad absorptions centered about 12 cm-1 below the assigned transitions are suggested as the most likely possibility for the missing transitions.**54**Murdock, D.; Burns, L. A.; Vaccaro, P. H. Vibrational specificity of proton-transfer dynamics in ground-state tropolone.*Phys. Chem. Chem. Phys.*2010,*12*, 8285– 8299, DOI: 10.1039/c003140b[Crossref], [PubMed], [CAS], Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXoslyqu7o%253D&md5=7621de33cb289884583cb1b246bba896Vibrational specificity of proton-transfer dynamics in ground-state tropoloneMurdock, Daniel; Burns, Lori A.; Vaccaro, Patrick H.Physical Chemistry Chemical Physics (2010), 12 (29), 8285-8299CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The vibrational dependence of large-amplitude proton transfer taking place in the ground electronic state (X~1A1) of tropolone has been explored by implementing a coherent variant of the stimulated emission pumping (SEP) technique within the framework of two-color resonant four-wave mixing (TC-RFWM) spectroscopy. The lowest 1700 cm-1 portion of this potential surface has been interrogated under ambient bulk-gas conditions, enabling rotationless term energies (Tv+) and tunneling-induced bifurcations to be extd. for 43 assigned vibrational features of a1 and b2 symmetry. The resulting values of reflect the state-specificity long attributed to the hydron-migration pathways of tropolone and range in magnitude from 0.0 cm-1 to 17.8 cm-1, where the former implies essentially complete quenching of unimol. dynamics while the latter represents nearly a twenty-fold increase in reaction rate over that of the zero-point level. This vibrational mediation of tunneling behavior is discussed in terms of attendant at. displacements and permutation-inversion symmetries, with choreographed motion of the five-member reaction site () found to exert the most significant influence on the efficacy of proton transfer.**55**Vener, M. V.; Scheiner, S.; Sokolov, N. D. Theoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropolone.*J. Chem. Phys.*1994,*101*, 9755– 9765, DOI: 10.1063/1.467941[Crossref], [CAS], Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXisFChu7o%253D&md5=27a24e6b7629d64c40180f87740dc3fbTheoretical study of hydrogen bonding and proton transfer in the ground and lowest excited singlet states of tropoloneVener, M. V.; Scheiner, Steve; Sokolov, N. D.Journal of Chemical Physics (1994), 101 (11), 9755-65CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Theor. models of hydrogen bonding and proton transfer in the ground (S0) and lowest excited ππ* singlet (S1) states of tropolone are developed in terms of the localized OH···O fragment model and ab initio three-dimensional potential energy surfaces (PESs). The PESs for proton transfer in the S0 and S1 states are calcd. using ab initio SCF and CIS methods, resp., with a 6031G basis set which includes polarization functions on the atoms involved in the internal H bond. The Schroedinger equation for nuclear vibrations is solved numerically using adiabatic sepn. of the variables. The calcd. values for the S0 state (geometry, relaxed barrier height, vibrational frequencies, tunnel splittings and H/D isotope effects) agree fairly well with available exptl. And theor. data. The calcd. data for the S1 state reproduce the principal exptl. trends, established for S1 ← S0 excitation in tropolone, but are less successful with other features of the dynamics of the excited state, e.g., the comparatively large value of vibrationless level tunnel splitting and its irregular increase with O···O excitation in S1. In order to overcome these discrepancies, a model 2-D PES is constructed by fitting an anal. approxn. of the CIS tropolone-OH. It is found that the specifics of the proton transfer in the S1 state are detd. by a relatively low barrier (only one doublet of the OH stretch lies under the barrier peak). Bending vibrations play a minor role in modulation of the proton transfer barrier, so correct description of tunnel splitting of the proton stretch levels in both electronic states can be obtained in terms of the two-dimensional stretching model, which includes O···O and O-H stretching vibration coordinates only.**56**Guo, Y.; Sewell, T. D.; Thompson, D. L. Semiclassical calculations of tunneling splitting in tropolone.*J. Phys. Chem. A*1998,*102*, 5040– 5048, DOI: 10.1021/jp980445y[ACS Full Text ], [CAS], Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXjs1Srs7w%253D&md5=7aa2a2e08d2c6ab12eb1e1ac079f36afSemiclassical calculations of tunneling splitting in tropoloneGuo, Yin; Sewell, Thomas D.; Thompson, Donald L.Journal of Physical Chemistry A (1998), 102 (26), 5040-5048CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)Energy-level splittings in tropolone are calcd. by using a semiclassical approach for tunneling in multidimensional systems. A potential-energy surface that includes all 39 vibrational degrees of freedom was constructed for the ground electronic state on the basis of ab initio MP2 results. Since the method incorporates tunneling within std. trajectory simulations, the full-dimensional dynamics were explicitly treated to provide a clear picture of the dynamical behavior of the system and its effect on tunneling. Level splittings for the ground states of the normal and deuterated species were calcd. The sensitivity of the splittings to the choice of tunneling path were also studied. Mode-selective excitations were used to study the effect of vibrational excitation on the tunneling. Some modes promote tunneling, some suppress it, and some do not affect it. This shows the multidimensional nature of the tunneling process and the importance of properly treating heavy-atom motions.