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Hamiltonian-Reservoir Replica Exchange and Machine Learning Potentials for Computational Organic Chemistry

  • Raimon Fabregat
    Raimon Fabregat
    Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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  • , 
  • Alberto Fabrizio
    Alberto Fabrizio
    Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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    Orcidhttp://orcid.org/0000-0002-4440-3149
  • , 
  • Benjamin Meyer
    Benjamin Meyer
    Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    More by Benjamin Meyer
  • , 
  • Daniel Hollas
    Daniel Hollas
    Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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    Orcidhttp://orcid.org/0000-0003-4075-6438
  • , and 
  • Clémence Corminboeuf*
    Clémence Corminboeuf
    Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    *[email protected]
    More by Clémence Corminboeuf
    Orcidhttp://orcid.org/0000-0001-7993-2879
Cite this: J. Chem. Theory Comput. 2020, 16, 5, 3084–3094
Publication Date (Web):March 26, 2020
https://doi.org/10.1021/acs.jctc.0c00100

Copyright © 2022 American Chemical Society. This publication is licensed under CC-BY-NC-ND.

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Abstract

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This work combines a machine learning potential energy function with a modular enhanced sampling scheme to obtain statistically converged thermodynamical properties of flexible medium-size organic molecules at high ab initio level. We offer a modular environment in the python package MORESIM that allows custom design of replica exchange simulations with any level of theory including ML-based potentials. Our specific combination of Hamiltonian and reservoir replica exchange is shown to be a powerful technique to accelerate enhanced sampling simulations and explore free energy landscapes with a quantum chemical accuracy unattainable otherwise (e.g., DLPNO-CCSD(T)/CBS quality). This engine is used to demonstrate the relevance of accessing the ab initio free energy landscapes of molecules whose stability is determined by a subtle interplay between variations in the underlying potential energy and conformational entropy (i.e., a bridged asymmetrically polarized dithiacyclophane and a widely used organocatalyst) both in the gas phase and in solution (implicit solvent).

1. Introduction

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Machine learning techniques are increasingly used to bypass expensive quantum chemical computations. Typical examples are machine learning-based potentials that are exploited to propagate the dynamical evolution of molecular systems on ab initio potentials at a fraction of the cost. The seminal work in the field comes from Behler and Parrinello, (1) who trained a generalized Artificial Neural Network (ANN) capable of predicting density functional theory-based energies and atomic forces and demonstrated its capability on bulk silicon (2) and then on carbon (3,4) and sodium. (5) Behler and Marquetand then applied the same approach to n-alkanes (6) and alanine tripeptides. (7) Comparable capabilities were achieved by Csanyi and co-workers, who used kernel-based method (i.e., the Gaussian approximation potential) (8) to propagate the density functional theory (DFT)–molecular dynamics (MD) of bulk crystal, (9) amorphous carbon, (10) and silicon. (11) Kernel ridge methods were also exploited for the “on-the-fly” propagation of the dynamic in the electronic states, circumventing the need for the explicit time dependent DFT or the CASSCF computations. (12) Roitberg et al. modified the Behler–Parrinello symmetry functions and proposed a deep neural network (ANAKIN-ME) to learn the potential of organic molecules approaching the CCSD(T)/CBS accuracy. (13−15) Such a high-accuracy level was also achieved by Tkatchenko and co-workers using gradient-domain machine learning (GDML). (16−18) The SchNet (19−21) deep learning architecture was also exploited to predict the potential energy surface and other quantum chemical properties of molecules and materials. Inspired by SchNet, Meuwly and Unke introduced the PhysNet architecture (22) for predicting energies, forces, or dipole moment of small organic molecules and polyalanines.
Overall, machine learning potentials (neural network or kernel-based) achieving post-Hartree–Fock or DFT accuracy were essentially employed for the molecular dynamics of fairly small and rigid systems (e.g., benzene, ethane and malonadehyde, aspirin, uracil, naphthalene, salicylic acid, and toluene) (16,17,23) or alternatively for larger systems with limited chemical diversity (e.g., peptides made of the same amino-acid type). (7) For these reasons, the associated (free) energy landscapes were explored using standard ab initio molecular dynamics without the need of making use of accelerated sampling approaches. Describing more flexible organic molecules (i.e., molecules that possess low-frequency (anharmonic) modes and multiple local minima close in energy) with machine learning potentials sets additional challenges, which influence both the accuracy of the ML potential and the convergence of the statistical sampling of complex potential energy surfaces.
In 2016, one of us demonstrated (24) the utility of coupling temperature replica exchange (25) (T-RE) molecular dynamic with the most recent variant of density functional tight binding, i.e., DFTB3 (26−28) to map the free energy landscapes of fluxional organic molecules in order to address organic chemistry problems that are not solvable solely relying on static electronic structure computations or standard molecular dynamics, the latter being too short to capture the interconversion between different possible states. A replica exchange molecular dynamics (REMD) simulation overcomes problems associated with running insufficiently long simulations by performing a series of energetically independent simulations (named replicas) of the same system in different equilibrium conditions and allowing them to occasionally exchange their configuration in a way that still ensures a canonical sampling within each replica. Replica exchange is especially appealing when relevant collective variables essential to a metadynamic (29) simulation are not easily identifiable (24) (see ref (30) for a recent example of metadynamics at the DFTB level). The most common version is T-RE, (25) where the replicas differ by their temperature. The additional insights provided by the coupling of REMD and DFTB3 (REMD@DFTB3) (24) were demonstrated on four examples including reaction energy pathways and conformational free energy differences, characteristic of organocatalysts, and flexible molecular rotors. While REMD@DFTB3 permits thorough exploration of potential energy surfaces at an affordable computational cost, the accuracy of the electronic structure method was sacrificed to ensure statistical convergence. In fact, the incompatibility associated with obtaining both converged statistical sampling and highly accurate energetics has traditionally prevented the ability to improve the quantum chemical description of moderately sized, yet highly flexible molecules that evolve on complex potential energy surfaces, (31−34) sometimes leading to catastrophic results. (35) In the present work, we achieve high-level ab initio accuracy by correcting semiempirical potentials with a machine learning model based on kernel ridge regression (36) combined with a more general enhanced sampling scheme connecting Hamiltonian (37) (H-RE) and reservoir (38) (resRE) replica exchange (i.e., resH-RE). With the former, the replicas evolve under a different Hamiltonian instead of a different temperature like in Temperature Replica Exchange, (i.e., T-RE). As for reservoir Replica Exchange, it was originally developed to improve T-RE by replacing the highest-temperature replica with a pool of structures (i.e., reservoir) acting as any other replica but exchanging conformations taken randomly from the pool. The proposed combination of Hamiltonian and reservoir RE (resH-RE) dramatically accelerates the exploration of ab initio free energy landscapes of archetypes flexible medium-size organic molecules that are dictated by a subtle energetic interplay originating from both enthalpic contributions and conformational entropy. The illustrative systems considered herein (Figure 1) are motivated by our previous work (24,39,40) and are (1) the bridged asymmetrically polarized dithiacyclophane, incorporating a thieno[2,3-b], (41) and (2) a prototypical cinchona alkaloid organocatalyst. (40,42,43) Specifically, the first molecule is chosen because its relative conformational stability is governed by subtle intramolecular noncovalent interactions that necessitates an accurate ab initio treatment, while the large conformational entropy effects can only be accounted for by using accelerated sampling techniques. The free energy landscape of the organocatalyst is a complementary example that depends on individual energy contributions arising from rotational isomerism.

Figure 1

Figure 1. (a) Dithiacyclophane and the collective variables used to characterize its global structure: the distance between the center of masses of each cyclic bulk and the angles between the average planes going through them. (b) Cinchona alkaloid organocatalyst and the two dihedral angles used to characterize its global structure.

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2. Methods and Computational Details

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Overview

The proposed protocol is schematically illustrated in the workflow given in Figure 2, whereas all the details on the quantum chemistry, machine learning models, and enhanced sampling approaches are described in the upcoming individual sections. In brief, a low-cost semiempirical approach is used as a quantum chemical baseline, while the targeted free energies are achieved at an accurate ab initio target level with machine-learned corrections that learn the difference (Δ) between the baseline and the target (Δ-ML correction). (44) The semiempirical level is first used to generate a canonical sampling using T-RE that serves two purposes: (a) a subset of structures extracted from this T-RE simulation is selected to build a training set of energies/structures to train the Δ-ML model, and (b) the pool of structures associated with the T-RE is used as a reservoir (vide infra). The thorough exploration of the free energy landscapes, which is finally performed using a potential corresponding to the semiempirical level + Δ-ML correction, combines two variants of replica exchange that are Hamiltonian and reservoir RE (resH-RE). The resH-RE simulations were performed with a modular in-house python implementation of replica exchange uploaded in git-hub (45) in the form of a Python library under the name Modular Replica Exchange Simulator (MORESIM).

Figure 2

Figure 2. Mind-map and workflow illustrating the proposed methodology.

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2.1. Quantum Chemical Potentials: Targets and Baseline

DFTB3 (26) with the 3OB parameters (27,28) and the Slater–Kirkwood dispersion correction (46) (DFTB-SK) using the DFTB+ (47) software is the chosen baseline for the Δ-ML model and for building the reservoir. The target potential is the domain-based local pair natural orbital coupled-cluster with perturbative triples (DLPNO-CCSD(T)/CBS) (48,49) as implemented in ORCA 4.0. (50) Complete Basis Set (CBS) extrapolations are performed following Neese’s scheme starting from Dunning basis sets (51,52) (i.e., cc-pVDZ and cc-pVTZ) computations. PBE0 (53)-D3 (54)/(6-31G) is also used as target. The TeraChem (55,56) implementation serves to provide a comparison with the direct (exact PBE0 as opposed to ML-based) free energy computations at the PBE0-D3/(6-31G) level. For the direct computation, we follow the work from Martinez et al. (56) and utilized an MPI interface between AMBER and TeraChem GPU to accelerate single-point computations performed during the PBE0-D3/(6-31G) and AMBER (57) T-RE simulations. At each step of the dynamics, the converged density from the previous step was passed as the initial point for the SCF computation. These PBE0 simulations enable comparison between the explicit ab initio free energy landscapes and the faster ML ansatz, a comparison that is not possible at the DLPNO-CCSD(T) level. Details on the relative computational cost are provided in Figure S1.
Solvent effects were included implicitly using the SMD (58) model (with the dielectric constant of chloroform) at the PBE0-D3/(6-31G) level, also in ORCA 4.0.

2.2. Machine Learning Models

The ML corrections trained to learn the difference between the baseline and target levels are based on Kernel Ridge Regression (36) (KRR) and use the Spectrum of London Axilrod–Teller–Muto (SLATM) (59) molecular representation developed by von Lilienfeld and Huang in the Quantum Machine Learning (QML) package. (60) Among all the tested molecular representations (e.g., Coulomb Matrix, (61) Bag of bonds (62)), SLATM offered the best accuracy for the class of problems investigated herein. The KRR space was generated with a Gaussian kernel. The training set is built on the basis of the most distinct structures extracted from the DFTB-SK T-RE simulations and corresponds to 1500 and 1800 structures and energies for the bridged asymmetrically polarized dithiacyclophane (a), and a prototypical cinchona alkaloid organocatalyst (b), respectively. These sets were divided into a training and a validation set (200 and 300 random structures) and were used for validation for each system, respectively. Among the initial 1500 and 1800 structures/energies, a random subset of 500 was used to optimize the hyper-parameters (i.e., the standard deviation of the Gaussian kernel σ, and the regularization parameter λ) optimized with a Nelder–Mead simplex algorithm. (63) The quality of the trained model is evaluated by the mean absolute errors (MAE; see Figure S2) for the predictions on the test set. Overall, the final Δ-ML models offer an accuracy reaching 1 kcal/mol for both the dithiacyclophane and the cinchona alkaloid organocatalyst in comparison to the electronic energy computed at the exact reference level (see learning curves in Figure S2). Achieving such accuracy was a sufficient reason to favor kernel methods over a neural network.

2.3. Hamiltonian-Reservoir Replica Exchange

Two complementary sampling techniques are used for the exploration of the free energy landscapes computed with the Δ-ML models: Hamiltonian Replica Exchange (37) (H-RE) and reservoir Replica (38) (resRE). Approaches based on replica exchange typically use parallel simulations with modified parameters (temperature, Hamiltonian, atomic masses, ...) to facilitate the crossing of energy barriers and thus accelerate the sampling of canonical probability distributions. (25,64,65) Over the course of the simulation, the original replica, operating at the target conditions, exchange molecular conformations with the modified replicas as a way to introduce significant jumps in the phase-space. To ensure nonvanishing exchange probabilities, a sufficient number of replicas connecting the original conditions with the other extreme is introduced.
In H-RE, the transition between states is accelerated by creating intermediate potentials (i.e., between the baseline and target condition) using a modified Hamiltonian for each of the replicas. (64,66,67) In our implementation, H-RE exploits a reservoir of DFTB-SK structures obtained from previous simulations (vide infra). The replicas evolve at the same temperature (300 K) and under a potential Vλ = (1 – λ)Vtarget + λVlow that transition from DFTB-SK (low) to DFTB-SK + Δ-ML corresponding to targeted post-Hartree–Fock or DFT accuracy. The replica with λ = 0 evolves with the pure accurate potential V0 = Vtarget = DFTB-SK + Δ-ML, while the replica with λ = 1 corresponds to the lower-level potential V1 = Vlow = DFTB-SK. In practice, the “highest” replica (λ = 1) is replaced by an available reservoir, generated with the low-level potential (i.e., DFTB-SK at 300 K), in the spirit of reservoir Replica Exchange (resRE) (see scheme in Figure 3). Here, the canonical DFTB-SK reservoirs (see Figures 4a and 5a) were taken from previous T-RE simulations (300 K) within i-PI. (68,69)

Figure 3

Figure 3. Schematic depiction of Hamiltonian reservoir Replica Exchange.

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Figure 4

Figure 4. (a) Free energy landscape (DFTB-SK/3OB level) of dithiacyclophane at 300 K (T-RE) projected on the 2D space generated by the collective variables visible in Figure 1a. (b) Projection of the data set made of 1500 dithiacyclophane structures extracted with farthest point sampling from the 300 K canonical ensemble of 40 000 structures and color coded on the basis of the single-point energy difference ΔE = ((DFTB-SK/3OB) – (DLPNO-CCSD(T)/CBS)). The continuous background is plotted using a Gaussian interpolation of the mean energy difference. The smooth histograms were constructed with a Gaussian Kernel Density Estimator (Gaussian KDE) using the SciPy (73) python library.

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Figure 5

Figure 5. (a) Free energy landscape (DFTB-SK/3OB level) of the cinchona alkaloid organocatalyst at 300 K projected on the 2D space generated by the collective variables visible in Figure 1b. Constructed with canonical structures generated with T-RE simulations with DFTB-SK as potential energy. (b) Projection of the 1800 data set structures obtained with FPS from a canonical ensemble of 32 000 structures at 300 K canonical ensemble and color coded on the basis of the single point energy difference ΔE = ((DFTB-SK/3OB) – (DLPNO-CCSD(T)/CBS)). (c) Structures representing each of the four conformational regions (i.e., basins).

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The rationale behind the use of a reservoir is to reduce the trajectory correlation time and thus the number of single point computations needed to achieve convergence. (38) Of course, resRE is only adequate to compute ensemble averages if the reservoir contains samples that follow a known physical distribution (in our case canonical), as otherwise it is not possible to derive a proper exchange probability with the other replicas.
By coupling the reservoir with H-RE rather than T-RE, we are able to explore the accurate ab initio level by accelerating the sampling without increasing the temperature, which leads to several advantages. In comparison to T-RE (achievable only at the semiempirical level), for which the jumps between free energy minima are generated by the exchange and acceptance probability with replica evolving at different equilibrium conditions (e.g., temperature), resH-RE exploits an existing reservoir of structures covering the entire conformational space that are accessible to the replica evolving at the target condition. In other words, by taking advantage of an a priori canonical sampling performed at an affordable semiempirical level, resH-RE will more efficiently simulate rare events. Additionally, fewer replicas (4/6 (H-RE) vs 16/48 (T-RE) (for the two considered molecules) are necessary to achieve optimal exchange probabilities, suggesting a larger overlap between the potential energy distributions of the replica than in T-RE.
In our context, another key advantage of exchanging with the reservoir is that replicas only serve to induce local diffusion in the phase-space, whereas the swaps between local minima in the free energy landscape (i.e., between basins) and crossings of energy barriers occur through the reservoir. The resH-RE simulation is thus achievable with thermalized Molecular Dynamics, but also with simple Monte Carlo (MC) moves (e.g., random particle moves) that are otherwise largely inefficient for systems with nonlinear potential energy surfaces like those investigated herein. (70)
In fact, many of the existing ML-based potentials have not yet been adapted to run molecular dynamics. With the kernel based approaches, the forces can be obtained from deriving the expression of the KRR (and thus of the molecular representation) with respect to the atomic coordinates, (12) but the task is not straightforward for the SLATM representation used here. The alternative, the Gradient Domain ML scheme developed by Müller et al., (16−18) consists of learning the forces directly is considerably more expensive and only applicable to small molecules.
This work uses resH-RE with MC moves not only because of the unavailability of the forces but also to illustrate that the broad applicability of the sampling scheme with any of the existing ML potentials.
The convergence of free energy computations was evaluated by analyzing the evolution of the estimated relative free energies between basins (see section 4 in the Supporting Information). Given that the crossing between basins represents the slowest dynamical mode, the stabilization of the estimated basin free energies represents a good indicator of convergence. Statistical error boundaries on the estimated free energies were evaluated using a block jackknife with a width of one-tenth of simulation time. (71)
Note that the adopted approaches are applicable to any molecule but is specially designed for situations when free energy perturbation is not sufficient or suffers from convergence problems. resH-RE is indeed not a simple reweighting scheme; the reservoir in resH-RE is used to accelerate jumps over the conformational space, but the data generated by the replica that samples the canonical distribution of the target potential correspond to an unbiased sampling of the adequate probability distribution.