**57**Giese, K.; Kühn, O. The all-cartesian reaction plane hamiltonian: Formulation and application to the H-atom Transfer in tropolone.*J. Chem. Phys.*2005,*123*, 054315, DOI: 10.1063/1.1978869[Crossref], [PubMed], [CAS], Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXos1egsrk%253D&md5=ee3e5631bdd34a2afd45e1c6e395ea3aThe all-Cartesian reaction plane Hamiltonian: Formulation and application to the H-atom transfer in tropoloneGiese, Kai; Kuhn, OliverJournal of Chemical Physics (2005), 123 (5), 054315/1-054315/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, i.e., the unique plane defined by the two min. and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approxn. which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calcns. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramol. O···H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm-1 for the normal and deuterated species, resp. We calcd. IR-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm-1 upon excitation.**58**Giese, K.; Petkovic, M.; Naundorf, H.; Kühn, O. Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bonds.*Phys. Rep.*2006,*430*, 211– 276, DOI: 10.1016/j.physrep.2006.04.005[Crossref], [CAS], Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmsVGiu78%253D&md5=5879c72836446ce346c8fc7b9803bd38Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bondsGiese, K.; Petkovic, M.; Naundorf, H.; Kuehn, O.Physics Reports (2006), 430 (4), 211-276CODEN: PRPLCM; ISSN:0370-1573. (Elsevier B.V.)A review. Hydrogen bonds are of outstanding importance for many processes in Chem., Biol., and Physics. From the theor. perspective the small mass of the proton in a hydrogen bond makes it the primary quantum nucleus and the phenomena one expects to surface in a particular clear way are, for instance, zero-point energy effects, quantum tunneling, or coherent wave packet dynamics. While this is well established in the limit of one-dimensional motion, the details of the multidimensional aspects of the dynamics of hydrogen bonds are just becoming accessible to expts. and numerical simulations. In this review we discuss the theor. treatment of multidimensional quantum dynamics of hydrogen-bonded systems in the context of IR spectroscopy. Here, the multidimensionality is reflected in the complex shape of linear IR absorption spectra which is related to combination transitions and resonances, but also to mode-selective tunneling splittings. The dynamics underlying these spectra can be unravelled by means of time-resolved nonlinear IR spectroscopy. As a fundamental theor. ingredient we outline the generation of potential energy surfaces for gas and condensed phase nonreactive and reactive systems. For nonreactive anharmonic vibrational dynamics in the vicinity of a min. geometry, expansions in terms of normal mode coordinates often provide a reasonable description. For reactive dynamics one can resort to reaction surface ideas, i.e., a combination of large amplitude motion of the reactive coordinates and orthogonal harmonic motion of the remaining coordinates. For isolated systems, dynamics and spectroscopy follow from the time-dependent Schroedinger equation. Here, the multiconfiguration time-dependent Hartree method is shown to allow for describing the correlated dynamics of many degrees of freedom. Classical trajectory based methods are also discussed as an alternative to quantum dynamics. Their merits and shortcomings are scrutinized in the context of incorporating tunneling effects in the calcn. of spectra. For the condensed phase, reduced d. operator based approaches such as the quantum master equation are introduced to properly account for the energy and phase relaxation processes due to the interaction of the hydrogen bond with its surroundings.**59**Wang, Y.; Bowman, J. M. One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal mode.*J. Chem. Phys.*2008,*129*, 121103, DOI: 10.1063/1.2978230[Crossref], [PubMed], [CAS], Google Scholar59https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXht1WnsLzF&md5=ce945fff02748db28261a2360be2e932One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal modeWang, Yimin; Bowman, Joel M.Journal of Chemical Physics (2008), 129 (12), 121103/1-121103/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors present tunneling calcns. using the reaction path Hamiltonian in the zero-curvature approxn. and a 1-dimensional Hamiltonian in the imaginary-frequency, rectilinear normal mode of a saddle point, neglecting the vibrational angular momentum terms. This latter Hamiltonian was recently introduced and applied to the tunneling splitting in full-dimensional malonaldehyde. The results using the latter method are much more accurate than those using the former one for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H2 reaction in three dimensions for zero total angular momentum. (c) 2008 American Institute of Physics.**60**Wang, Y.; Bowman, J. M. Mode-specific tunneling using the*Q*_{im}path: Theory and an application to full-dimensional malonaldehyde.*J. Chem. Phys.