2.4. Technical Details

The 300 K free energy landscape of dithiacyclophane was obtained with a resH-RE simulation using four replicas (λ = 0, 0.33, 0.66, 1) exploiting a reservoir of 40 000 structures taken from a previous DFTB-SK (24) canonical distribution of structures obtained with T-RE at 300 K using the Langevin thermostat. The T-RE DFTB-SK simulation corresponds to 16 replicas with temperatures ranging from 300 to 1500 K in logarithmic intervals, and a time-step of 0.25 fs ran for 2.5 × 106 MD steps. A subset with the 1500 most distinct structures was extracted from the reservoir with Farthest Point Sampling (9) (FPS) (Figure 4b) and used to train the Δ-ML corrections. Six replicas (λ = 0, 0.2, 0.6, 0.8, 1) were required for the resH-RE simulations of the cinchona-based asymmetric organocatalyst, and the 1800 most distinct structures (Figure 5b) extracted from a reservoir of 32 000 structures obtained as discussed above (i.e., T-RE simulations) were used for the training. For both resH-RE simulations, it was ensured that the exchange rate between replicas reaches an optimal ∼30%. (72) Exchange between replicas was attempted every 20 MC steps consisting of a Gaussian random displacement of all atoms (in Cartesian coordinates) with standard deviation σ = 0.003 Å set to 50% acceptance rate. The MC simulations correspond to a total of 106 steps for both systems.
The 300 K canonical sampling at the direct PBE0-D3/(6-31G) level was also generated with a T-RE simulation using TeraChem (55,56) in combination with AMBER. (57) The simulation corresponds to 10 replicas with temperatures ranging from 300 to 1500 K in logarithmic intervals, and a time-step of 0.75 fs ran for 1.5 × 106 MD steps.

3. Results

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3.1. Dithiacyclophane

The three conformational regions of dithiacyclophane, previously investigated by one of us, (24) and visible in Figure 4a, are controlled by very distinct enthalpic and entropic contributions. The π-stacked “closed” conformer is stabilized by long-range correlation effects and only captured at the DFT level upon the addition of a London dispersion correction. (39,40,74) In sharp contrast, the open conformer is highly flexible and driven by entropy and large anharmonic effects. The third “disarticulated” conformer is rigid but less sensitive to London dispersion forces in comparison to the closed region. Our former T-RE DFTB simulations that captured all the conformational entropy effects, highlighted the limitation of the harmonic approximation for describing the relative stability of the most floppy (i.e., open) conformer (see Figure 4a).
The harmonic approximation fails to account for the full conformational entropy contributions and the anharmonic nature of the open state (2) (see ref (75) for relevant examples of approximations for anharmonic free energies) and to a lesser extent of the closed conformational region (1). The large entropic contributions characterizing the open region (see Figure 4a) makes it the lowest-energy conformer at the DFTB-SK level at 300 K and temperatures above. Yet, the DFTB relative free energies between the three conformers are very small (within 1 kcal mol–1). Converging the statistical sampling comes with a quantum chemical cost and the affordable semiempirical level is not expected to capture all these subtle energy differences accurately.
The ML correction to DFTB-SK offers access to converged DLPNO-CCSD(T) free energy profiles at a fraction of the cost (vide supra). Prior to obtaining the full free energy landscapes with resH-RE, it is interesting to identify the trends emerging from the Δ-ML correction added to the DFTB-SK energy of the structures in the reservoir (Figure 6). The 0.79 regression slope between DFTB-SK and ML-DLPNO-CCSD(T) is indicative of the much flatter potential energy surface of the former or, in other words, an underestimation of the energy differences and barriers across the energy landscape (with PBE0-D3/(6-31G) the slope is 0.74; see Figure S3).

Figure 6

Figure 6. Comparison between the DFTB-SK electronic energy and the ML-DLPNO-CCSD(T)/CBS predictions (i.e., DFTB-SK + ΔML correction) for the 40 000 structures in the reservoir.

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The consequence of these energy discrepancies is clear when comparing the full free energy landscapes and relative free energies (upon integration within the free energy basins, (24)Figure 7) obtained with resH-RE sampling at different quantum chemical levels. Overall, the shape of the ML-DLPNO-CCSD(T)/CBS and DFTB-SK profiles are very similar but the disarticulated basin is strongly favored by CCSD(T) at the detriment of the close conformer (>2 kcal mol–1 higher). In contrast to the flat DFTB-SK free energy profile, the ML-DLPNO-CCSD(T) landscape is clearly uneven highlighting the difficulties of the tight-binding method to reproduce the delicate interaction interplay characterizing the conformational regions of this illustrative system. The PBE0 free energy landscapes are even less flat and favor the disarticulated state even more with the closed structure being around 3 kcal mol–1 higher. Yet, the excellent agreement between PBE0-D3/(6-31G) and ML-PBE0-D3/(6-31G) is a proof-of-principle demonstration that this trend is not an artifact from the ML potentials (see Figure 7d,e).

Figure 7

Figure 7. Free energy landscapes at 300 K generated with the potential: (a) DFTB-SK; (b) ML-DLPNO-CCSD(T)/CBS; (c) ML-[PBE0-D3/(6-31G)(SMD Chloroform)]; (d) PBE0-D3/(6-31G); (e) ML-PBE0-D3/(6-31G). (f) Relative free energies by integration within the local minima. (24) The free energies are all given relative to the Disarticulated state except for the solvated system, where the open state is used as a reference. The striped columns correspond to the static relative free energy using the harmonic approximation (for the solvated system the harmonic free energies were computed with the true potential, and not with the machine learning version). All the free energies maps come from resH-RE expect for the direct PBE0, which uses T-RE, as described in the methods section.

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Note that a direct approach using DLPNO-CCSD(T)/CBS is not achievable, given the intrinsic computational cost of the method. For this specific reason, a relatively small basis set was chosen for the DFT profiles. While some of the deviations between DFTB-SK and the higher-level approaches (i.e., much smaller energy differences) are already apparent in the static picture (see the harmonic free energies in Figure 7), the deviations between methods are more pronounced when accounting for thermal fluctuations. With PBE0-D3, the approximated barriers between each conformational regions are over 5 kcal mol–1, which is significantly higher than the DFTB-SK (<2 kcal mol–1).
The Monte Carlo approaches used in this work are not easily compatible with the inclusion of explicit solvent, but the effect of the environment is, of course, essential to decipher the true molecular behavior and its associated PES. As a compromise, solvent effects were incorporated implicitly with the SMD continuum model (with the chloroform dielectric constant (41)) at the PBE0 level. The inclusion of these effects severely affects the relative energetic stability and flatten the entire profile looking much more similar to the gas phase DFTB-SK profile. The limitation associated with the continuum model could be overcome by using an additional potential that models the interaction between the solute and explicit solvent within a dynamic simulation, a possibility that we will explore in future work.

3.2. Cinchona Alkaloid

The same methodology is applied to a common cinchona-based asymmetric organocatalyst for which we also generated the ab initio free energy landscape (Figure 8). (24) The 2D conformational map extracted from the 2016 T-RE simulations at the DFTB level revealed four easily accessible conformational regions (1–4) and one that is much less populated (2′). Unexpected from previous static computations was the dihedral angle (open rather than close) characteristic of the conformational state 3. Other added values from the T-RE simulation were the demonstration of the pronounced entropic nature of 1 at 300 K reversing the relative stability between 1 and 4 in comparison with the static computation and the appearance of region 2′. Yet, the 1 and 4 conformational regions were within 2 kcal mol–1 stressing the importance of improving upon the DFTB level.

Figure 8

Figure 8. Free energy landscapes at 300 K generated with the potential: (a) DFTB-SK; (b) ML-DLPNO-CCSD(T)/CBS; (c) ML-[PBE0-D3/(6-31G)(SMD Chloroform)]. (d) Free energies upon integration within the free energy basins. The free energies are all given relative to the Disarticulated state. The stripped columns are the free energy predictions of the basins using the static free energies using the harmonic correction.

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With a slope much smaller than 1 (i.e., 0.76), Figure S6 confirms the general flatness of the DFTB-SK potential compared to that of DLPNO-CCSD(T). Note that the DFTB3 underestimation of the rotational barriers and of the relative energy differences, which originates from the limited amount of atomic overlap afforded by the use of a minimal basis set, is reminiscent of other examples in the literature. (27,76)
Figure 8 compares the full DFTB profile with those obtained with ML-DLPNO-CCSD(T) and ML-PBE0-D3 accounting for the implicit effect of the chloroform environment. (77) The general shape of the ML-DLPNO-CCSD(T)/CBS free energy landscape of the organocatalyst is once again similar to the DFTB-SK one but with significant differences. Specifically, 4 is clearly enthalpically stabilized at the higher level, whereas the flexibility of the conformational region 1 is enhanced (i.e., larger spread over the dihedral angle characteristic of the syn/anti conformation). The metastable region 2′ is also more populated at this level. Quantitatively, these trends translate into 1 and 4 lying very close in energies (within 0.5 kcal mol–1) with state 3 being nearly 3 kcal mol–1 higher and disconnected from region 1 (i.e., a high barrier separating the two regions). Akin to the dithiacyclophane, the PBE0 gas-phase profile (Figure S8) is much closer to ML-DLPNO-CCSD(T)/CBS than the implicit solvated (in chloroform) profile but the flattening of the free energy landscape of the cinchona derivatives upon implicit solvation is less pronounced than for the dithiacyclophane (see Figure 8c and Figure S8). Overall, the effect of the solvent on conformer 3 is negligible but the metastable 2′ specie disappears, while 2/4 are more/less populated.
These two complementary examples are associated with different energetic driving forces that are the interplays between pronounced intramolecular vdW interactions and conformational entropy in the first case and the individual contributions arising from rotational isomerism in the second.

4. Conclusions

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In 2016, we highlighted the importance of thorough mappings of the free energy landscapes for solving problems in computational organic chemistry. In this subsequent step, we demonstrate how to exploit a variant of Hamiltonian replica exchange and kernel-based machine learning potentials to achieve a remarkable accuracy/cost ratio and accelerate the accurate predictions of relative free energies, which is one of the most challenging goals in computational quantum chemistry. Overall, our results stress the relevance of improving the entropic and enthalpic description of flexible organic molecules having complex free energy landscapes dictated by subtle energetic interplays. In particular, based on comparisons between the DFTB-SK baseline and the ML-DLPNO-CCSD(T) target, one concludes that the semiempirical method generally leads to much flatter free energy landscapes. Similarly, such systems are poorly described by the picture arising from static free energies, which underestimate the conformational entropy of the most flexible conformational regions. For all these reasons, our original combination of Hamiltonian and reservoir replica exchange and its implementation into a modular environment (the python package MORESIM) represents a powerful solution capable of accelerating enhanced sampling simulations involving any machine learning-based or ab initio potential energies.
Subsequent objectives will consist of using the same workflow but circumventing the reduced transferability associated with the use of a global molecular machine learning representation by deriving a differentiable kernel approach based on local atomic environment that is also compatible with molecular dynamic simulations.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.0c00100.

  • Histogram of the cost of computations, learning curves, energy comparisons, basin potential energies, energies scatter plot, free energy landscapes and convergences, and detailed information on the training procedure (PDF)

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Author Information

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  • Corresponding Author
    • Clémence Corminboeuf - Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  Orcidhttp://orcid.org/0000-0001-7993-2879;  Email: [email protected]
  • Authors
    • Raimon Fabregat - Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    • Alberto Fabrizio - Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  Orcidhttp://orcid.org/0000-0002-4440-3149
    • Benjamin Meyer - Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
    • Daniel Hollas - Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, École polytechnique fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland;  Orcidhttp://orcid.org/0000-0003-4075-6438
  • Notes
    The authors declare no competing financial interest.

    The data that support the findings of this study are openly available in Materials Cloud at https://doi.org/10.24435/materialscloud:2020.0033/v1, while the Modular Replica Exchange Simulator (MORESIM) framework is available on github http://doi.org/10.5281/zenodo.3630553.

Acknowledgments

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This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 817977). AF. and B.M. acknowledge the National Centre of Competence in Research (NCCR) “Materials’ Revolution: Computational Design and Discovery of Novel Materials (MARVEL)” of the Swiss National Science Foundation (SNSF) for financial support.

References

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This article references 77 other publications.