*2013,*139*, 154303, DOI: 10.1063/1.4824713[Crossref], [PubMed], [CAS], Google Scholar60https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1Wit73P&md5=07e482216ece63c4981fe93e78fb87d7Mode-specific tunneling using the Qim path: Theory and an application to full-dimensional malonaldehydeWang, Yimin; Bowman, Joel M.Journal of Chemical Physics (2013), 139 (15), 154303/1-154303/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a theory of mode-specific tunneling that makes use of the general tunneling path along the imaginary-frequency normal mode of the saddle point, Qim, and the assocd. relaxed potential, V(Qim). The novel aspect of the theory is the projection of the normal modes of a min. onto the Qim path and the detn. of turning points on V(Qim). From that projection, the change in tunneling upon mode excitation can be calcd. If the projection is zero, no enhancement of tunneling is predicted. In that case vibrationally adiabatic (VA) theory could apply. However, if the projection is large then VA theory is not applicable. The approach is applied to mode-specific tunneling in full-dimensional malonaldehyde, using an accurate full-dimensional potential energy surface. Results are in semi-quant. agreement with expt. for modes that show large enhancement of the tunneling, relative to the ground state tunneling splitting. For the six out-of-plane modes, which have zero projection on the planar Qim path, VA theory does apply, and results from that theory agree qual. and even semi-quant. with expt. We also verify the failure of simple VA theory for modes that show large enhancement of tunneling. (c) 2013 American Institute of Physics.**61**Collins, M. A.; Bettens, R. P. A. Energy-based molecular fragmentation methods.*Chem. Rev.*2015,*115*, 5607– 5642, DOI: 10.1021/cr500455b[ACS Full Text ], [CAS], Google Scholar61https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtVajsbY%253D&md5=a83ac50604af530b6d89c94f1a6b6df6Energy-Based Molecular Fragmentation MethodsCollins, Michael A.; Bettens, Ryan P. A.Chemical Reviews (Washington, DC, United States) (2015), 115 (12), 5607-5642CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review including the following topics: methods and principles, applications and examples, and speculations and future developments etc.**62**Gadre, S. R.; Shirsat, R. N.; Limaye, A. C. Molecular tailoring approach for simulation of electrostatic properties.*J. Phys. Chem.*1994,*98*, 9165– 9169, DOI: 10.1021/j100088a013[ACS Full Text ], [CAS], Google Scholar62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXls1Cgtb0%253D&md5=8cc186eed0f00621147f1aea9732fa87Molecular Tailoring Approach for Simulation of Electrostatic PropertiesGadre, Shridhar R.; Shirsat, Rajendra N.; Limaye, Ajay C.Journal of Physical Chemistry (1994), 98 (37), 9165-9CODEN: JPCHAX; ISSN:0022-3654.A method for synthesizing ab initio mol. electrostatic potential (MESP) and field (MEF) by "stitching" together suitably tailored smaller fragments is presented. The procedure is assessed for its ability to mimic the ab initio MESP and its topog. for the model cases of zeolite silicon pentamer (Si5O16H12) and decamer (Si10O10H20) and has been found fairly reliable. A further application to di- and tripeptides is shown to simulate well the ab initio MESP and MEF with the resp. MESP min. reproduced to within 1% or less. This reliability, coupled with bypassing of the SCF computation of the tailored mol., makes the approach an attractive one for exploring one-electron properties of large mol. systems.**63**Ganesh, V.; Dongare, R. K.; Balanarayan, P.; Gadre, S. R. Molecular tailoring approach for geometry optimization of large molecules: Energy evaluation and parallelization strategies.*J. Chem. Phys.*2006,*125*, 104109, DOI: 10.1063/1.2339019[Crossref], [PubMed], [CAS], Google Scholar63https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XpvV2hsrw%253D&md5=1b61a9df6829c4d08d3426c4efc921d4Molecular tailoring approach for geometry optimization of large molecules: Energy evaluation and parallelization strategiesGanesh, V.; Dongare, Rameshwar K.; Balanarayan, P.; Gadre, Shridhar R.Journal of Chemical Physics (2006), 125 (10), 104109/1-104109/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A linear-scaling scheme for estg. the electronic energy, gradients, and Hessian of a large mol. at ab initio level of theory based on fragment set cardinality is presented. With this proposition, a general, cardinality-guided mol. tailoring approach (CG-MTA) for ab initio geometry optimization of large mols. is implemented. The method employs energy gradients extd. from fragment wave functions, enabling computations otherwise impractical on PC hardware. Further, the method is readily amenable to large scale coarse-grain parallelization with minimal communication among nodes, resulting in a near-linear speedup. CG-MTA is applied for d.-functional-theory-based geometry optimization of a variety of mols. including α-tocopherol, taxol, γ-cyclodextrin, and two conformations of polyglycine. In the tests performed, energy and gradient ests. obtained from CG-MTA during optimization runs show an excellent agreement with those obtained from actual computation. Accuracy of the Hessian obtained employing CG-MTA provides good hope for the application of Hessian-based geometry optimization to large mols.**64**Rahalkar, A. P.; Katouda, M.; Gadre, S. R.; Nagase, S. Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: A comparison with fragment molecular orbital method.*J. Comput. Chem.*2010,*31*, 2405– 2418, DOI: 10.1002/jcc.21533[Crossref], [PubMed], [CAS], Google Scholar64https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXptFOltbs%253D&md5=1a08953eeb1b2cf2f6266c8b65d50b44Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: a comparison with fragment molecular orbital methodRahalkar, Anuja P.; Katouda, Michio; Gadre, Shridhar R.; Nagase, ShigeruJournal of Computational Chemistry (2010), 31 (13), 2405-2418CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)Many Divide-and-Conquer based approaches are being developed to overcome the high scaling problem of the ab initio methods. In this work, one such method, Mol. Tailoring Approach (MTA) has been interfaced with recently developed efficient Moller-Plesset second order perturbation theory (MP2) codes viz. IMS-MP2 and RI-MP2 to reap the advantage of both. An external driver script is developed for implementing MTA at the front-end and the MP2 codes at the back-end. The present version of the driver script is written only for a single point energy evaluation of a mol. system at a fixed geometry. The performance of these newly developed MTA-IMS-MP2 and MTA-RI-MP2 codes is extensively benchmarked for a variety of mol. systems vis-a-vis the corresponding actual runs. In addn. to this, the performance of these programs is also critically compared with Fragment MO (FMO), another popular fragment-based method. It is obsd. that FMO2/2 is superior to FMO3/2 and MTA with respect to time advantage; however, the errors of FMO2 are much beyond chem. accuracy. However, FMO3/2 is a highly accurate method for biol. systems but is unsuccessful in case of water clusters. MTA produces ests. with errors within 1 kcal/mol uniformly for all systems with reasonable time advantage. Anal. carried out employing various basis sets shows that FMO gives its optimum performance only for basis sets, which does not include diffuse functions. On the contrary, MTA performance is found to be similar for any basis set used. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010.**65**Furtado, J. P.; Rahalkar, A. P.; Shanker, S.; Bandyopadhyay, P.; Gadre, S. R. Facilitating minima search for large water clusters at the MP2 level via molecular tailoring.*J. Phys. Chem. Lett.*2012,*3*, 2253– 2258, DOI: 10.1021/jz300663u[ACS Full Text ], [CAS], Google Scholar65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFWhsrrE&md5=a4f5783ee90ea5e32d262a4127f31875Facilitating Minima Search for Large Water Clusters at the MP2 Level via Molecular TailoringFurtado, Jonathan P.; Rahalkar, Anuja P.; Shanker, Sudhanshu; Bandyopadhyay, Pradipta; Gadre, Shridhar R.Journal of Physical Chemistry Letters (2012), 3 (16), 2253-2258CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Water clusters (H2O)20 and (H2O)25 are explored at the Moller-Plesset second-order perturbation (MP2) level of theory. Geometry optimization is carried out on favorable structures, initially generated by the temp. basin paving (TBP) method, utilizing the fragment-based mol. tailoring approach (MTA). MTA-based stabilization energies at the complete basis set limit are accurately estd. by grafting the energy correction using a smaller basis set. For prototypical cases, the min. are established via MTA-based vibrational frequency calcns. at the MP2/aug-cc-pVDZ level. The potential of MTA in tackling large clusters is further demonstrated by performing geometry optimization at MP2/aug-cc-pVDZ starting with the global min. of (H2O)30 reported by Monte Carlo (MC) and mol. dynamics (MD) investigations. The present study brings out the efficacy of MTA in performing computationally expensive ab initio calcns. with minimal off-the-shelf hardware without significant loss of accuracy.**66**Sahu, N.; Gadre, S. R. Molecular tailoring approach: A route for*ab initio*rreatment of large clusters.*Acc. Chem. Res.*2014,*47*, 2739– 2747, DOI: 10.1021/ar500079b[ACS Full Text ], [CAS], Google Scholar66https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXnsVehsbo%253D&md5=f8e37a08a65e23f60ec8f0350c1411f4Molecular Tailoring Approach: A Route for ab Initio Treatment of Large ClustersSahu, Nityananda; Gadre, Shridhar R.Accounts of Chemical Research (2014), 47 (9), 2739-2747CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)A review. Chem. on the scale of mol. clusters may be dramatically different from that in the macroscopic bulk. Greater understanding of chem. in this size regime could greatly influence fields such as materials science and atm. and environmental chem. Recent advances in exptl. techniques and computational resources have led to accurate investigations of the energies and spectral properties of weakly bonded mol. clusters. These have enabled researchers to learn how the physicochem. properties evolve from individual mols. to bulk materials and to understand the growth patterns of clusters. Exptl. techniques such as IR, microwave, and photoelectron spectroscopy are the most popular and powerful tools for probing mol. clusters. In general, these exptl. techniques do not directly reveal the atomistic details of the clusters but provide data from which the structural details need to be unearthed. Furthermore, the resoln. of the spectral properties of energetically close cluster conformers can be prohibitively difficult. Thus, these investigations of mol. aggregates require a combination of expts. and theory. On the theor. front, researchers have been actively engaged in quantum chem. ab initio calcns. as well as simulation-based studies for the last few decades. To obtain reliable results, there is a need to use correlated methods such as Moller-Plesset second order method, coupled cluster theory, or dispersion cor. d. functional theory. However, due to nonlinear scaling of these methods, optimizing the geometry of large clusters still remains a formidable quantum chem. challenge. Fragment-based methods, such as divide-and-conquer, mol. tailoring approach (MTA), fragment MOs, and generalized energy-based fragmentation approach, provide alternatives for overcoming the scaling problem for spatially extended mol. systems. Within MTA, a large system is broken down into two or more subsystems that can be readily