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    A review. Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate mol. IR spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects - typically neglected by conventional quantum chem. approaches - we base our machine learning strategy on ab initio mol. dynamics simulations. While these simulations are usually extremely time consuming even for small mols., we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a mol. dipole moment model based on environment dependent neural network charges and combine it with the neural network potential approach of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of IR spectra based on only a few hundreds of electronic structure ref. points. This is made possible through the use of mol. forces during neural network potential training and the introduction of a fully automated sampling scheme. We demonstrate the power of our machine learning approach by applying it to model the IR spectra of a methanol mol., n-alkanes contg. up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all of these case studies we find an excellent agreement between the IR spectra predicted via machine learning models and the resp. theor. and exptl. spectra.
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    We study the deposition of tetrahedral amorphous carbon (ta-C) films from mol. dynamics simulations based on a machine-learned interat. potential trained from d.-functional theory data. For the first time, the high sp3 fractions in excess of 85% obsd. exptl. are reproduced by means of computational simulation, and the deposition energy dependence of the film's characteristics is also accurately described. High confidence in the potential and direct access to the at. interactions allow us to infer the microscopic growth mechanism in this material. While the widespread view is that ta-C grows by "subplantation," we show that the so-called "peening" model is actually the dominant mechanism responsible for the high sp3 content. We show that pressure waves lead to bond rearrangement away from the impact site of the incident ion, and high sp3 fractions arise from a delicate balance of transitions between three- and fourfold coordinated carbon atoms. These results open the door for a microscopic understanding of carbon nanostructure formation with an unprecedented level of predictive power.
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    Amorphous silicon (a-Si) is a widely studied noncryst. material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained using a machine-learning-based interat. potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 1011 K/s (i.e., on the 10 ns time scale), contains less than 2% defects, and agrees with expts. regarding excess energies, diffraction data, and 29Si NMR chem. shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with expts. to date. Our study demonstrates the broader impact of machine-learning potentials for elucidating structures and properties of technol. important amorphous materials.
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    Inclusion of Machine Learning Kernel Ridge Regression Potential Energy Surfaces in On-the-Fly Nonadiabatic Molecular Dynamics Simulation
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    Journal of Physical Chemistry Letters (2018), 9 (11), 2725-2732CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
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    A review. Deep learning is revolutionizing many areas of science and technol., esp. image, text, and speech recognition. In this paper, we demonstrate how a deep neural network (NN) trained on quantum mech. (QM) DFT calcns. can learn an accurate and transferable potential for org. mols. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Mol. Energies) or ANI for short. ANI is a new method designed with the intent of developing transferable neural network potentials that utilize a highly-modified version of the Behler and Parrinello symmetry functions to build single-atom at. environment vectors (AEV) as a mol. representation. AEVs provide the ability to train neural networks to data that spans both configurational and conformational space, a feat not previously accomplished on this scale. We utilized ANI to build a potential called ANI-1, which was trained on a subset of the GDB databases with up to 8 heavy atoms in order to predict total energies for org. mols. contg. four atom types: H, C, N, and O. To obtain an accelerated but phys. relevant sampling of mol. potential surfaces, we also proposed a Normal Mode Sampling (NMS) method for generating mol. conformations. Through a series of case studies, we show that ANI-1 is chem. accurate compared to ref. DFT calcns. on much larger mol. systems (up to 54 atoms) than those included in the training data set.
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    Smith, J. S.; Nebgen, B.; Lubbers, N.; Isayev, O.; Roitberg, A. E. Less Is More: Sampling Chemical Space with Active Learning. J. Chem. Phys. 2018, 148 (24), 241733,  DOI: 10.1063/1.5023802
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    Less is more: Sampling chemical space with active learning
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    Journal of Chemical Physics (2018), 148 (24), 241733/1-241733/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The development of accurate and transferable machine learning (ML) potentials for predicting mol. energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chem. space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of org. mols. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single mols. or materials, while remaining applicable to the general class of org. mols. composed of the elements CHNO. (c) 2018 American Institute of Physics.
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  15. 15
    Smith, J. S.; Nebgen, B. T.; Zubatyuk, R.; Lubbers, N.; Devereux, C.; Barros, K.; Tretiak, S.; Isayev, O.; Roitberg, A. E. Approaching Coupled Cluster Accuracy with a General-Purpose Neural Network Potential through Transfer Learning. Nat. Commun. 2019, 10 (1), 2903,  DOI: 10.1038/s41467-019-10827-4
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    15
    Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning
    Smith Justin S; Devereux Christian; Roitberg Adrian E; Smith Justin S; Nebgen Benjamin T; Zubatyuk Roman; Lubbers Nicholas; Barros Kipton; Tretiak Sergei; Smith Justin S; Lubbers Nicholas; Nebgen Benjamin T; Tretiak Sergei; Zubatyuk Roman; Isayev Olexandr
    Nature communications (2019), 10 (1), 2903 ISSN:.
    Computational modeling of chemical and biological systems at atomic resolution is a crucial tool in the chemist's toolset. The use of computer simulations requires a balance between cost and accuracy: quantum-mechanical methods provide high accuracy but are computationally expensive and scale poorly to large systems, while classical force fields are cheap and scalable, but lack transferability to new systems. Machine learning can be used to achieve the best of both approaches. Here we train a general-purpose neural network potential (ANI-1ccx) that approaches CCSD(T)/CBS accuracy on benchmarks for reaction thermochemistry, isomerization, and drug-like molecular torsions. This is achieved by training a network to DFT data then using transfer learning techniques to retrain on a dataset of gold standard QM calculations (CCSD(T)/CBS) that optimally spans chemical space. The resulting potential is broadly applicable to materials science, biology, and chemistry, and billions of times faster than CCSD(T)/CBS calculations.
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  16. 16
    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 (5), e1603015  DOI: 10.1126/sciadv.1603015
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    16
    Machine learning of accurate energy-conserving molecular force fields
    Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schuett, Kristof T.; Mueller, Klaus-Robert
    Science 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.
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  17. 17
    Chmiela, S.; Sauceda, H. E.; Müller, K. R.; Tkatchenko, A. Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields. Nat. Commun. 2018, 9 (1), 3887,  DOI: 10.1038/s41467-018-06169-2
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    17
    Towards exact molecular dynamics simulations with machine-learned force fields
    Chmiela Stefan; Muller Klaus-Robert; Sauceda Huziel E; Muller Klaus-Robert; Muller Klaus-Robert; Tkatchenko Alexandre
    Nature communications (2018), 9 (1), 3887 ISSN:.
    Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.
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  18. 18
    Sauceda, H. E.; Chmiela, S.; Poltavsky, I.; Müller, K. R.; Tkatchenko, A. Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces. J. Chem. Phys. 2019, 150 (11), 114102,  DOI: 10.1063/1.5078687
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    18
    Molecular force fields with gradient-domain machine learning: Construction and application to dynamics of small molecules with coupled cluster forces
    Sauceda, Huziel E.; Chmiela, Stefan; Poltavsky, Igor; Mueller, Klaus-Robert; Tkatchenko, Alexandre
    Journal of Chemical Physics (2019), 150 (11), 114102/1-114102/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present the construction of mol. force fields for small mols. (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018) and Chmiela et al., Sci. Adv. 3, e1603015 (2017)]. This approach is able to accurately reconstruct complex high-dimensional potential-energy surfaces from just a few 100s of mol. conformations extd. from ab initio mol. dynamics trajectories. The data efficiency of the sGDML approach implies that at. forces for these conformations can be computed with high-level wavefunction-based approaches, such as the "gold std." coupled-cluster theory with single, double and perturbative triple excitations [CCSD(T)]. We demonstrate that the flexible nature of the sGDML model recovers local and non-local electronic interactions (e.g., H-bonding, proton transfer, lone pairs, changes in hybridization states, steric repulsion, and n → π* interactions) without imposing any restriction on the nature of interat. potentials. The anal. of sGDML mol. dynamics trajectories yields new qual. insights into dynamics and spectroscopy of small mols. close to spectroscopic accuracy. (c) 2019 American Institute of Physics.
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  19. 19
    Schütt, K. T.; Arbabzadah, F.; Chmiela, S.; Müller, K. R.; Tkatchenko, A. Quantum-Chemical Insights from Deep Tensor Neural Networks. Nat. Commun. 2017, 8 (1), 13890,  DOI: 10.1038/ncomms13890
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    19
    Quantum-chemical insights from deep tensor neural networks
    Schuett, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Mueller, Klaus R.; Tkatchenko, Alexandre
    Nature Communications (2017), 8 (), 13890CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems. Here we develop an efficient deep learning approach that enables spatially and chem. resolved insights into quantum-mech. observables of mol. systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol-1) predictions in compositional and configurational chem. space for mols. of intermediate size. As an example of chem. relevance, the model reveals a classification of arom. rings with respect to their stability. Further applications of our model for predicting at. energies and local chem. potentials in mols., reliable isomer energies, and mols. with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chem. systems.
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  20. 20
    Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet-A Deep Learning Architecture for Molecules and Materials. J. Chem. Phys. 2018, 148 (24), 241722,  DOI: 10.1063/1.5019779
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    20
    SchNet - A deep learning architecture for molecules and materials
    Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
    Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
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  21. 21
    Schütt, K. T.; Kessel, P.; Gastegger, M.; Nicoli, K. A.; Tkatchenko, A.; Müller, K. R. SchNetPack: A Deep Learning Toolbox for Atomistic Systems. J. Chem. Theory Comput. 2019, 15 (1), 448– 455,  DOI: 10.1021/acs.jctc.8b00908
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    21
    SchNetPack: A Deep Learning Toolbox For Atomistic Systems
    Schuett, K. T.; Kessel, P.; Gastegger, M.; Nicoli, K. A.; Tkatchenko, A.; Mueller, K.-R.
    Journal of Chemical Theory and Computation (2019), 15 (1), 448-455CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    SchNetPack is a toolbox for the development and application of deep neural networks that predict potential energy surfaces and other quantum-chem. properties of mols. and materials. It contains basic building blocks of atomistic neural networks, manages their training, and provides simple access to common benchmark datasets. This allows for an easy implementation and evaluation of new models. For now, SchNetPack includes implementations of (weighted) atom-centered symmetry functions and the deep tensor neural network SchNet, as well as ready-to-use scripts that allow one to train these models on mol. and material datasets. Based on the PyTorch deep learning framework, SchNetPack allows one to efficiently apply the neural networks to large datasets with millions of ref. calcns., as well as parallelize the model across multiple GPUs. Finally, SchNetPack provides an interface to the Atomic Simulation Environment in order to make trained models easily accessible to researchers that are not yet familiar with neural networks.
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  22. 22
    Unke, O. T.; Meuwly, M. PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges. J. Chem. Theory Comput. 2019, 15 (6), 3678– 3693,  DOI: 10.1021/acs.jctc.9b00181
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    22
    PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges
    Unke, Oliver T.; Meuwly, Markus
    Journal of Chemical Theory and Computation (2019), 15 (6), 3678-3693CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    In recent years, machine learning (ML) methods have become increasingly popular in computational chem. After being trained on appropriate ab initio ref. data, these methods allow for accurately predicting the properties of chem. systems, circumventing the need for explicitly solving the electronic Schrodinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chem. applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chem. systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chem. reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qual. correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased mol. dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol-1 according to the ref. ab initio calcns.
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    Brockherde, F.; Vogt, L.; Li, L.; Tuckerman, M. E.; Burke, K.; Müller, K. R. Bypassing the Kohn-Sham Equations with Machine Learning. Nat. Commun. 2017, 8 (1), 872,  DOI: 10.1038/s41467-017-00839-3
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    23
    Bypassing the Kohn-Sham equations with machine learning
    Brockherde Felix; Muller Klaus-Robert; Brockherde Felix; Vogt Leslie; Tuckerman Mark E; Li Li; Burke Kieron; Tuckerman Mark E; Tuckerman Mark E; Burke Kieron; Muller Klaus-Robert; Muller Klaus-Robert
    Nature communications (2017), 8 (1), 872 ISSN:.
    Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.Machine learning allows electronic structure calculations to access larger system sizes and, in dynamical simulations, longer time scales. Here, the authors perform such a simulation using a machine-learned density functional that avoids direct solution of the Kohn-Sham equations.
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    Petraglia, R.; Nicolaï, A.; Wodrich, M. D.; Ceriotti, M.; Corminboeuf, C. Beyond Static Structures: Putting Forth REMD as a Tool to Solve Problems in Computational Organic Chemistry. J. Comput. Chem. 2016, 37 (1), 83– 92,  DOI: 10.1002/jcc.24025
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    24
    Beyond static structures: Putting forth REMD as a tool to solve problems in computational organic chemistry
    Petraglia, Riccardo; Nicolai, Adrien; Wodrich, Matthew D.; Ceriotti, Michele; Corminboeuf, Clemence
    Journal of Computational Chemistry (2016), 37 (1), 83-92CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    Computational studies of org. systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chem. systems are dynamic entities where a multitude of mol. conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biol. simulations, together with empirical force fields, and apply it to org. chem. problems. Replica-exchange mol. dynamics (REMD) permits thorough exploration of the PES. We combined REMD with d. functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small mol. systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temp.-dependent rotational processes, and catalysis, we reveal new insights and chem. that likely would be missed using static electronic structure computations. The REMD-DFTB methodol. at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes. © 2015 Wiley Periodicals, Inc.
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    Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding. Chem. Phys. Lett. 1999, 314, 141– 151,  DOI: 10.1016/S0009-2614(99)01123-9
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    Replica-exchange molecular dynamics method for protein folding
    Sugita, Y.; Okamoto, Y.
    Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
    We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
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    Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB). J. Chem. Theory Comput. 2011, 7 (4), 931– 948,  DOI: 10.1021/ct100684s
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    26
    DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB)
    Gaus, Michael; Cui, Qiang; Elstner, Marcus
    Journal of Chemical Theory and Computation (2011), 7 (4), 931-948CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The self-consistent-charge d.-functional tight-binding method (SCC-DFTB) is an approx. quantum chem. method derived from d. functional theory (DFT) based on a second-order expansion of the DFT total energy around a ref. d. In the present study, we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between at. partial charges and, second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodol. called DFTB3, which substantially improves the description of charged systems contg. elements C, H, N, O, and P, esp. regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomol. systems. Remaining challenges and possible solns. are also briefly discussed.
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    Gaus, M.; Goez, A.; Elstner, M. Parametrization and Benchmark of DFTB3 for Organic Molecules. J. Chem. Theory Comput. 2013, 9 (1), 338– 354,  DOI: 10.1021/ct300849w
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    27
    Parametrization and Benchmark of DFTB3 for Organic Molecules
    Gaus, Michael; Goez, Albrecht; Elstner, Marcus
    Journal of Chemical Theory and Computation (2013), 9 (1), 338-354CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    DFTB3 is a recent extension of the self-consistent-charge d.-functional tight-binding method (SCC-DFTB) and derived from a third order expansion of the d. functional theory (DFT) total energy around a given ref. d. Being applied in combination with the parametrization of its predecessor (MIO), DFTB3 improves for hydrogen binding energies, proton affinities, and hydrogen transfer barriers. In the present study, parameters esp. designed for DFTB3 are presented, and its performance is evaluated for small org. mols. focusing on thermochem., geometries, and vibrational frequencies from our own and several databases from literature. The new parameters remove significant overbinding errors, reduce errors for geometries of noncovalent interactions, and improve the overall performance.
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    Gaus, M.; Lu, X.; Elstner, M.; Cui, Q. Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications. J. Chem. Theory Comput. 2014, 10 (4), 1518– 1537,  DOI: 10.1021/ct401002w
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    28
    Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications
    Gaus, Michael; Lu, Xiya; Elstner, Marcus; Cui, Qiang
    Journal of Chemical Theory and Computation (2014), 10 (4), 1518-1537CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We report the parametrization of the approx. d. functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of org. and biol. relevant mols. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of mols. of biol. relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these mols.; vibrational frequencies are also examd., although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, esp. for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant redn. of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calcns., DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination no. of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary soln.; this suggests that the current DFTB3 methodol. has limited transferability for complex phosphorus chem. at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodol. are needed for a reliable method that describes phosphorus chem. without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calcns. for studying phosphorus/sulfur chem. in condensed phase systems, esp. as a low-level method that drives the sampling in a dual-level QM/MM framework.
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    Laio, A.; Parrinello, M. Escaping free-energy minima. Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (20), 12562– 12566,  DOI: 10.1073/pnas.202427399
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    29
    Escaping free-energy minima
    Laio, Alessandro; Parrinello, Michele
    Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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    Grimme, S. Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations. J. Chem. Theory Comput. 2019, 15 (5), 2847– 2862,  DOI: 10.1021/acs.jctc.9b00143
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    30
    Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations
    Grimme, Stefan
    Journal of Chemical Theory and Computation (2019), 15 (5), 2847-2862CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The semiempirical tight-binding based quantum chem. method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chem. compd., conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chem. reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the at. RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approx. character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, d. functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized mols. with a few hundred atoms. Furthermore, the underlying potential energy surface for mols. contg. almost all elements (Z = 1-86) is globally consistent including the covalent dissocn. process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decompn., ethyne oligomerization, the oxidn. of hydrocarbons (by oxygen and a P 450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramol. cyclization reaction are shown. For typical conformational search problems of org. drug mols., the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.
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    Kaczor, A.; Reva, I. D.; Proniewicz, L. M.; Fausto, R. Importance of Entropy in the Conformational Equilibrium of Phenylalanine: A Matrix-Isolation Infrared Spectroscopy and Density Functional Theory Study. J. Phys. Chem. A 2006, 110 (7), 2360– 2370,  DOI: 10.1021/jp0550715
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    Importance of Entropy in the Conformational Equilibrium of Phenylalanine: A Matrix-Isolation Infrared Spectroscopy and Density Functional Theory Study
    Kaczor, A.; Reva, I. D.; Proniewicz, L. M.; Fausto, R.
    Journal of Physical Chemistry A (2006), 110 (7), 2360-2370CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The conformational behavior and IR spectrum of L-phenylalanine were studied by matrix-isolation IR spectroscopy and DFT [B3LYP/6-311++G(d,p)] calcns. The fourteen most stable structures were predicted to differ in energy by less than 10 kJ mol-1, eight of them with abundances higher than 5% at the temp. of evapn. of the compd. (423 K). Exptl. results suggest that six conformers contribute to the spectrum of the isolated compd., whereas two conformers (IIb3 and IIIb3) relax in matrix to a more stable form (IIb2) due to low energy barriers for conformational isomerization (conformational cooling). The two lowest-energy conformers (Ib1, Ia) differ only in the arrangement of the amino acid group relative to the Ph ring; they exhibit a relatively strong stabilizing intramol. hydrogen bond of the O-H···N type and the carboxylic group in the trans configuration (O:C-O-H dihedral angle ca. 180°). Type II conformers have a weaker H-bond of the N-H···O=C type, but they bear the more favorable cis arrangement of the carboxylic group. Being considerably more flexible, type II conformers are stabilized by entropy and the relative abundances of two conformers of this type (IIb2 and IIc1) are shown to significantly increase with temp. due to entropic stabilization. At 423 K, these conformers are found to be the first and third most abundant species present in the conformational equil., with relative populations of ca. 15% each, whereas their populations could be expected to be only ca. 5% if entropy effects were not taken into consideration. Indeed, phenylalanine can be considered a notable example of a mol. where entropy plays an essential role in detg. the relative abundance of the possible low-energy conformational states and then, the thermodn. of the compd., even at moderate temps. Upon UV irradn. (λ > 235 nm) of the matrix-isolated compd., unimol. photodecompn. of phenylalanine is obsd. with prodn. of CO2 and phenethylamine.
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    Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N. Bifurcations on Potential Energy Surfaces of Organic Reactions. Angew. Chem., Int. Ed. 2008, 47 (40), 7592– 7601,  DOI: 10.1002/anie.200800918
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    Bifurcations on potential energy surfaces of organic reactions
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    Angewandte Chemie, International Edition (2008), 47 (40), 7592-7601CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy min. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Mini review covers recent investigations of org. reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect exptl. observables such as kinetic isotope effects and product distributions.
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    Rehbein, J.; Carpenter, B. K. Do We Fully Understand What Controls Chemical Selectivity?. Phys. Chem. Chem. Phys. 2011, 13 (47), 20906,  DOI: 10.1039/c1cp22565k
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    Do we fully understand what controls chemical selectivity?
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    Reaction rates and product selectivity of kinetically controlled reactions are not always sufficiently described by std. RRKM or TST theory. Reactions taking place on potential energy surfaces featuring a valley ridge inflection point belong to this class of reactions. Though various research groups could show that reaction path bifurcations are far from being an exception in org. reactions the underlying principles that govern product distributions of those bifurcating reaction pathways are yet not fully understood. This Perspective has the intention to provide an overview of how far our understanding and the development of the theor. foundation have progressed.