treated computationally. Finally, the properties of the large system are obtained by patching the corresponding properties of all the subsystems. Due to these approxns., the resulting MTA-based energies carry some error in comparison with calcns. based on the full system. An approach for correcting these errors has been attempted by grafting the error at a lower basis set onto a higher basis set. Furthermore, investigating the growth patterns and nucleation processes in clusters is necessary for understanding the structural transitions and the phenomena of magic nos. in cluster chem. Therefore, systematic building-up or the introduction of stochastics for generating mol. assemblies is the most crucial step for studying large clusters. In this Account, we discuss the working principle of MTA for probing mol. clusters at ab initio level followed by a brief summary of an automated and electrostatics-guided algorithm for building mol. assemblies. The mol. aggregates presented here as test cases are generated based on either an electrostatic criterion or the basin hopping method. At MP2 level computation, the errors in MTA-based grafted energies are typically reduced to a submillihartree level, reflecting the potential of finding accurate energies of mol. clusters much more quickly. In summary, MTA provides a platform for effectively studying large mol. clusters at ab initio level of theory using minimal computer hardware.**67**Khire, S. S.; Gurav, N. D.; Nandi, A.; Gadre, S. R. Enabling rapid and accurate construction of CCSD(T)-level potential energy surface of large molecules using molecular tailoring approach.*J. Phys. Chem. A*2022,*126*, 1458– 1464, DOI: 10.1021/acs.jpca.2c00025[ACS Full Text ], [CAS], Google Scholar67https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjslWgt7k%253D&md5=3ad6d07296b3f36833c7d283a97b3fd2Enabling Rapid and Accurate Construction of CCSD(T)-Level Potential Energy Surface of Large Molecules Using Molecular Tailoring ApproachKhire, Subodh S.; Gurav, Nalini D.; Nandi, Apurba; Gadre, Shridhar R.Journal of Physical Chemistry A (2022), 126 (8), 1458-1464CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)The construction of a potential energy surface (PES) of even a medium-sized mol. employing correlated theory, such as CCSD(T), is arduous due to the high computational cost involved. The present study reports the possibility of efficiently constructing such a PES of mols. contg. up to 15 atoms and 550 basis functions by employing the fragment-based mol. tailoring approach (MTA) on off-the-shelf hardware. The MTA energies at the CCSD(T)/aug-cc-pVTZ level for several geometries of three test mols., viz., acetylacetone, N-methylacetamide, and tropolone, are reported. These energies are in excellent agreement with their full calcn. counterparts with a time advantage factor of 3-5. The energy barrier from the ground to transition state is also accurately captured. Further, we demonstrate the accuracy and efficiency of MTA for estg. the energy gradients at the CCSD(T) level. As a further application of our MTA methodol., the energies of acetylacetone at ∼ 430 geometries are computed at the CCSD(T)/aug-cc-pVTZ level and used for generating a Δ-machine learning (Δ-ML) PES. This leads to the H-transfer barrier of 3.02 kcal/mol, well in agreement with the benchmarked barrier of 3.19 kcal/mol. The fidelity of this Δ-ML PES is examd. by geometry optimization and normal mode frequency calcns. of global min. and saddle point geometries. We trust that the present work is a major development for the rapid and accurate construction of PES at the CCSD(T) level for mols. contg. up to 20 atoms and 600 basis functions using off-the-shelf hardware.**68**McDaniel, J. G.; Schmidt, J. Next-generation force fields from symmetry-adapted perturbation theory.*Annu. Rev. Phys. Chem.*2016,*67*, 467– 488, DOI: 10.1146/annurev-physchem-040215-112047[Crossref], [PubMed], [CAS], Google Scholar68https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmtVamtrg%253D&md5=9a252853aac46abd18c82fb5db9e00e6Next-Generation Force Fields from Symmetry-Adapted Perturbation TheoryMcDaniel, Jesse G.; Schmidt, J. R.Annual Review of Physical Chemistry (2016), 67 (), 467-488CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)Symmetry-adapted perturbation theory (SAPT) provides a unique set of advantages for parameterizing next-generation force fields from first principles. SAPT provides a direct, basis-set superposition error free est. of mol. interaction energies, a phys. intuitive energy decompn., and a seamless transition to an asymptotic picture of intermol. interactions. These properties have been exploited throughout the literature to develop next-generation force fields for a variety of applications, including classical mol. dynamics simulations, crystal structure prediction, and quantum dynamics/spectroscopy. This review provides a brief overview of the formalism and theory of SAPT, along with a practical discussion of the various methodologies utilized to parameterize force fields from SAPT calcns. It also highlights a no. of applications of SAPT-based force fields for chem. systems of particular interest. Finally, the review ends with a brief outlook on the future opportunities and challenges that remain for next-generation force fields based on SAPT.**69**Jing, Z.; Liu, C.; Cheng, S. Y.; Qi, R.; Walker, B. D.; Piquemal, J.-P.; Ren, P. Polarizable force fields for biomolecular simulations: Recent advances and applications.*Annu. Rev. Biophys.