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    Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. Methylhydroxycarbene: Tunneling Control of a Chemical Reaction. Science 2011, 332 (6035), 1300– 1303,  DOI: 10.1126/science.1203761
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    Methylhydroxycarbene: Tunneling Control of a Chemical Reaction
    Schreiner, Peter R.; Reisenauer, Hans Peter; Ley, David; Gerbig, Dennis; Wu, Chia-Hua; Allen, Wesley D.
    Science (Washington, DC, United States) (2011), 332 (6035), 1300-1303CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Chem. reactivity is conventionally understood in broad terms of kinetic vs. thermodn. control, wherein the decisive factor is the lowest activation barrier among the various reaction paths or the lowest free energy of the final products, resp. We demonstrate that quantum-mech. tunneling can supersede traditional kinetic control and direct a reaction exclusively to a product whose reaction path has a higher barrier. Specifically, we prepd. methylhydroxycarbene (H3C-C-OH) via vacuum pyrolysis of pyruvic acid at about 1200 K (K), followed by argon matrix trapping at 11 K. The previously elusive carbene, characterized by UV and IR spectroscopy as well as exacting quantum-mech. computations, undergoes a facile [1,2]hydrogen shift to acetaldehyde via tunneling under a barrier of 28.0 kcal per mol (kcal mol-1), with a half-life of around 1 h. The analogous isomerization to vinyl alc. has a substantially lower barrier of 22.6 kcal mol-1 but is precluded at low temp. by the greater width of the potential energy profile for tunneling.
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    Plata, R. E.; Singleton, D. A. A Case Study of the Mechanism of Alcohol-Mediated Morita Baylis-Hillman Reactions. The Importance of Experimental Observations. J. Am. Chem. Soc. 2015, 137 (11), 3811– 3826,  DOI: 10.1021/ja5111392
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    A Case Study of the Mechanism of Alcohol-Mediated Morita Baylis-Hillman Reactions. The Importance of Experimental Observations
    Plata, R. Erik; Singleton, Daniel A.
    Journal of the American Chemical Society (2015), 137 (11), 3811-3826CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The mechanism of the Morita Baylis-Hillman reaction has been heavily studied in the literature, and a long series of computational studies have defined complete theor. energy profiles in these reactions. We employ here a combination of mechanistic probes, including the observation of intermediates, the independent generation and partitioning of intermediates, thermodn. and kinetic measurements on the main reaction and side reactions, isotopic incorporation from solvent, and kinetic isotope effects, to define the mechanism and an exptl. mechanistic free-energy profile for a prototypical Morita Baylis-Hillman reaction in methanol. The results are then used to critically evaluate the ability of computations to predict the mechanism. The most notable prediction of the many computational studies, that of a proton-shuttle pathway, is refuted in favor of a simple but computationally intractable acid-base mechanism. Computational predictions vary vastly, and it is not clear that any significant accurate information that was not already apparent from expt. could have been garnered from computations. With care, entropy calcns. are only a minor contributor to the larger computational error, while literature entropy-correction processes lead to absurd free-energy predictions. The computations aid in interpreting observations but fail utterly as a replacement for expt.
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    Fukunishi, H.; Watanabe, O.; Takada, S. On the Hamiltonian Replica Exchange Method for Efficient Sampling of Biomolecular Systems: Application to Protein Structure Prediction. J. Chem. Phys. 2002, 116 (20), 9058– 9067,  DOI: 10.1063/1.1472510
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    On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction
    Fukunishi, Hiroaki; Watanabe, Osamu; Takada, Shoji
    Journal of Chemical Physics (2002), 116 (20), 9058-9067CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Motivated by the protein structure prediction problem, we develop two variants of the Hamiltonian replica exchange methods (REMs) for efficient configuration sampling, (1) the scaled hydrophobicity REM and (2) the phantom chain REM, and compare their performance with the ordinary REM. We first point out that the ordinary REM has a shortage for the application to large systems such as biomols. and that the Hamiltonian REM, an alternative formulation of the REM, can give a remedy for it. We then propose two examples of the Hamiltonian REM that are suitable for a coarse-grained protein model. (1) The scaled hydrophobicity REM preps. replicas that are characterized by various strengths of hydrophobic interaction. The strongest interaction that mimics aq. soln. environment makes proteins folding, while weakened hydrophobicity unfolds proteins as in org. solvent. Exchange between these environments enables proteins to escape from misfolded traps and accelerate conformational search. This resembles the roles of mol. chaperone that assist proteins to fold in vivo. (2) The phantom chain REM uses replicas that allow various degrees of at. overlaps. By allowing at. overlap in some of replicas, the peptide chain can cross over itself, which can accelerate conformation sampling. Using a coarse-gained model we developed, we compute equil. probability distributions for poly-alanine 16-mer and for a small protein by these REMs and compare the accuracy of the results. We see that the scaled hydrophobicity REM is the most efficient method among the three REMs studied.
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    Okur, A.; Roe, D. R.; Cui, G.; Hornak, V.; Simmerling, C. Improving Convergence of Replica Exchange Simulations through Coupling to a High-Temperature Structure Reservoir. J. Chem. Theory Comput. 2007, 3 (2), 557– 568,  DOI: 10.1021/ct600263e
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    Improving Convergence of Replica-Exchange Simulations through Coupling to a High-Temperature Structure Reservoir
    Okur, Asim; Roe, Daniel R.; Cui, Guanglei; Hornak, Viktor; Simmerling, Carlos
    Journal of Chemical Theory and Computation (2007), 3 (2), 557-568CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Parallel tempering or replica-exchange mol. dynamics (REMD) significantly increases the efficiency of conformational sampling for complex mol. systems. However, obtaining converged data with REMD remains challenging, esp. for large systems with complex topologies. We propose a new variant to REMD where the replicas are also permitted to exchange with an ensemble of structures that have been generated in advance using high-temp. MD simulations, similar in spirit to J-walking methods. We tested this approach on two non-trivial model systems, a β-hairpin and a 3-stranded β-sheet and compared the results to those obtained from very long ( > 100 ns) std. REMD simulations. The resulting ensembles were indistinguishable, including relative populations of different conformations on the unfolded state. The use of the reservoir is shown to significantly reduce the time required for convergence.
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    Brémond, É.; Golubev, N.; Steinmann, S. N.; Corminboeuf, C. How Important Is Self-Consistency for the dDsC Density Dependent Dispersion Correction?. J. Chem. Phys. 2014, 140, 18A516,  DOI: 10.1063/1.4867195
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    Petraglia, R.; Steinmann, S. N.; Corminboeuf, C. A Fast Charge-Dependent Atom-Pairwise Dispersion Correction for DFTB3. Int. J. Quantum Chem. 2015, 115 (18), 1265– 1272,  DOI: 10.1002/qua.24887
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    Petraglia, Riccardo; Steinmann, Stephan N.; Corminboeuf, Clemence
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    Org. electronic materials remarkably illustrate the importance of the "weak" dispersion interactions that are neglected in the most cost-efficient electronic structure approaches. This work introduces a fast atom-pairwise dispersion correction, dDMC that is compatible with the most recent variant of self-consistent charge d. functional tight binding (SCC-DFTB). The emphasis is placed on improving the description of π-π stacked motifs featuring sulfur-contg. mols. that are known to be esp. challenging for DFTB. Our scheme relies upon the use of Mulliken charges using minimal basis set that are readily available from the DFTB computations at no addnl. cost. The performance and efficiency of the dDMC correction are validated on examples targeting energies, geometries, and mol. dynamic trajectories.
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    Mashraqui, S. H.; Sangvikar, Y. S.; Meetsma, A. Synthesis and Structures of Thieno[2,3-b]Thiophene Incorporated [3.3]Dithiacyclophanes. Enhanced First Hyperpolarizability in an Unsymmetrically Polarized Cyclophane. Tetrahedron Lett. 2006, 47 (31), 5599– 5602,  DOI: 10.1016/j.tetlet.2006.05.098
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    Synthesis and structures of thieno[2,3-b]thiophene incorporated [3.3]dithiacyclophanes. Enhanced first hyperpolarizability in an unsymmetrically polarized cyclophane
    Mashraqui, Sabir H.; Sangvikar, Yogesh S.; Meetsma, Auke
    Tetrahedron Letters (2006), 47 (31), 5599-5602CODEN: TELEAY; ISSN:0040-4039. (Elsevier B.V.)
    Dithiacyclophanes incorporating thieno[2,3-b]thiophene have been synthesized, in order to investigate the nonlinear optical properties of donor-acceptor cyclophane I. I displayed significantly higher first hyperpolarizability β (21.6 × 10-30 esu) compared to model II (9.58 × 10-30esu). Relatively higher β in I presumably arises from an extra electron redistribution arising from through-space charge transfer, a feature lacking in II. Moreover, the thermal decompn. temp. of I (300 °C) is higher than that reported for the NLO prototype DANS (295 °C).
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    Conformational study of cinchona alkaloids. A combined NMR, molecular mechanics and x-ray approach
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    Journal of the American Chemical Society (1989), 111 (21), 8069-76CODEN: JACSAT; ISSN:0002-7863.
    A conformational study of cinchona alkaloids is presented. The conformations of the alkaloids in soln. have been detd. by NOE difference and NOESY NMR technique. The necessary chem. shift assignments of the cinchona alkaloids have been elucidated by combination of COSY and NOE NMR expts. Min. energy conformations of the alkaloids have been calcd. by mol. mechanics. The first known x-ray structure of a cinchona alkaloid with a closed conformation is presented. Finally, the conformational effects of protonation and complexation on the tertiary nitrogen of the quinuclidine ring have been investigated.
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    Primary-amine-catalyzed enantioselective intramolecular aldolizations
    Zhou, Jian; Wakchaure, Vijay; Kraft, Philip; List, Benjamin
    Angewandte Chemie, International Edition (2008), 47 (40), 7656-7658CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Aldol cyclodehydration of 4-substituted-2,6-heptanediones leads to enantiomerically enriched 5-substituted-3-methyl-2-cyclohexene-1-ones, which serve as perfume ingredients and valuable synthetic building blocks. Primary amines derived from cinchona alkaloids in combination with acetic acid are efficient catalysts for this transformation, which deliver both enantiomers of the celery ketone.
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    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 (5), 2087– 2096,  DOI: 10.1021/acs.jctc.5b00099
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    Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach
    Ramakrishnan, Raghunathan; Dral, Pavlo O.; Rupp, Matthias; von Lilienfeld, O. Anatole
    Journal 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.
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    Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen Bonding and Stacking Interactions of Nucleic Acid Base Pairs: A Density-Functional-Theory Based Treatment. J. Chem. Phys. 2001, 114 (12), 5149– 5155,  DOI: 10.1063/1.1329889
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    Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment
    Elstner, Marcus; Hobza, Pavel; Frauenheim, Thomas; Suhai, Sandor; Kaxiras, Efthimios
    Journal of Chemical Physics (2001), 114 (12), 5149-5155CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We extend an approx. d. functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irresp. of the correlation function applied. An empirical formula, consisting of an R-6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coeff., which is calcd. from exptl. at. polarizabilities, can be consistently added to the total energy expression of the method. We apply this approx. DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.
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    Aradi, B.; Hourahine, B.; Frauenheim, T. DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method. J. Phys. Chem. A 2007, 111 (26), 5678– 5684,  DOI: 10.1021/jp070186p
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    DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method
    Aradi, B.; Hourahine, B.; Frauenheim, Th.
    Journal of Physical Chemistry A (2007), 111 (26), 5678-5684CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    A new Fortran 95 implementation of the DFTB (d. functional-based tight binding) method was developed, where the sparsity of the DFTB system of equations was exploited. Conventional dense algebra was used only to evaluate the eigenproblems of the system and long-range Coulombic terms, but drop-in O(N) or O(N2) modules were planned to replace the small code sections that these entail. The developed sparse storage structure is discussed in detail, and a short overview of other features of the new code is given.
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    Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138 (3), 034106,  DOI: 10.1063/1.4773581
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    An efficient and near linear scaling pair natural orbital based local coupled cluster method
    Riplinger, Christoph; Neese, Frank
    Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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    Neese, F.; Valeev, E. F. Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?. J. Chem. Theory Comput. 2011, 7 (1), 33– 43,  DOI: 10.1021/ct100396y
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    Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?
    Neese, Frank; Valeev, Edward F.
    Journal of Chemical Theory and Computation (2011), 7 (1), 33-43CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The performance of several families of basis sets for correlated wave function calcns. on mols. is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of at. natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in at. multireference av. coupled pair functional (MR-ACPF) calcns. Segmented basis sets optimized for SCF calcns. (def2-SVP, def2-TZVPP, and def2-QZVPP as well as "pc-n", n = 1, 2, 3) were also tested. Ref. Hartree-Fock energies are detd. with the uncontracted aug-cc-pV6Z basis set for a set of 21 small mols. built from H, B, C, N, O, and F. Ref. coupled cluster CCSD(T) correlation energies were detd. from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3 at each cardinal no. In addn., the ano-pVXZ consistently recovers more correlation energy than their competitors at each cardinal no. The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated. A conclusion by Truhlar is confirmed that the optimum exponent for correlation energy extrapolations at the DZ/TZ level is ∼2.4. All TZ/QZ basis set pairs lead to an optimum exponent close to the expected value of 3. The SCF energy extrapolation proposed by Petersson and co-workers is found to be effective. At the DZ/TZ level, errors in total energies of less than 2 mEh are found for the test set, while at the TZ/QZ level one obtains the total energies within ∼0.3 mEh of the basis set limit. For extrapolation, the "cc" and "ano" bases are found to be similarly successful. Extrapolation results were compared to explicitly correlated calcns. with dedicated basis sets (cc-pVXZ-F12) as well as the ano-pVXZ bases. It is found that the ano-pVXZ + basis sets perform as well as the cc-pVXZ-F12 family (both are of comparable size); addnl. improvement should be possible by reoptimizing the ANO basis sets for explicitly correlated calcns. The error of the extrapolated energies is about 2-3 times smaller than what was found in the explicitly correlated calcns. However, the error in the explicitly correlated calcns. is more systematic, and hence the same conclusion may not hold for the computation of energy differences.
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    A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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    Dunning, Thom H., Jr.
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    Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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    Kendall, Rick A.; Dunning, Thom H., Jr.; Harrison, Robert J.
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    The authors describe a reliable procedure for calcg. the electron affinity of an atom and present results for H, B, C, O, and F (H is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the at. anion coupled with a straightforward, uniform expansion of the ref. space for multireference singles and doubles configuration-interaction (MRSD-CI) calcns. A comparison is given with previous results and with corresponding full CI calcns. The most accurate EAs obtained from the MRSD-CI calcns. are (with exptl. values in parentheses): H 0.740 eV (0.754), B 0.258 (0.277), C 1.245 (1.263), O 1.384 (1.461), and F 3.337 (3.401). The EAs obtained from the MR-SDCI calcns. differ by less than 0.03 eV from those predicted by the full CI calcns.
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    Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0Model. J. Chem. Phys. 1999, 110 (13), 6158– 6170,  DOI: 10.1063/1.478522
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    Journal of Chemical Physics (1999), 110 (13), 6158-6170CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present an anal. of the performances of a parameter free d. functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amt. of exact exchange. The results obtained for structural, thermodn., kinetic and spectroscopic (magnetic, IR and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chem. and condensed matter physics.
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    Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104,  DOI: 10.1063/1.3382344
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    Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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    Ufimtsev, I. S.; Martinez, T. J. Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics. J. Chem. Theory Comput. 2009, 5 (10), 2619– 2628,  DOI: 10.1021/ct9003004
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    Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics
    Ufimtsev, Ivan S.; Martinez, Todd J.
    Journal of Chemical Theory and Computation (2009), 5 (10), 2619-2628CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We demonstrate that a video gaming machine contg. two consumer graphical cards can outpace a state-of-the-art quad-core processor workstation by a factor of more than 180× in Hartree-Fock energy + gradient calcns. Such performance makes it possible to run large scale Hartree-Fock and D. Functional Theory calcns., which typically require hundreds of traditional processor cores, on a single workstation. Benchmark Born-Oppenheimer mol. dynamics simulations are performed on two mol. systems using the 3-21G basis set - a hydronium ion solvated by 30 waters (94 atoms, 405 basis functions) and an aspartic acid mol. solvated by 147 waters (457 atoms, 2014 basis functions). Our GPU implementation can perform 27 ps/day and 0.7 ps/day of ab initio mol. dynamics simulation on a single desktop computer for these systems.
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    Titov, A. V.; Ufimtsev, I. S.; Luehr, N.; Martinez, T. J. Generating Efficient Quantum Chemistry Codes for Novel Architectures. J. Chem. Theory Comput. 2013, 9 (1), 213– 221,  DOI: 10.1021/ct300321a
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    Generating Efficient Quantum Chemistry Codes for Novel Architectures
    Titov, Alexey V.; Ufimtsev, Ivan S.; Luehr, Nathan; Martinez, Todd J.
    Journal of Chemical Theory and Computation (2013), 9 (1), 213-221CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We describe an extension of our graphics processing unit (GPU) electronic structure program TeraChem to include atom-centered Gaussian basis sets with d angular momentum functions. This was made possible by a "meta-programming" strategy that leverages computer algebra systems for the derivation of equations and their transformation to correct code. We generate a multitude of code fragments that are formally math. equiv., but differ in their memory and floating-point operation footprints. We then select between different code fragments using empirical testing to find the highest performing code variant. This leads to an optimal balance of floating-point operations and memory bandwidth for a given target architecture without laborious manual tuning. We show that this approach is capable of similar performance compared to our hand-tuned GPU kernels for basis sets with s and p angular momenta. We also demonstrate that mixed precision schemes (using both single and double precision) remain stable and accurate for mols. with d functions. We provide benchmarks of the execution time of entire SCF calcns. using our GPU code and compare to mature CPU based codes, showing the benefits of the GPU architecture for electronic structure theory with appropriately redesigned algorithms. We suggest that the meta-programming and empirical performance optimization approach may be important in future computational chem. applications, esp. in the face of quickly evolving computer architectures.
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    Pearlman, D. A.; Case, D. A.; Caldwell, J. W.; Ross, W. S.; Cheatham, T. E.; DeBolt, S.; Ferguson, D.; Seibel, G.; Kollman, P. AMBER, a Package of Computer Programs for Applying Molecular Mechanics, Normal Mode Analysis, Molecular Dynamics and Free Energy Calculations to Simulate the Structural and Energetic Properties of Molecules. Comput. Phys. Commun. 1995, 91 (1), 1– 41,  DOI: 10.1016/0010-4655(95)00041-D
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    "AMBER", a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to stimulate the structural and energetic properties of molecules
    Pearlman, David A.; Case, David A.; Caldwell, James W.; Ross, Wilson S.; Cheatham, Thomas E. III; DeBolt, Steve; Ferguson, David; Seibel, George; Kollman, Peter
    Computer Physics Communications (1995), 91 (1-3), 1-42CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
    We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a no. of the powerful tools of modern computational chem.-mol. dynamics and free energy calcns.
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    Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113 (18), 6378– 6396,  DOI: 10.1021/jp810292n
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    Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions
    Marenich, Aleksandr V.; Cramer, Christopher J.; Truhlar, Donald G.
    Journal of Physical Chemistry B (2009), 113 (18), 6378-6396CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We present a new continuum solvation model based on the quantum mech. charge d. of a solute mol. interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "d." to denote that the full solute electron d. is used without defining partial at. charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielec. medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liq. medium for which a few key descriptors are known (in particular, dielec. const., refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the soln. of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calcn. are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent mols. in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality consts. called at. surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aq. ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and DMSO, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaq. org. solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 org. solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic at. Coulomb radii and at. surface tension coeffs.) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calcns. in which the solute is represented by its electron d. in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on av. for ions with either Gaussian03 or GAMESS.
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    Fast and accurate modeling of molecular atomization energies with machine learning
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    Physical Review Letters (2012), 108 (5), 058301/1-058301/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The authors introduce a machine learning model to predict atomization energies of a diverse set of org. mols., based on nuclear charges and at. positions only. The problem of solving the mol. Schrodinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid d.-functional theory. Cross validation over more than seven thousand org. mols. yields a mean abs. error of ∼10 kcal/mol. Applicability is demonstrated for the prediction of mol. atomization potential energy curves.
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    Hansen, K.; Biegler, F.; Ramakrishnan, R.; Pronobis, W.; Von Lilienfeld, O. A.; Müller, K. R.; Tkatchenko, A. Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space. J. Phys. Chem. Lett. 2015, 6 (12), 2326– 2331,  DOI: 10.1021/acs.jpclett.5b00831
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    Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space
    Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; Pronobis, Wiktor; von Lilienfeld, O. Anatole; Mueller, Klaus-Robert; Tkatchenko, Alexandre
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    Simultaneously accurate and efficient prediction of mol. properties throughout chem. compd. space is a crit. ingredient toward rational compd. design in chem. and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to est. atomization and total energies of mols. These methods range from a simple sum over atoms, to addn. of bond energies, to pairwise interat. force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equil. mol. geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calcd. using d. functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the "holy grail" of chem. accuracy of 1 kcal/mol for both equil. and out-of-equil. geometries. This remarkable accuracy is achieved by a vectorized representation of mols. (so-called Bag of Bonds model) that exhibits strong nonlocality in chem. space. In addn., the same representation allows us to predict accurate electronic properties of mols., such as their polarizability and mol. frontier orbital energies.
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This article is cited by 10 publications.