*2019,*48*, 371– 394, DOI: 10.1146/annurev-biophys-070317-033349[Crossref], [PubMed], [CAS], Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXmtVGnu7s%253D&md5=87b2bbf40c3e1977cd0e55e90b314d45Polarizable Force Fields for Biomolecular Simulations: Recent Advances and ApplicationsJing, Zhifeng; Liu, Chengwen; Cheng, Sara Y.; Qi, Rui; Walker, Brandon D.; Piquemal, Jean-Philip; Ren, PengyuAnnual Review of Biophysics (2019), 48 (), 371-394CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)A review. Realistic modeling of biomol. systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in phys. models, simulation algorithms, and computing hardware, biomol. simulations with advanced force fields at biol. relevant timescales are becoming increasingly promising. These advancements have not only led to new biophys. insights but also afforded opportunities to advance our understanding of fundamental intermol. forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomol. simulations.**70**Inakollu, V. S.; Geerke, D. P.; Rowley, C. N.; Yu, H. Polarisable force fields: what do they add in biomolecular simulations?.*Curr. Opin. Struct. Biol.*2020,*61*, 182– 190, DOI: 10.1016/j.sbi.2019.12.012[Crossref], [PubMed], [CAS], Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitFehurc%253D&md5=505957eb301190f636028eec3fdddb04Polarisable force fields: what do they add in biomolecular simulationsInakollu, V. S. Sandeep; Geerke, Daan P.; Rowley, Christopher N.; Yu, HaiboCurrent Opinion in Structural Biology (2020), 61 (), 182-190CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)A review. The quality of biomol. simulations critically depends on the accuracy of the force field used to calc. the potential energy of the mol. configurations. Currently, most simulations employ non-polarisable force fields, which describe electrostatic interactions as the sum of Coulombic interactions between fixed at. charges. Polarisation of these charge distributions is incorporated only in a mean-field manner. In the past decade, extensive efforts have been devoted to developing simple, efficient, and yet generally applicable polarisable force fields for biomol. simulations. In this review, we summarise the latest developments in accounting for key biomol. interactions with polarisable force fields and applications to address challenging biol. questions. In the end, we provide an outlook for future development in polarisable force fields.**71**Partridge, H.; Schwenke, D. W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio Calculations and Experimental Data.*J. Chem. Phys.*1997,*106*, 4618, DOI: 10.1063/1.473987[Crossref], [CAS], Google Scholar71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXhvVyiuro%253D&md5=b5dd1c238894f2288fd0b70942bd7865The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental dataPartridge, Harry; Schwenke, David W.Journal of Chemical Physics (1997), 106 (11), 4618-4639CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We report on the detn. of a high quality ab initio potential energy surface (PES) and dipole moment function for water. This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J ≤ 5 for H216O. The changes in the PES are small, nonetheless including an est. of core (oxygen 1s) electron correlation greatly improves the agreement with the expt. Using this adjusted PES, we can match 30 092 of the 30 117 transitions in the HITRAN 96 data base for H216O with theor. lines. The 10, 25, 50, 75, and 90 percentiles of the difference between the calcd. and tabulated line positions are -0.11, -0.04, -0.01, 0.02, and 0.07 cm-1. Nonadiabatic effects are not explicitly included. About 3% of the tabulated line positions appear to be incorrect. Similar agreement using this adjusted PES is obtained for the 17O and 18O isotopes. For HD16O, the agreement is not as good, with a root-mean-square error of 0.25 cm-1 for lines with J ≤ 5. This error is reduced to 0.02 cm-1 by including a small asym. correction to the PES, which is parameterized by simultaneously fitting to HD16O and D216O data. Scaling this correction by mass factors yields good results for T2O and HTO. The intensities summed over vibrational bands are usually in good agreement between the calcns. and the tabulated results, but individual line strengths can differ greatly. A high-temp. list consisting of 307 721 352 lines is generated for H216O using our PES and dipole moment function.**72**Yu, Q.; Qu, C.; Houston, P. L.; Conte, R.; Nandi, A.; Bowman, J. M. q-AQUA: A many-body CCSD(T) water potential, including 4-body interactions, demonstrates the quantum nature of water from clusters to the liquid phase.*J. Phys. Chem. Lett.*2022,*13*, 5068– 5074, DOI: 10.1021/acs.jpclett.2c00966[ACS Full Text ], [CAS], Google Scholar72https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsVWmu7jO&md5=0454787c7c4d803194b5ad2b36f1de03q-AQUA: A Many-Body CCSD(T) Water Potential, Including Four-Body Interactions, Demonstrates the Quantum Nature of Water from Clusters to the Liquid PhaseYu, Qi; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Nandi, Apurba; Bowman, Joel M.Journal of Physical Chemistry Letters (2022), 13 (22), 5068-5074CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)Many model potential energy surfaces (PESs) have been reported for water; however, none are strictly from "first-principles". Here we report such a potential, based on a many-body representation at the CCSD(T) level of theory up to the four-body interaction. The new PES is benchmarked for the isomers of the water hexamer for dissocn. energies, harmonic frequencies, and unrestricted diffusion Monte Carlo (DMC) calcns. of the zero-point energies of the Prism, Book, and Cage isomers. Dissocn. energies of several isomers of the 20-mer agree well with recent benchmark energies. Exploratory DMC calcns. on this cluster verify the robustness of the new PES for quantum simulations. The accuracy and speed of the new PES are demonstrated for std. condensed phase properties, i.e., the radial distribution function and the self-diffusion const. Quantum effects are shown to be substantial for these observables and also needed to bring theory into excellent agreement with expt.