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  • Abstract

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    Figure 1

    Figure 1. (a) Dithiacyclophane and the collective variables used to characterize its global structure: the distance between the center of masses of each cyclic bulk and the angles between the average planes going through them. (b) Cinchona alkaloid organocatalyst and the two dihedral angles used to characterize its global structure.

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    Figure 2

    Figure 2. Mind-map and workflow illustrating the proposed methodology.

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    Figure 3

    Figure 3. Schematic depiction of Hamiltonian reservoir Replica Exchange.

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    Figure 4

    Figure 4. (a) Free energy landscape (DFTB-SK/3OB level) of dithiacyclophane at 300 K (T-RE) projected on the 2D space generated by the collective variables visible in Figure 1a. (b) Projection of the data set made of 1500 dithiacyclophane structures extracted with farthest point sampling from the 300 K canonical ensemble of 40 000 structures and color coded on the basis of the single-point energy difference ΔE = ((DFTB-SK/3OB) – (DLPNO-CCSD(T)/CBS)). The continuous background is plotted using a Gaussian interpolation of the mean energy difference. The smooth histograms were constructed with a Gaussian Kernel Density Estimator (Gaussian KDE) using the SciPy (73) python library.

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    Figure 5

    Figure 5. (a) Free energy landscape (DFTB-SK/3OB level) of the cinchona alkaloid organocatalyst at 300 K projected on the 2D space generated by the collective variables visible in Figure 1b. Constructed with canonical structures generated with T-RE simulations with DFTB-SK as potential energy. (b) Projection of the 1800 data set structures obtained with FPS from a canonical ensemble of 32 000 structures at 300 K canonical ensemble and color coded on the basis of the single point energy difference ΔE = ((DFTB-SK/3OB) – (DLPNO-CCSD(T)/CBS)). (c) Structures representing each of the four conformational regions (i.e., basins).

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    Figure 6

    Figure 6. Comparison between the DFTB-SK electronic energy and the ML-DLPNO-CCSD(T)/CBS predictions (i.e., DFTB-SK + ΔML correction) for the 40 000 structures in the reservoir.

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    Figure 7

    Figure 7. Free energy landscapes at 300 K generated with the potential: (a) DFTB-SK; (b) ML-DLPNO-CCSD(T)/CBS; (c) ML-[PBE0-D3/(6-31G)(SMD Chloroform)]; (d) PBE0-D3/(6-31G); (e) ML-PBE0-D3/(6-31G). (f) Relative free energies by integration within the local minima. (24) The free energies are all given relative to the Disarticulated state except for the solvated system, where the open state is used as a reference. The striped columns correspond to the static relative free energy using the harmonic approximation (for the solvated system the harmonic free energies were computed with the true potential, and not with the machine learning version). All the free energies maps come from resH-RE expect for the direct PBE0, which uses T-RE, as described in the methods section.

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    Figure 8

    Figure 8. Free energy landscapes at 300 K generated with the potential: (a) DFTB-SK; (b) ML-DLPNO-CCSD(T)/CBS; (c) ML-[PBE0-D3/(6-31G)(SMD Chloroform)]. (d) Free energies upon integration within the free energy basins. The free energies are all given relative to the Disarticulated state. The stripped columns are the free energy predictions of the basins using the static free energies using the harmonic correction.

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    1. 1
      Behler, J.; Parrinello, M. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Phys. Rev. Lett. 2007, 98 (14), 146401,  DOI: 10.1103/PhysRevLett.98.146401
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      1
      Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
      Behler, Jorg; Parrinello, Michele
      Physical Review Letters (2007), 98 (14), 146401/1-146401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The accurate description of chem. processes often requires the use of computationally demanding methods like d.-functional theory (DFT), making long simulations of large systems unfeasible. In this Letter we introduce a new kind of neural-network representation of DFT potential-energy surfaces, which provides the energy and forces as a function of all at. positions in systems of arbitrary size and is several orders of magnitude faster than DFT. The high accuracy of the method is demonstrated for bulk silicon and compared with empirical potentials and DFT. The method is general and can be applied to all types of periodic and nonperiodic systems.
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    2. 2
      Behler, J.; Marto crnnák, R.; Donadio, D.; Parrinello, M. Metadynamics Simulations of the High-Pressure Phases of Silicon Employing a High-Dimensional Neural Network Potential. Phys. Rev. Lett. 2008, 100 (18), 185501,  DOI: 10.1103/PhysRevLett.100.185501
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      2
      Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential
      Behler, Joerg; Martonak, Roman; Donadio, Davide; Parrinello, Michele
      Physical Review Letters (2008), 100 (18), 185501/1-185501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We study in a systematic way the complex sequence of the high-pressure phases of silicon obtained upon compression by combining an accurate high-dimensional neural network representation of the d.-functional theory potential energy surface with the metadynamics scheme. Starting from the thermodynamically stable diamond structure at ambient conditions we are able to identify all structural phase transitions up to the highest-pressure fcc phase at about 100 GPa. The results are in excellent agreement with expt. The method developed promises to be of great value in the study of inorg. solids, including those having metallic phases.
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    3. 3
      Khaliullin, R. Z.; Eshet, H.; Kühne, T. D.; Behler, J.; Parrinello, M. Graphite-Diamond Phase Coexistence Study Employing a Neural-Network Mapping of the Ab Initio Potential Energy Surface. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (10), 100103,  DOI: 10.1103/PhysRevB.81.100103
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      3
      Graphite-diamond phase coexistence study employing a neural-network mapping of the ab initio potential energy surface
      Khaliullin, Rustam Z.; Eshet, Hagai; Kuhne, Thomas D.; Behler, Jorg; Parrinello, Michele
      Physical Review B: Condensed Matter and Materials Physics (2010), 81 (10), 100103/1-100103/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      An interat. potential for the diamond and graphite phases of carbon has been created using a neural-network (NN) representation of the ab initio potential energy surface. The NN potential combines the accuracy of a first-principles description of both phases with the efficiency of empirical force fields and allows one to perform a mol.-dynamics study, of ab initio quality, of the thermodn. of graphite-diamond coexistence. Good agreement between the exptl. and calcd. coexistence curves is achieved if nuclear quantum effects are included in the simulation.
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    4. 4
      Khaliullin, R. Z.; Eshet, H.; Kühne, T. D.; Behler, J.; Parrinello, M. Nucleation Mechanism for the Direct Graphite-to-Diamond Phase Transition. Nat. Mater. 2011, 10 (9), 693,  DOI: 10.1038/nmat3078
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      4
      Nucleation mechanism for the direct graphite-to-diamond phase transition
      Khaliullin, Rustam Z.; Eshet, Hagai; Kuehne, Thomas D.; Behler, Joerg; Parrinello, Michele
      Nature Materials (2011), 10 (9), 693-697CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Graphite and diamond have comparable free energies, yet forming diamond from graphite in the absence of a catalyst requires pressures that are significantly higher than those at equil. coexistence. At lower temps., the formation of the metastable hexagonal polymorph of diamond is favored instead of the more stable cubic diamond. These phenomena cannot be explained by the concerted mechanism suggested in previous theor. studies. Using an ab initio quality neural-network potential, we carried out a large-scale study of the graphite-to-diamond transition assuming that it occurs through nucleation. The nucleation mechanism accounts for the obsd. phenomenol. and reveals its microscopic origins. We demonstrate that the large lattice distortions that accompany the formation of diamond nuclei inhibit the phase transition at low pressure, and direct it towards the hexagonal diamond phase at higher pressure. The proposed nucleation mechanism should improve our understanding of structural transformations in a wide range of carbon-based materials.
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    5. 5
      Eshet, H.; Khaliullin, R. Z.; Kühne, T. D.; Behler, J.; Parrinello, M. Ab Initio Quality Neural-Network Potential for Sodium. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (18), 184107,  DOI: 10.1103/PhysRevB.81.184107
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      5
      Ab initio quality neural-network potential for sodium
      Eshet, Hagai; Khaliullin, Rustam Z.; Kuhne, Thomas D.; Behler, Jorg; Parrinello, Michele
      Physical Review B: Condensed Matter and Materials Physics (2010), 81 (18), 184107/1-184107/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      An interat. potential for high-pressure high-temp. (HPHT) cryst. and liq. phases of sodium is created using a neural-network (NN) representation of the ab initio potential-energy surface. It is demonstrated that the NN potential provides an ab initio quality description of multiple properties of liq. sodium and bcc, fcc, and cI16 crystal phases in the P-T region up to 120 GPa and 1200 K. The unique combination of computational efficiency of the NN potential and its ability to reproduce quant. exptl. properties of sodium in the wide P-T range enables mol.-dynamics simulations of physicochem. processes in HPHT sodium of unprecedented quality.
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    6. 6
      Gastegger, M.; Kauffmann, C.; Behler, J.; Marquetand, P. Comparing the Accuracy of High-Dimensional Neural Network Potentials and the Systematic Molecular Fragmentation Method: A Benchmark Study for All-Trans Alkanes. J. Chem. Phys. 2016, 144 (19), 194110,  DOI: 10.1063/1.4950815
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      6
      Comparing the accuracy of high-dimensional neural network potentials and the systematic molecular fragmentation method: A benchmark study for all-trans alkanes
      Gastegger, Michael; Kauffmann, Clemens; Behler, Joerg; Marquetand, Philipp
      Journal of Chemical Physics (2016), 144 (19), 194110/1-194110/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Many approaches, which have been developed to express the potential energy of large systems, exploit the locality of the at. interactions. A prominent example is the fragmentation methods in which the quantum chem. calcns. are carried out for overlapping small fragments of a given mol. that are then combined in a second step to yield the system's total energy. Here we compare the accuracy of the systematic mol. fragmentation approach with the performance of high-dimensional neural network (HDNN) potentials introduced by Behler and Parrinello. HDNN potentials are similar in spirit to the fragmentation approach in that the total energy is constructed as a sum of environment-dependent at. energies, which are derived indirectly from electronic structure calcns. As a benchmark set, we use all-trans alkanes contg. up to eleven carbon atoms at the coupled cluster level of theory. These mols. have been chosen because they allow to extrapolate reliable ref. energies for very long chains, enabling an assessment of the energies obtained by both methods for alkanes including up to 10 000 carbon atoms. We find that both methods predict high-quality energies with the HDNN potentials yielding smaller errors with respect to the coupled cluster ref. (c) 2016 American Institute of Physics.
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    7. 7
      Gastegger, M.; Behler, J.; Marquetand, P. Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra. Chem. Sci. 2017, 8 (10), 6924– 6935,  DOI: 10.1039/C7SC02267K
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      7
      Machine learning molecular dynamics for the simulation of infrared spectra
      Gastegger, Michael; Behler, Joerg; Marquetand, Philipp
      Chemical Science (2017), 8 (10), 6924-6935CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      A review. Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate mol. IR spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects - typically neglected by conventional quantum chem. approaches - we base our machine learning strategy on ab initio mol. dynamics simulations. While these simulations are usually extremely time consuming even for small mols., we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a mol. dipole moment model based on environment dependent neural network charges and combine it with the neural network potential approach of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of IR spectra based on only a few hundreds of electronic structure ref. points. This is made possible through the use of mol. forces during neural network potential training and the introduction of a fully automated sampling scheme. We demonstrate the power of our machine learning approach by applying it to model the IR spectra of a methanol mol., n-alkanes contg. up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all of these case studies we find an excellent agreement between the IR spectra predicted via machine learning models and the resp. theor. and exptl. spectra.
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    8. 8
      Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian Approximation Potentials: the Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett. 2010, 104 (13), 136403,  DOI: 10.1103/PhysRevLett.104.136403
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      8
      Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
      Bartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, Gabor
      Physical Review Letters (2010), 104 (13), 136403/1-136403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We introduce a class of interat. potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mech. calcns. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calcg. properties at high temps. Using the interat. potential to generate the long mol. dynamics trajectories required for such calcns. saves orders of magnitude in computational cost.
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    9. 9
      Bartók, A. P.; De, S.; Poelking, C.; Bernstein, N.; Kermode, J. R.; Csányi, G.; Ceriotti, M. Machine Learning Unifies the Modeling of Materials and Molecules. Sci. Adv. 2017, 3 (12), e1701816  DOI: 10.1126/sciadv.1701816
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      9
      Machine learning unifies the modeling of materials and molecules
      Bartok, Albert P.; De, Sandip; Poelking, Carl; Bernstein, Noam; Kermode, James R.; Csanyi, Gabor; Ceriotti, Michele
      Science Advances (2017), 3 (12), e1701816/1-e1701816/8CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
      Detg. the stability of mols. and condensed phases is the cornerstone of atomistic modeling, underpinning our understanding of chem. and materials properties and transformations. We show that a machine-learning model, based on a local description of chem. environments and Bayesian statistical learning, provides a unified framework to predict at.-scale properties. It captures the quantum mech. effects governing the complex surface reconstructions of silicon, predicts the stability of different classes of mols. with chem. accuracy, and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of our framework provide new insight into the potential energy surface of materials and mols.
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    10. 10
      Caro, M. A.; Deringer, V. L.; Koskinen, J.; Laurila, T.; Csányi, G. Growth Mechanism and Origin of High Sp3 Content in Tetrahedral Amorphous Carbon. Phys. Rev. Lett. 2018, 120, 166101,  DOI: 10.1103/PhysRevLett.120.166101
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      10
      Growth Mechanism and Origin of High sp3 Content in Tetrahedral Amorphous Carbon
      Caro, Miguel A.; Deringer, Volker L.; Koskinen, Jari; Laurila, Tomi; Csanyi, Gabor
      Physical Review Letters (2018), 120 (16), 166101CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      We study the deposition of tetrahedral amorphous carbon (ta-C) films from mol. dynamics simulations based on a machine-learned interat. potential trained from d.-functional theory data. For the first time, the high sp3 fractions in excess of 85% obsd. exptl. are reproduced by means of computational simulation, and the deposition energy dependence of the film's characteristics is also accurately described. High confidence in the potential and direct access to the at. interactions allow us to infer the microscopic growth mechanism in this material. While the widespread view is that ta-C grows by "subplantation," we show that the so-called "peening" model is actually the dominant mechanism responsible for the high sp3 content. We show that pressure waves lead to bond rearrangement away from the impact site of the incident ion, and high sp3 fractions arise from a delicate balance of transitions between three- and fourfold coordinated carbon atoms. These results open the door for a microscopic understanding of carbon nanostructure formation with an unprecedented level of predictive power.
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    11. 11
      Deringer, V. L.; Bernstein, N.; Bartók, A. P.; Cliffe, M. J.; Kerber, R. N.; Marbella, L. E.; Grey, C. P.; Elliott, S. R.; Csányi, G. Realistic Atomistic Structure of Amorphous Silicon from Machine-Learning-Driven Molecular Dynamics. J. Phys. Chem. Lett. 2018, 9 (11), 2879– 2885,  DOI: 10.1021/acs.jpclett.8b00902
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      11
      Realistic Atomistic Structure of Amorphous Silicon from Machine-Learning-Driven Molecular Dynamics
      Deringer, Volker L.; Bernstein, Noam; Bartok, Albert P.; Cliffe, Matthew J.; Kerber, Rachel N.; Marbella, Lauren E.; Grey, Clare P.; Elliott, Stephen R.; Csanyi, Gabor
      Journal of Physical Chemistry Letters (2018), 9 (11), 2879-2885CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Amorphous silicon (a-Si) is a widely studied noncryst. material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained using a machine-learning-based interat. potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 1011 K/s (i.e., on the 10 ns time scale), contains less than 2% defects, and agrees with expts. regarding excess energies, diffraction data, and 29Si NMR chem. shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with expts. to date. Our study demonstrates the broader impact of machine-learning potentials for elucidating structures and properties of technol. important amorphous materials.
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    12. 12
      Hu, D.; Xie, Y.; Li, X.; Li, L.; Lan, Z. Inclusion of Machine Learning Kernel Ridge Regression Potential Energy Surfaces in On-the-Fly Nonadiabatic Molecular Dynamics Simulation. J. Phys. Chem. Lett. 2018, 9 (11), 2725– 2732,  DOI: 10.1021/acs.jpclett.8b00684
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      12
      Inclusion of Machine Learning Kernel Ridge Regression Potential Energy Surfaces in On-the-Fly Nonadiabatic Molecular Dynamics Simulation
      Hu, Deping; Xie, Yu; Li, Xusong; Li, Lingyue; Lan, Zhenggang
      Journal of Physical Chemistry Letters (2018), 9 (11), 2725-2732CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      We discuss a theor. approach that employs machine learning potential energy surfaces (ML-PESs) in the nonadiabatic dynamics simulation of polyat. systems by taking 6-aminopyrimidine as a typical example. The Zhu-Nakamura theory is employed in the surface hopping dynamics, which does not require the calcn. of the nonadiabatic coupling vectors. The kernel ridge regression is used in the construction of the adiabatic PESs. In the nonadiabatic dynamics simulation, we use ML-PESs for most geometries and switch back to the electronic structure calcns. for a few geometries either near the S1/S0 conical intersections or in the out-of-confidence regions. The dynamics results based on ML-PESs are consistent with those based on CASSCF PESs. The ML-PESs are further used to achieve the highly efficient massive dynamics simulations with a large no. of trajectories. This work displays the powerful role of ML methods in the nonadiabatic dynamics simulation of polyat. systems.
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    13. 13
      Smith, J. S.; Isayev, O.; Roitberg, A. E. ANI-1: An Extensible Neural Network Potential with DFT Accuracy at Force Field Computational Cost. Chem. Sci. 2017, 8 (4), 3192– 3203,  DOI: 10.1039/C6SC05720A
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      13
      ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost
      Smith, J. S.; Isayev, O.; Roitberg, A. E.
      Chemical Science (2017), 8 (4), 3192-3203CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      A review. Deep learning is revolutionizing many areas of science and technol., esp. image, text, and speech recognition. In this paper, we demonstrate how a deep neural network (NN) trained on quantum mech. (QM) DFT calcns. can learn an accurate and transferable potential for org. mols. We introduce ANAKIN-ME (Accurate NeurAl networK engINe for Mol. Energies) or ANI for short. ANI is a new method designed with the intent of developing transferable neural network potentials that utilize a highly-modified version of the Behler and Parrinello symmetry functions to build single-atom at. environment vectors (AEV) as a mol. representation. AEVs provide the ability to train neural networks to data that spans both configurational and conformational space, a feat not previously accomplished on this scale. We utilized ANI to build a potential called ANI-1, which was trained on a subset of the GDB databases with up to 8 heavy atoms in order to predict total energies for org. mols. contg. four atom types: H, C, N, and O. To obtain an accelerated but phys. relevant sampling of mol. potential surfaces, we also proposed a Normal Mode Sampling (NMS) method for generating mol. conformations. Through a series of case studies, we show that ANI-1 is chem. accurate compared to ref. DFT calcns. on much larger mol. systems (up to 54 atoms) than those included in the training data set.
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    14. 14
      Smith, J. S.; Nebgen, B.; Lubbers, N.; Isayev, O.; Roitberg, A. E. Less Is More: Sampling Chemical Space with Active Learning. J. Chem. Phys. 2018, 148 (24), 241733,  DOI: 10.1063/1.5023802
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      14
      Less is more: Sampling chemical space with active learning
      Smith, Justin S.; Nebgen, Ben; Lubbers, Nicholas; Isayev, Olexandr; Roitberg, Adrian E.
      Journal of Chemical Physics (2018), 148 (24), 241733/1-241733/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The development of accurate and transferable machine learning (ML) potentials for predicting mol. energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chem. space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of org. mols. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single mols. or materials, while remaining applicable to the general class of org. mols. composed of the elements CHNO. (c) 2018 American Institute of Physics.
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    15. 15
      Smith, J. S.; Nebgen, B. T.; Zubatyuk, R.; Lubbers, N.; Devereux, C.; Barros, K.; Tretiak, S.; Isayev, O.; Roitberg, A. E. Approaching Coupled Cluster Accuracy with a General-Purpose Neural Network Potential through Transfer Learning. Nat. Commun. 2019, 10 (1), 2903,  DOI: 10.1038/s41467-019-10827-4
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      15
      Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning
      Smith Justin S; Devereux Christian; Roitberg Adrian E; Smith Justin S; Nebgen Benjamin T; Zubatyuk Roman; Lubbers Nicholas; Barros Kipton; Tretiak Sergei; Smith Justin S; Lubbers Nicholas; Nebgen Benjamin T; Tretiak Sergei; Zubatyuk Roman; Isayev Olexandr
      Nature communications (2019), 10 (1), 2903 ISSN:.
      Computational modeling of chemical and biological systems at atomic resolution is a crucial tool in the chemist's toolset. The use of computer simulations requires a balance between cost and accuracy: quantum-mechanical methods provide high accuracy but are computationally expensive and scale poorly to large systems, while classical force fields are cheap and scalable, but lack transferability to new systems. Machine learning can be used to achieve the best of both approaches. Here we train a general-purpose neural network potential (ANI-1ccx) that approaches CCSD(T)/CBS accuracy on benchmarks for reaction thermochemistry, isomerization, and drug-like molecular torsions. This is achieved by training a network to DFT data then using transfer learning techniques to retrain on a dataset of gold standard QM calculations (CCSD(T)/CBS) that optimally spans chemical space. The resulting potential is broadly applicable to materials science, biology, and chemistry, and billions of times faster than CCSD(T)/CBS calculations.
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    16. 16
      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 (5), e1603015  DOI: 10.1126/sciadv.1603015
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      16
      Machine learning of accurate energy-conserving molecular force fields
      Chmiela, Stefan; Tkatchenko, Alexandre; Sauceda, Huziel E.; Poltavsky, Igor; Schuett, Kristof T.; Mueller, Klaus-Robert
      Science 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.
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    17. 17
      Chmiela, S.; Sauceda, H. E.; Müller, K. R.; Tkatchenko, A. Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields. Nat. Commun. 2018, 9 (1), 3887,  DOI: 10.1038/s41467-018-06169-2
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      17
      Towards exact molecular dynamics simulations with machine-learned force fields
      Chmiela Stefan; Muller Klaus-Robert; Sauceda Huziel E; Muller Klaus-Robert; Muller Klaus-Robert; Tkatchenko Alexandre
      Nature communications (2018), 9 (1), 3887 ISSN:.
      Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.
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    18. 18
      Sauceda, H. E.; Chmiela, S.; Poltavsky, I.; Müller, K. R.; Tkatchenko, A. Molecular Force Fields with Gradient-Domain Machine Learning: Construction and Application to Dynamics of Small Molecules with Coupled Cluster Forces. J. Chem. Phys. 2019, 150 (11), 114102,  DOI: 10.1063/1.5078687
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      18
      Molecular force fields with gradient-domain machine learning: Construction and application to dynamics of small molecules with coupled cluster forces
      Sauceda, Huziel E.; Chmiela, Stefan; Poltavsky, Igor; Mueller, Klaus-Robert; Tkatchenko, Alexandre
      Journal of Chemical Physics (2019), 150 (11), 114102/1-114102/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present the construction of mol. force fields for small mols. (less than 25 atoms) using the recently developed symmetrized gradient-domain machine learning (sGDML) approach [Chmiela et al., Nat. Commun. 9, 3887 (2018) and Chmiela et al., Sci. Adv. 3, e1603015 (2017)]. This approach is able to accurately reconstruct complex high-dimensional potential-energy surfaces from just a few 100s of mol. conformations extd. from ab initio mol. dynamics trajectories. The data efficiency of the sGDML approach implies that at. forces for these conformations can be computed with high-level wavefunction-based approaches, such as the "gold std." coupled-cluster theory with single, double and perturbative triple excitations [CCSD(T)]. We demonstrate that the flexible nature of the sGDML model recovers local and non-local electronic interactions (e.g., H-bonding, proton transfer, lone pairs, changes in hybridization states, steric repulsion, and n → π* interactions) without imposing any restriction on the nature of interat. potentials. The anal. of sGDML mol. dynamics trajectories yields new qual. insights into dynamics and spectroscopy of small mols. close to spectroscopic accuracy. (c) 2019 American Institute of Physics.