**73**Heindel, J. P.; Xantheas, S. S. The many-body expansion for aqueous systems revisited: I. water–water interactions.*J. Chem. Theory Comput.*2020,*16*, 6843– 6855, DOI: 10.1021/acs.jctc.9b00749[ACS Full Text ], [CAS], Google Scholar73https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitVyku7bL&md5=5d6f0287f24676a3da2c9d1fb2178d25The Many-Body Expansion for Aqueous Systems Revisited: I. Water-Water InteractionsHeindel, Joseph P.; Xantheas, Sotiris S.Journal of Chemical Theory and Computation (2020), 16 (11), 6843-6855CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We revisit the many-body expansion (MBE) for water-water interactions by examg. the effects of the basis set, including those resulting from the basis set superposition error (BSSE) correction, and electron correlation on the various terms for selected sizes of water clusters up to n = 21. The anal. is performed at the second-order Moller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality (aug-cc-pVxZ, x = D, T, Q, 5) for the (H2O)n, n = 7, 10, 13, 16, and 21, clusters for which we report either the complete MBE (for n = 7, 10) or the ones through the 6-body (for n = 13) and the 5-body terms (for n = 16, 21). For the n = 3 and 7 clusters, we also report the anal. at the coupled cluster with single, double, and perturbative triple replacements in order to assess the effects of a higher correlation on the magnitude and percentage of the various MBE terms. Our results suggest that the oscillatory behavior around zero found for the 5-body and larger terms is solely an artifact of the (small) size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero upon increasing the size of the basis set toward the complete basis set (CBS) limit. In that respect, the BSSE-cor. 5-body and above terms do not exhibit the oscillatory behavior on either side of zero with the basis set obsd. for the BSSE-uncorrected terms. In addn., the magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSE-cor.) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small so that neglecting the correlation contribution in all terms above the 3-body results in an error of the order of 0.1%. The BSSE correction to the largest 2-body term in the MBE was accurately estd. from the function a[1 + erf( - b·R)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are sepd. by R with the consts. a and b fitted to the calcd. BSSE corrections for the individual 2-body terms of the clusters with each basis set and R is the distance between oxygen atoms. Our results demonstrate that the MBE for water-water interactions converges by the 4-body term since any finite terms above the 4-body are artifacts of the size of the basis set. The MBE can thus be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the smaller aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate ab initio based many-body mol. dynamics simulations for aq. systems.**74**Nandi, A.; Qu, C.; Houston, P. L.; Conte, R.; Yu, Q.; Bowman, J. M. A CCSD(T)-based 4-body potential for water.*J. Phys. Chem. Lett.*2021,*12*, 10318– 10324, DOI: 10.1021/acs.jpclett.1c03152[ACS Full Text ], [CAS], Google Scholar74https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1Cqtr3O&md5=5e33ce3c2c2c22d11b680b7a35afd5e9A CCSD(T)-Based 4-Body Potential for WaterNandi, Apurba; Qu, Chen; Houston, Paul L.; Conte, Riccardo; Yu, Qi; Bowman, Joel M.Journal of Physical Chemistry Letters (2021), 12 (42), 10318-10324CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)High-level, ab initio calcns. find that the 4-body (4-b) interaction is needed to account for near-100% of the total interaction energy for water clusters as large as the 21-mer. Motivated by this, we report a permutationally invariant polynomial potential energy surface (PES) for the 4-body interaction. This machine-learned PES is a fit to 2119 symmetry-unique, CCSD(T)-F12a/haTZ 4-b interaction energies. Configurations for these come from tetramer direct-dynamics calcns., fragments from an MD water simulation at 300 K, and tetramer fragments in a variety of water clusters. The PIP basis is purified to ensure that the PES goes rigorously to zero in monomer + trimer and dimer + dimer dissocns. The 4-b energies of isomers of the hexamer calcd. with the new PES are shown to be in better agreement with benchmark CCSD(T) results than those from the MB-pol potential. Tests on larger clusters further validate the high-fidelity of the PES. The PES is shown to be fast to evaluate, taking 2.4 s for 105 evaluations on a single core of 2.4 GHz Intel Xeon processor, and significantly faster using a parallel version of the PES.**75**Conte, R.; Qu, C.; Bowman, J. M. Permutationally invariant fitting of many-body, non-covalent interactions with application to three-body methane–water–water.*J. Chem. Theory Comput.