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    19. 19
      Schütt, K. T.; Arbabzadah, F.; Chmiela, S.; Müller, K. R.; Tkatchenko, A. Quantum-Chemical Insights from Deep Tensor Neural Networks. Nat. Commun. 2017, 8 (1), 13890,  DOI: 10.1038/ncomms13890
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      19
      Quantum-chemical insights from deep tensor neural networks
      Schuett, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Mueller, Klaus R.; Tkatchenko, Alexandre
      Nature Communications (2017), 8 (), 13890CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems. Here we develop an efficient deep learning approach that enables spatially and chem. resolved insights into quantum-mech. observables of mol. systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol-1) predictions in compositional and configurational chem. space for mols. of intermediate size. As an example of chem. relevance, the model reveals a classification of arom. rings with respect to their stability. Further applications of our model for predicting at. energies and local chem. potentials in mols., reliable isomer energies, and mols. with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex quantum-chem. systems.
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    20. 20
      Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet-A Deep Learning Architecture for Molecules and Materials. J. Chem. Phys. 2018, 148 (24), 241722,  DOI: 10.1063/1.5019779
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      20
      SchNet - A deep learning architecture for molecules and materials
      Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
      Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
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    21. 21
      Schütt, K. T.; Kessel, P.; Gastegger, M.; Nicoli, K. A.; Tkatchenko, A.; Müller, K. R. SchNetPack: A Deep Learning Toolbox for Atomistic Systems. J. Chem. Theory Comput. 2019, 15 (1), 448– 455,  DOI: 10.1021/acs.jctc.8b00908
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      21
      SchNetPack: A Deep Learning Toolbox For Atomistic Systems
      Schuett, K. T.; Kessel, P.; Gastegger, M.; Nicoli, K. A.; Tkatchenko, A.; Mueller, K.-R.
      Journal of Chemical Theory and Computation (2019), 15 (1), 448-455CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      SchNetPack is a toolbox for the development and application of deep neural networks that predict potential energy surfaces and other quantum-chem. properties of mols. and materials. It contains basic building blocks of atomistic neural networks, manages their training, and provides simple access to common benchmark datasets. This allows for an easy implementation and evaluation of new models. For now, SchNetPack includes implementations of (weighted) atom-centered symmetry functions and the deep tensor neural network SchNet, as well as ready-to-use scripts that allow one to train these models on mol. and material datasets. Based on the PyTorch deep learning framework, SchNetPack allows one to efficiently apply the neural networks to large datasets with millions of ref. calcns., as well as parallelize the model across multiple GPUs. Finally, SchNetPack provides an interface to the Atomic Simulation Environment in order to make trained models easily accessible to researchers that are not yet familiar with neural networks.
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    22. 22
      Unke, O. T.; Meuwly, M. PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges. J. Chem. Theory Comput. 2019, 15 (6), 3678– 3693,  DOI: 10.1021/acs.jctc.9b00181
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      22
      PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges
      Unke, Oliver T.; Meuwly, Markus
      Journal of Chemical Theory and Computation (2019), 15 (6), 3678-3693CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      In recent years, machine learning (ML) methods have become increasingly popular in computational chem. After being trained on appropriate ab initio ref. data, these methods allow for accurately predicting the properties of chem. systems, circumventing the need for explicitly solving the electronic Schrodinger equation. Because of their computational efficiency and scalability to large data sets, deep neural networks (DNNs) are a particularly promising ML algorithm for chem. applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces, and dipole moments of chem. systems. PhysNet achieves state-of-the-art performance on the QM9, MD17, and ISO17 benchmarks. Further, two new data sets are generated in order to probe the performance of ML models for describing chem. reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qual. correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala10): The optimized geometry of helical Ala10 predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased mol. dynamics (MD) simulations of Ala10 on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala10 folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol-1 according to the ref. ab initio calcns.
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    23. 23
      Brockherde, F.; Vogt, L.; Li, L.; Tuckerman, M. E.; Burke, K.; Müller, K. R. Bypassing the Kohn-Sham Equations with Machine Learning. Nat. Commun. 2017, 8 (1), 872,  DOI: 10.1038/s41467-017-00839-3
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      23
      Bypassing the Kohn-Sham equations with machine learning
      Brockherde Felix; Muller Klaus-Robert; Brockherde Felix; Vogt Leslie; Tuckerman Mark E; Li Li; Burke Kieron; Tuckerman Mark E; Tuckerman Mark E; Burke Kieron; Muller Klaus-Robert; Muller Klaus-Robert
      Nature communications (2017), 8 (1), 872 ISSN:.
      Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.Machine learning allows electronic structure calculations to access larger system sizes and, in dynamical simulations, longer time scales. Here, the authors perform such a simulation using a machine-learned density functional that avoids direct solution of the Kohn-Sham equations.
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      Petraglia, R.; Nicolaï, A.; Wodrich, M. D.; Ceriotti, M.; Corminboeuf, C. Beyond Static Structures: Putting Forth REMD as a Tool to Solve Problems in Computational Organic Chemistry. J. Comput. Chem. 2016, 37 (1), 83– 92,  DOI: 10.1002/jcc.24025
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      24
      Beyond static structures: Putting forth REMD as a tool to solve problems in computational organic chemistry
      Petraglia, Riccardo; Nicolai, Adrien; Wodrich, Matthew D.; Ceriotti, Michele; Corminboeuf, Clemence
      Journal of Computational Chemistry (2016), 37 (1), 83-92CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      Computational studies of org. systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chem. systems are dynamic entities where a multitude of mol. conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biol. simulations, together with empirical force fields, and apply it to org. chem. problems. Replica-exchange mol. dynamics (REMD) permits thorough exploration of the PES. We combined REMD with d. functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small mol. systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temp.-dependent rotational processes, and catalysis, we reveal new insights and chem. that likely would be missed using static electronic structure computations. The REMD-DFTB methodol. at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes. © 2015 Wiley Periodicals, Inc.
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      Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding. Chem. Phys. Lett. 1999, 314, 141– 151,  DOI: 10.1016/S0009-2614(99)01123-9
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      Replica-exchange molecular dynamics method for protein folding
      Sugita, Y.; Okamoto, Y.
      Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
      We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
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      Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB). J. Chem. Theory Comput. 2011, 7 (4), 931– 948,  DOI: 10.1021/ct100684s
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      26
      DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB)
      Gaus, Michael; Cui, Qiang; Elstner, Marcus
      Journal of Chemical Theory and Computation (2011), 7 (4), 931-948CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The self-consistent-charge d.-functional tight-binding method (SCC-DFTB) is an approx. quantum chem. method derived from d. functional theory (DFT) based on a second-order expansion of the DFT total energy around a ref. d. In the present study, we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between at. partial charges and, second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodol. called DFTB3, which substantially improves the description of charged systems contg. elements C, H, N, O, and P, esp. regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomol. systems. Remaining challenges and possible solns. are also briefly discussed.
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      Gaus, M.; Goez, A.; Elstner, M. Parametrization and Benchmark of DFTB3 for Organic Molecules. J. Chem. Theory Comput. 2013, 9 (1), 338– 354,  DOI: 10.1021/ct300849w
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      27
      Parametrization and Benchmark of DFTB3 for Organic Molecules
      Gaus, Michael; Goez, Albrecht; Elstner, Marcus
      Journal of Chemical Theory and Computation (2013), 9 (1), 338-354CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      DFTB3 is a recent extension of the self-consistent-charge d.-functional tight-binding method (SCC-DFTB) and derived from a third order expansion of the d. functional theory (DFT) total energy around a given ref. d. Being applied in combination with the parametrization of its predecessor (MIO), DFTB3 improves for hydrogen binding energies, proton affinities, and hydrogen transfer barriers. In the present study, parameters esp. designed for DFTB3 are presented, and its performance is evaluated for small org. mols. focusing on thermochem., geometries, and vibrational frequencies from our own and several databases from literature. The new parameters remove significant overbinding errors, reduce errors for geometries of noncovalent interactions, and improve the overall performance.
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      Gaus, M.; Lu, X.; Elstner, M.; Cui, Q. Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications. J. Chem. Theory Comput. 2014, 10 (4), 1518– 1537,  DOI: 10.1021/ct401002w
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      28
      Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications
      Gaus, Michael; Lu, Xiya; Elstner, Marcus; Cui, Qiang
      Journal of Chemical Theory and Computation (2014), 10 (4), 1518-1537CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We report the parametrization of the approx. d. functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of org. and biol. relevant mols. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of mols. of biol. relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these mols.; vibrational frequencies are also examd., although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, esp. for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant redn. of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calcns., DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination no. of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary soln.; this suggests that the current DFTB3 methodol. has limited transferability for complex phosphorus chem. at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodol. are needed for a reliable method that describes phosphorus chem. without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calcns. for studying phosphorus/sulfur chem. in condensed phase systems, esp. as a low-level method that drives the sampling in a dual-level QM/MM framework.
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      Laio, A.; Parrinello, M. Escaping free-energy minima. Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (20), 12562– 12566,  DOI: 10.1073/pnas.202427399
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      29
      Escaping free-energy minima
      Laio, Alessandro; Parrinello, Michele
      Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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      Grimme, S. Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations. J. Chem. Theory Comput. 2019, 15 (5), 2847– 2862,  DOI: 10.1021/acs.jctc.9b00143
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      30
      Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations
      Grimme, Stefan
      Journal of Chemical Theory and Computation (2019), 15 (5), 2847-2862CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The semiempirical tight-binding based quantum chem. method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chem. compd., conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chem. reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the at. RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approx. character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, d. functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized mols. with a few hundred atoms. Furthermore, the underlying potential energy surface for mols. contg. almost all elements (Z = 1-86) is globally consistent including the covalent dissocn. process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decompn., ethyne oligomerization, the oxidn. of hydrocarbons (by oxygen and a P 450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramol. cyclization reaction are shown. For typical conformational search problems of org. drug mols., the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.
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      Kaczor, A.; Reva, I. D.; Proniewicz, L. M.; Fausto, R. Importance of Entropy in the Conformational Equilibrium of Phenylalanine: A Matrix-Isolation Infrared Spectroscopy and Density Functional Theory Study. J. Phys. Chem. A 2006, 110 (7), 2360– 2370,  DOI: 10.1021/jp0550715
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      31
      Importance of Entropy in the Conformational Equilibrium of Phenylalanine: A Matrix-Isolation Infrared Spectroscopy and Density Functional Theory Study
      Kaczor, A.; Reva, I. D.; Proniewicz, L. M.; Fausto, R.
      Journal of Physical Chemistry A (2006), 110 (7), 2360-2370CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      The conformational behavior and IR spectrum of L-phenylalanine were studied by matrix-isolation IR spectroscopy and DFT [B3LYP/6-311++G(d,p)] calcns. The fourteen most stable structures were predicted to differ in energy by less than 10 kJ mol-1, eight of them with abundances higher than 5% at the temp. of evapn. of the compd. (423 K). Exptl. results suggest that six conformers contribute to the spectrum of the isolated compd., whereas two conformers (IIb3 and IIIb3) relax in matrix to a more stable form (IIb2) due to low energy barriers for conformational isomerization (conformational cooling). The two lowest-energy conformers (Ib1, Ia) differ only in the arrangement of the amino acid group relative to the Ph ring; they exhibit a relatively strong stabilizing intramol. hydrogen bond of the O-H···N type and the carboxylic group in the trans configuration (O:C-O-H dihedral angle ca. 180°). Type II conformers have a weaker H-bond of the N-H···O=C type, but they bear the more favorable cis arrangement of the carboxylic group. Being considerably more flexible, type II conformers are stabilized by entropy and the relative abundances of two conformers of this type (IIb2 and IIc1) are shown to significantly increase with temp. due to entropic stabilization. At 423 K, these conformers are found to be the first and third most abundant species present in the conformational equil., with relative populations of ca. 15% each, whereas their populations could be expected to be only ca. 5% if entropy effects were not taken into consideration. Indeed, phenylalanine can be considered a notable example of a mol. where entropy plays an essential role in detg. the relative abundance of the possible low-energy conformational states and then, the thermodn. of the compd., even at moderate temps. Upon UV irradn. (λ > 235 nm) of the matrix-isolated compd., unimol. photodecompn. of phenylalanine is obsd. with prodn. of CO2 and phenethylamine.
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      Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N. Bifurcations on Potential Energy Surfaces of Organic Reactions. Angew. Chem., Int. Ed. 2008, 47 (40), 7592– 7601,  DOI: 10.1002/anie.200800918
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      Bifurcations on potential energy surfaces of organic reactions
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      A review. A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy min. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Mini review covers recent investigations of org. reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect exptl. observables such as kinetic isotope effects and product distributions.
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      Rehbein, J.; Carpenter, B. K. Do We Fully Understand What Controls Chemical Selectivity?. Phys. Chem. Chem. Phys. 2011, 13 (47), 20906,  DOI: 10.1039/c1cp22565k
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      Do we fully understand what controls chemical selectivity?
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      Reaction rates and product selectivity of kinetically controlled reactions are not always sufficiently described by std. RRKM or TST theory. Reactions taking place on potential energy surfaces featuring a valley ridge inflection point belong to this class of reactions. Though various research groups could show that reaction path bifurcations are far from being an exception in org. reactions the underlying principles that govern product distributions of those bifurcating reaction pathways are yet not fully understood. This Perspective has the intention to provide an overview of how far our understanding and the development of the theor. foundation have progressed.
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      Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. Methylhydroxycarbene: Tunneling Control of a Chemical Reaction. Science 2011, 332 (6035), 1300– 1303,  DOI: 10.1126/science.1203761
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      Methylhydroxycarbene: Tunneling Control of a Chemical Reaction
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      Science (Washington, DC, United States) (2011), 332 (6035), 1300-1303CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Chem. reactivity is conventionally understood in broad terms of kinetic vs. thermodn. control, wherein the decisive factor is the lowest activation barrier among the various reaction paths or the lowest free energy of the final products, resp. We demonstrate that quantum-mech. tunneling can supersede traditional kinetic control and direct a reaction exclusively to a product whose reaction path has a higher barrier. Specifically, we prepd. methylhydroxycarbene (H3C-C-OH) via vacuum pyrolysis of pyruvic acid at about 1200 K (K), followed by argon matrix trapping at 11 K. The previously elusive carbene, characterized by UV and IR spectroscopy as well as exacting quantum-mech. computations, undergoes a facile [1,2]hydrogen shift to acetaldehyde via tunneling under a barrier of 28.0 kcal per mol (kcal mol-1), with a half-life of around 1 h. The analogous isomerization to vinyl alc. has a substantially lower barrier of 22.6 kcal mol-1 but is precluded at low temp. by the greater width of the potential energy profile for tunneling.
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      Plata, R. E.; Singleton, D. A. A Case Study of the Mechanism of Alcohol-Mediated Morita Baylis-Hillman Reactions. The Importance of Experimental Observations. J. Am. Chem. Soc. 2015, 137 (11), 3811– 3826,  DOI: 10.1021/ja5111392
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      A Case Study of the Mechanism of Alcohol-Mediated Morita Baylis-Hillman Reactions. The Importance of Experimental Observations
      Plata, R. Erik; Singleton, Daniel A.
      Journal of the American Chemical Society (2015), 137 (11), 3811-3826CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The mechanism of the Morita Baylis-Hillman reaction has been heavily studied in the literature, and a long series of computational studies have defined complete theor. energy profiles in these reactions. We employ here a combination of mechanistic probes, including the observation of intermediates, the independent generation and partitioning of intermediates, thermodn. and kinetic measurements on the main reaction and side reactions, isotopic incorporation from solvent, and kinetic isotope effects, to define the mechanism and an exptl. mechanistic free-energy profile for a prototypical Morita Baylis-Hillman reaction in methanol. The results are then used to critically evaluate the ability of computations to predict the mechanism. The most notable prediction of the many computational studies, that of a proton-shuttle pathway, is refuted in favor of a simple but computationally intractable acid-base mechanism. Computational predictions vary vastly, and it is not clear that any significant accurate information that was not already apparent from expt. could have been garnered from computations. With care, entropy calcns. are only a minor contributor to the larger computational error, while literature entropy-correction processes lead to absurd free-energy predictions. The computations aid in interpreting observations but fail utterly as a replacement for expt.
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      On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction
      Fukunishi, Hiroaki; Watanabe, Osamu; Takada, Shoji
      Journal of Chemical Physics (2002), 116 (20), 9058-9067CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Motivated by the protein structure prediction problem, we develop two variants of the Hamiltonian replica exchange methods (REMs) for efficient configuration sampling, (1) the scaled hydrophobicity REM and (2) the phantom chain REM, and compare their performance with the ordinary REM. We first point out that the ordinary REM has a shortage for the application to large systems such as biomols. and that the Hamiltonian REM, an alternative formulation of the REM, can give a remedy for it. We then propose two examples of the Hamiltonian REM that are suitable for a coarse-grained protein model. (1) The scaled hydrophobicity REM preps. replicas that are characterized by various strengths of hydrophobic interaction. The strongest interaction that mimics aq. soln. environment makes proteins folding, while weakened hydrophobicity unfolds proteins as in org. solvent. Exchange between these environments enables proteins to escape from misfolded traps and accelerate conformational search. This resembles the roles of mol. chaperone that assist proteins to fold in vivo. (2) The phantom chain REM uses replicas that allow various degrees of at. overlaps. By allowing at. overlap in some of replicas, the peptide chain can cross over itself, which can accelerate conformation sampling. Using a coarse-gained model we developed, we compute equil. probability distributions for poly-alanine 16-mer and for a small protein by these REMs and compare the accuracy of the results. We see that the scaled hydrophobicity REM is the most efficient method among the three REMs studied.
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      Okur, A.; Roe, D. R.; Cui, G.; Hornak, V.; Simmerling, C. Improving Convergence of Replica Exchange Simulations through Coupling to a High-Temperature Structure Reservoir. J. Chem. Theory Comput. 2007, 3 (2), 557– 568,  DOI: 10.1021/ct600263e
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      Improving Convergence of Replica-Exchange Simulations through Coupling to a High-Temperature Structure Reservoir
      Okur, Asim; Roe, Daniel R.; Cui, Guanglei; Hornak, Viktor; Simmerling, Carlos