*2015,*11*, 1631, DOI: 10.1021/acs.jctc.5b00091[ACS Full Text ], [CAS], Google Scholar75https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXjvVOhsrs%253D&md5=5a08d4fa1f8c5b521d4fe52e796c4013Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane-Water-WaterConte, Riccardo; Qu, Chen; Bowman, Joel M.Journal of Chemical Theory and Computation (2015), 11 (4), 1631-1638CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A modified, computationally efficient method to provide permutationally invariant polynomial bases for mol. energy surface fitting via monomial symmetrization (Xie Z.; Bowman J. M. J. Chem. Theory Comput.2010, 6, 26-34) is reported for applications to complex systems, characterized by many-body, non-covalent interactions. Two approaches, each able to ensure the asymptotic zero-interaction limit of intrinsic potentials, are presented. They are both based on the tailored selection of a subset of the polynomials of the original basis. A computationally efficient approach exploits reduced permutational invariance and provides a compact fitting basis dependent only on intermol. distances. We apply the original and new techniques to obtain a no. of full-dimensional potentials for the intrinsic three-body methane-water-water interaction by fitting a database made of 22,592 ab initio energies calcd. at the MP2-F12 level of theory with haTZ (aug-cc-pVTZ for C and O, cc-pVTZ for H) basis set. An investigation of the effects of permutational symmetry on fitting accuracy and computational costs is reported. Several of the fitted potentials are then employed to evaluate with high accuracy the three-body contribution to the CH4-H2O-H2O binding energy and the three-body energy of three conformers of the [email protected](H2O)20 cluster.**76**Liu, K.; Brown, M.; Carter, C.; Saykally, R.; Gregory, J.; Clary, D. Characterization of a cage form of the water hexamer.*Nature*1996,*381*, 501– 503, DOI: 10.1038/381501a0[Crossref], [CAS], Google Scholar76https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XjsVWisLs%253D&md5=b7f94d0867748c08052407744e0f3ad0Characterization of a cage form of the water hexamerLiu, K.; Brown, M. G.; Carter, C.; Saykally, R. J.; Gregory, J. K.; Clary, D. C.Nature (London) (1996), 381 (6582), 501-503CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)Water has been studied more extensively than any other liq., yet its microscopic properties remain poorly understood. The difficulty in obtaining a rigorous mol.-scale description of water structure is largely a consequence of the extended, dynamic hydrogen-bonded network that exists throughout the liq. Studies of the structure and dynamics of isolated small clusters of water mols. provide a means of quantifying the intermol. forces and hydrogen-bond rearrangements that occur in condensed phases. Expts. and theory strongly suggest that the water trimer, tetramer and pentamer have cyclic min. energy structures. Larger water clusters are expected to have three-dimensional geometries, with the hexamer representing the transition from cyclic to such three-dimensional structures. Here we report investigations by terahertz laser vibration-rotation tunneling spectroscopy of the structure of the water hexamer. A comparison of our results with quantum Monte Carlo simulations of this species suggests that the most stable form of (H2O)6 is indeed a cage-like structure, held together by eight hydrogen bonds.**77**Lambros, E.; Paesani, F. How good are polarizable and flexible models for water: Insights from a many-body perspective.*J. Chem. Phys.*2020,*153*, 060901, DOI: 10.1063/5.0017590[Crossref], [PubMed], [CAS], Google Scholar77https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFyhtL%252FN&md5=c1c047fd27facf1b9fcf9abaf76a0f6bHow good are polarizable and flexible models for water: Insights from a many-body perspectiveLambros, Eleftherios; Paesani, FrancescoJournal of Chemical Physics (2020), 153 (6), 060901CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a systematic anal. of state-of-the-art polarizable and flexible water models from a many-body perspective, with a specific focus on their ability to represent the Born-Oppenheimer potential energy surface of water from the gas to the liq. phase. Using coupled cluster data in the complete basis set limit as a ref., we examine the accuracy of the polarizable models in reproducing individual many-body contributions to interaction energies and harmonic frequencies of water clusters and compare their performance with that of MB-pol, an explicit many-body model that has been shown to correctly predict the properties of water across the entire phase diagram. Based on these comparisons, we use MB-pol as a ref. to analyze the ability of the polarizable models to reproduce the energy landscape of liq. water under ambient conditions. We find that, while correctly reproducing the energetics of min.-energy structures, the polarizable models examd. in this study suffer from inadequate representations of many-body effects for distorted configurations. To investigate the role played by geometry-dependent representations of 1-body charge distributions in reproducing coupled cluster data for both interaction and many-body energies, we introduce a simplified version of MB-pol that adopts fixed at. charges and demonstrate that the new model retains the same accuracy as the original MB-pol model. Based on the analyses presented in this study, we believe that future developments of both polarizable and explicit many-body models should continue in parallel and would benefit from synergistic efforts aimed at integrating the best aspects of the two theor./computational frameworks. (c) 2020 American Institute of Physics.**78**Reddy, S. K.; Straight, S. C.; Bajaj, P.; Huy Pham, C.; Riera, M.; Moberg, D. R.; Morales, M. A.; Knight, C.; Götz, A. W.; Paesani, F. On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice.*J. Chem. Phys.*2016,*145*, 194504, DOI: 10.1063/1.4967719