      Journal of Chemical Theory and Computation (2007), 3 (2), 557-568CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Parallel tempering or replica-exchange mol. dynamics (REMD) significantly increases the efficiency of conformational sampling for complex mol. systems. However, obtaining converged data with REMD remains challenging, esp. for large systems with complex topologies. We propose a new variant to REMD where the replicas are also permitted to exchange with an ensemble of structures that have been generated in advance using high-temp. MD simulations, similar in spirit to J-walking methods. We tested this approach on two non-trivial model systems, a β-hairpin and a 3-stranded β-sheet and compared the results to those obtained from very long ( > 100 ns) std. REMD simulations. The resulting ensembles were indistinguishable, including relative populations of different conformations on the unfolded state. The use of the reservoir is shown to significantly reduce the time required for convergence.
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      Brémond, É.; Golubev, N.; Steinmann, S. N.; Corminboeuf, C. How Important Is Self-Consistency for the dDsC Density Dependent Dispersion Correction?. J. Chem. Phys. 2014, 140, 18A516,  DOI: 10.1063/1.4867195
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      Petraglia, R.; Steinmann, S. N.; Corminboeuf, C. A Fast Charge-Dependent Atom-Pairwise Dispersion Correction for DFTB3. Int. J. Quantum Chem. 2015, 115 (18), 1265– 1272,  DOI: 10.1002/qua.24887
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      Org. electronic materials remarkably illustrate the importance of the "weak" dispersion interactions that are neglected in the most cost-efficient electronic structure approaches. This work introduces a fast atom-pairwise dispersion correction, dDMC that is compatible with the most recent variant of self-consistent charge d. functional tight binding (SCC-DFTB). The emphasis is placed on improving the description of π-π stacked motifs featuring sulfur-contg. mols. that are known to be esp. challenging for DFTB. Our scheme relies upon the use of Mulliken charges using minimal basis set that are readily available from the DFTB computations at no addnl. cost. The performance and efficiency of the dDMC correction are validated on examples targeting energies, geometries, and mol. dynamic trajectories.
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      Synthesis and structures of thieno[2,3-b]thiophene incorporated [3.3]dithiacyclophanes. Enhanced first hyperpolarizability in an unsymmetrically polarized cyclophane
      Mashraqui, Sabir H.; Sangvikar, Yogesh S.; Meetsma, Auke
      Tetrahedron Letters (2006), 47 (31), 5599-5602CODEN: TELEAY; ISSN:0040-4039. (Elsevier B.V.)
      Dithiacyclophanes incorporating thieno[2,3-b]thiophene have been synthesized, in order to investigate the nonlinear optical properties of donor-acceptor cyclophane I. I displayed significantly higher first hyperpolarizability β (21.6 × 10-30 esu) compared to model II (9.58 × 10-30esu). Relatively higher β in I presumably arises from an extra electron redistribution arising from through-space charge transfer, a feature lacking in II. Moreover, the thermal decompn. temp. of I (300 °C) is higher than that reported for the NLO prototype DANS (295 °C).
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      Conformational study of cinchona alkaloids. A combined NMR, molecular mechanics and x-ray approach
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      Journal of the American Chemical Society (1989), 111 (21), 8069-76CODEN: JACSAT; ISSN:0002-7863.
      A conformational study of cinchona alkaloids is presented. The conformations of the alkaloids in soln. have been detd. by NOE difference and NOESY NMR technique. The necessary chem. shift assignments of the cinchona alkaloids have been elucidated by combination of COSY and NOE NMR expts. Min. energy conformations of the alkaloids have been calcd. by mol. mechanics. The first known x-ray structure of a cinchona alkaloid with a closed conformation is presented. Finally, the conformational effects of protonation and complexation on the tertiary nitrogen of the quinuclidine ring have been investigated.
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      Zhou, J.; Wakchaure, V.; Kraft, P.; List, B. Primary-Amine-Catalyzed Enantioselective Intramolecular Aldolizations. Angew. Chem., Int. Ed. 2008, 47 (40), 7656,  DOI: 10.1002/anie.200802497
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      Primary-amine-catalyzed enantioselective intramolecular aldolizations
      Zhou, Jian; Wakchaure, Vijay; Kraft, Philip; List, Benjamin
      Angewandte Chemie, International Edition (2008), 47 (40), 7656-7658CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Aldol cyclodehydration of 4-substituted-2,6-heptanediones leads to enantiomerically enriched 5-substituted-3-methyl-2-cyclohexene-1-ones, which serve as perfume ingredients and valuable synthetic building blocks. Primary amines derived from cinchona alkaloids in combination with acetic acid are efficient catalysts for this transformation, which deliver both enantiomers of the celery ketone.
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      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 (5), 2087– 2096,  DOI: 10.1021/acs.jctc.5b00099
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      Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach
      Ramakrishnan, Raghunathan; Dral, Pavlo O.; Rupp, Matthias; von Lilienfeld, O. Anatole
      Journal 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.
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      Fabregat, R. Modular Replica Exchange Simulatior. http://doi.org/10.5281/zenodo.3630553, 2020.
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      Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen Bonding and Stacking Interactions of Nucleic Acid Base Pairs: A Density-Functional-Theory Based Treatment. J. Chem. Phys. 2001, 114 (12), 5149– 5155,  DOI: 10.1063/1.1329889
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      Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment
      Elstner, Marcus; Hobza, Pavel; Frauenheim, Thomas; Suhai, Sandor; Kaxiras, Efthimios
      Journal of Chemical Physics (2001), 114 (12), 5149-5155CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We extend an approx. d. functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irresp. of the correlation function applied. An empirical formula, consisting of an R-6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coeff., which is calcd. from exptl. at. polarizabilities, can be consistently added to the total energy expression of the method. We apply this approx. DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.
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      Aradi, B.; Hourahine, B.; Frauenheim, T. DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method. J. Phys. Chem. A 2007, 111 (26), 5678– 5684,  DOI: 10.1021/jp070186p
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      DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method
      Aradi, B.; Hourahine, B.; Frauenheim, Th.
      Journal of Physical Chemistry A (2007), 111 (26), 5678-5684CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      A new Fortran 95 implementation of the DFTB (d. functional-based tight binding) method was developed, where the sparsity of the DFTB system of equations was exploited. Conventional dense algebra was used only to evaluate the eigenproblems of the system and long-range Coulombic terms, but drop-in O(N) or O(N2) modules were planned to replace the small code sections that these entail. The developed sparse storage structure is discussed in detail, and a short overview of other features of the new code is given.
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      Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method. J. Chem. Phys. 2013, 138 (3), 034106,  DOI: 10.1063/1.4773581
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      An efficient and near linear scaling pair natural orbital based local coupled cluster method
      Riplinger, Christoph; Neese, Frank
      Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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      Neese, F.; Valeev, E. F. Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?. J. Chem. Theory Comput. 2011, 7 (1), 33– 43,  DOI: 10.1021/ct100396y
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      Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?
      Neese, Frank; Valeev, Edward F.
      Journal of Chemical Theory and Computation (2011), 7 (1), 33-43CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The performance of several families of basis sets for correlated wave function calcns. on mols. is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of at. natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in at. multireference av. coupled pair functional (MR-ACPF) calcns. Segmented basis sets optimized for SCF calcns. (def2-SVP, def2-TZVPP, and def2-QZVPP as well as "pc-n", n = 1, 2, 3) were also tested. Ref. Hartree-Fock energies are detd. with the uncontracted aug-cc-pV6Z basis set for a set of 21 small mols. built from H, B, C, N, O, and F. Ref. coupled cluster CCSD(T) correlation energies were detd. from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3 at each cardinal no. In addn., the ano-pVXZ consistently recovers more correlation energy than their competitors at each cardinal no. The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated. A conclusion by Truhlar is confirmed that the optimum exponent for correlation energy extrapolations at the DZ/TZ level is ∼2.4. All TZ/QZ basis set pairs lead to an optimum exponent close to the expected value of 3. The SCF energy extrapolation proposed by Petersson and co-workers is found to be effective. At the DZ/TZ level, errors in total energies of less than 2 mEh are found for the test set, while at the TZ/QZ level one obtains the total energies within ∼0.3 mEh of the basis set limit. For extrapolation, the "cc" and "ano" bases are found to be similarly successful. Extrapolation results were compared to explicitly correlated calcns. with dedicated basis sets (cc-pVXZ-F12) as well as the ano-pVXZ bases. It is found that the ano-pVXZ + basis sets perform as well as the cc-pVXZ-F12 family (both are of comparable size); addnl. improvement should be possible by reoptimizing the ANO basis sets for explicitly correlated calcns. The error of the extrapolated energies is about 2-3 times smaller than what was found in the explicitly correlated calcns. However, the error in the explicitly correlated calcns. is more systematic, and hence the same conclusion may not hold for the computation of energy differences.
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      A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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      Dunning, Thom H., Jr.
      Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
      Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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      Kendall, R. A.; Dunning, T. H.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96 (9), 6796– 6806,  DOI: 10.1063/1.462569
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      The authors describe a reliable procedure for calcg. the electron affinity of an atom and present results for H, B, C, O, and F (H is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the at. anion coupled with a straightforward, uniform expansion of the ref. space for multireference singles and doubles configuration-interaction (MRSD-CI) calcns. A comparison is given with previous results and with corresponding full CI calcns. The most accurate EAs obtained from the MRSD-CI calcns. are (with exptl. values in parentheses): H 0.740 eV (0.754), B 0.258 (0.277), C 1.245 (1.263), O 1.384 (1.461), and F 3.337 (3.401). The EAs obtained from the MR-SDCI calcns. differ by less than 0.03 eV from those predicted by the full CI calcns.
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      Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0Model. J. Chem. Phys. 1999, 110 (13), 6158– 6170,  DOI: 10.1063/1.478522
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      Journal of Chemical Physics (1999), 110 (13), 6158-6170CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We present an anal. of the performances of a parameter free d. functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amt. of exact exchange. The results obtained for structural, thermodn., kinetic and spectroscopic (magnetic, IR and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chem. and condensed matter physics.
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      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132 (15), 154104,  DOI: 10.1063/1.3382344
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      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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      Ufimtsev, I. S.; Martinez, T. J. Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics. J. Chem. Theory Comput. 2009, 5 (10), 2619– 2628,  DOI: 10.1021/ct9003004
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      Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics
      Ufimtsev, Ivan S.; Martinez, Todd J.
      Journal of Chemical Theory and Computation (2009), 5 (10), 2619-2628CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We demonstrate that a video gaming machine contg. two consumer graphical cards can outpace a state-of-the-art quad-core processor workstation by a factor of more than 180× in Hartree-Fock energy + gradient calcns. Such performance makes it possible to run large scale Hartree-Fock and D. Functional Theory calcns., which typically require hundreds of traditional processor cores, on a single workstation. Benchmark Born-Oppenheimer mol. dynamics simulations are performed on two mol. systems using the 3-21G basis set - a hydronium ion solvated by 30 waters (94 atoms, 405 basis functions) and an aspartic acid mol. solvated by 147 waters (457 atoms, 2014 basis functions). Our GPU implementation can perform 27 ps/day and 0.7 ps/day of ab initio mol. dynamics simulation on a single desktop computer for these systems.
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      Titov, A. V.; Ufimtsev, I. S.; Luehr, N.; Martinez, T. J. Generating Efficient Quantum Chemistry Codes for Novel Architectures. J. Chem. Theory Comput. 2013, 9 (1), 213– 221,  DOI: 10.1021/ct300321a
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      Generating Efficient Quantum Chemistry Codes for Novel Architectures
      Titov, Alexey V.; Ufimtsev, Ivan S.; Luehr, Nathan; Martinez, Todd J.
      Journal of Chemical Theory and Computation (2013), 9 (1), 213-221CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We describe an extension of our graphics processing unit (GPU) electronic structure program TeraChem to include atom-centered Gaussian basis sets with d angular momentum functions. This was made possible by a "meta-programming" strategy that leverages computer algebra systems for the derivation of equations and their transformation to correct code. We generate a multitude of code fragments that are formally math. equiv., but differ in their memory and floating-point operation footprints. We then select between different code fragments using empirical testing to find the highest performing code variant. This leads to an optimal balance of floating-point operations and memory bandwidth for a given target architecture without laborious manual tuning. We show that this approach is capable of similar performance compared to our hand-tuned GPU kernels for basis sets with s and p angular momenta. We also demonstrate that mixed precision schemes (using both single and double precision) remain stable and accurate for mols. with d functions. We provide benchmarks of the execution time of entire SCF calcns. using our GPU code and compare to mature CPU based codes, showing the benefits of the GPU architecture for electronic structure theory with appropriately redesigned algorithms. We suggest that the meta-programming and empirical performance optimization approach may be important in future computational chem. applications, esp. in the face of quickly evolving computer architectures.
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      Pearlman, D. A.; Case, D. A.; Caldwell, J. W.; Ross, W. S.; Cheatham, T. E.; DeBolt, S.; Ferguson, D.; Seibel, G.; Kollman, P. AMBER, a Package of Computer Programs for Applying Molecular Mechanics, Normal Mode Analysis, Molecular Dynamics and Free Energy Calculations to Simulate the Structural and Energetic Properties of Molecules. Comput. Phys. Commun. 1995, 91 (1), 1– 41,  DOI: 10.1016/0010-4655(95)00041-D
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      "AMBER", a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to stimulate the structural and energetic properties of molecules
      Pearlman, David A.; Case, David A.; Caldwell, James W.; Ross, Wilson S.; Cheatham, Thomas E. III; DeBolt, Steve; Ferguson, David; Seibel, George; Kollman, Peter
      Computer Physics Communications (1995), 91 (1-3), 1-42CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
      We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a no. of the powerful tools of modern computational chem.-mol. dynamics and free energy calcns.
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      Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113 (18), 6378– 6396,  DOI: 10.1021/jp810292n
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      Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions
      Marenich, Aleksandr V.; Cramer, Christopher J.; Truhlar, Donald G.
      Journal of Physical Chemistry B (2009), 113 (18), 6378-6396CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We present a new continuum solvation model based on the quantum mech. charge d. of a solute mol. interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "d." to denote that the full solute electron d. is used without defining partial at. charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielec. medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liq. medium for which a few key descriptors are known (in particular, dielec. const., refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the soln. of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calcn. are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent mols. in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality consts. called at. surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aq. ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and DMSO, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaq. org. solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 org. solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic at. Coulomb radii and at. surface tension coeffs.) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calcns. in which the solute is represented by its electron d. in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on av. for ions with either Gaussian03 or GAMESS.
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      Rupp, M.; Tkatchenko, A.; Müller, K. R.; Lilienfeld, V.; Anatole, O. Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning. Phys. Rev. Lett. 2012, 108 (5), 058301,  DOI: 10.1103/PhysRevLett.108.058301
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      Fast and accurate modeling of molecular atomization energies with machine learning
      Rupp, Matthias; Tkatchenko, Alexandre; Mueller, Klaus-Robert; von Lilienfeld, O. Anatole
      Physical Review Letters (2012), 108 (5), 058301/1-058301/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The authors introduce a machine learning model to predict atomization energies of a diverse set of org. mols., based on nuclear charges and at. positions only. The problem of solving the mol. Schrodinger equation is mapped onto a nonlinear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid d.-functional theory. Cross validation over more than seven thousand org. mols. yields a mean abs. error of ∼10 kcal/mol. Applicability is demonstrated for the prediction of mol. atomization potential energy curves.
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      Hansen, K.; Biegler, F.; Ramakrishnan, R.; Pronobis, W.; Von Lilienfeld, O. A.; Müller, K. R.; Tkatchenko, A. Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space. J. Phys. Chem. Lett. 2015, 6 (12), 2326– 2331,  DOI: 10.1021/acs.jpclett.5b00831
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      Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space
      Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; Pronobis, Wiktor; von Lilienfeld, O. Anatole; Mueller, Klaus-Robert; Tkatchenko, Alexandre
      Journal of Physical Chemistry Letters (2015), 6 (12), 2326-2331CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Simultaneously accurate and efficient prediction of mol. properties throughout chem. compd. space is a crit. ingredient toward rational compd. design in chem. and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to est. atomization and total energies of mols. These methods range from a simple sum over atoms, to addn. of bond energies, to pairwise interat. force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equil. mol. geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calcd. using d. functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the "holy grail" of chem. accuracy of 1 kcal/mol for both equil. and out-of-equil. geometries. This remarkable accuracy is achieved by a vectorized representation of mols. (so-called Bag of Bonds model) that exhibits strong nonlocality in chem. space. In addn., the same representation allows us to predict accurate electronic properties of mols., such as their polarizability and mol. frontier orbital energies.
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      Journal of Chemical Physics (2002), 116 (20), 9058-9067CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Motivated by the protein structure prediction problem, we develop two variants of the Hamiltonian replica exchange methods (REMs) for efficient configuration sampling, (1) the scaled hydrophobicity REM and (2) the phantom chain REM, and compare their performance with the ordinary REM. We first point out that the ordinary REM has a shortage for the application to large systems such as biomols. and that the Hamiltonian REM, an alternative formulation of the REM, can give a remedy for it. We then propose two examples of the Hamiltonian REM that are suitable for a coarse-grained protein model. (1) The scaled hydrophobicity REM preps. replicas that are characterized by various strengths of hydrophobic interaction. The strongest interaction that mimics aq. soln. environment makes proteins folding, while weakened hydrophobicity unfolds proteins as in org. solvent. Exchange between these environments enables proteins to escape from misfolded traps and accelerate conformational search. This resembles the roles of mol. chaperone that assist proteins to fold in vivo. (2) The phantom chain REM uses replicas that allow various degrees of at. overlaps. By allowing at. overlap in some of replicas, the peptide chain can cross over itself, which can accelerate conformation sampling. Using a coarse-gained model we developed, we compute equil. probability distributions for poly-alanine 16-mer and for a small protein by these REMs and compare the accuracy of the results. We see that the scaled hydrophobicity REM is the most efficient method among the three REMs studied.
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      Affentranger, R.; Tavernelli, I.; Di Iorio, E. E. A Novel Hamiltonian Replica Exchange MD Protocol to Enhance Protein Conformational Space Sampling. J. Chem. Theory Comput. 2006, 2 (2), 217– 228,  DOI: 10.1021/ct050250b
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      A Novel Hamiltonian Replica Exchange MD Protocol to Enhance Protein Conformational Space Sampling
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      Limited searching in the conformational space is one of the major obstacles for investigating protein dynamics by numerical approaches. For this reason, classical all-atom mol. dynamics (MD) simulations of proteins tend to be confined to local energy min., particularly when the bulk solvent is treated explicitly. To overcome this problem, the authors have developed a novel replica exchange protocol that uses modified force-field parameters to treat interparticle nonbonded potentials within the protein and between protein and solvent atoms, leaving unperturbed those relative to solvent-solvent interactions. The authors have tested the new protocol on the 18-residue-long tip of the P domain of calreticulin in an explicit solvent. With only eight replicas, the authors have been able to considerably enhance the conformational space sampled during a 100 ns simulation, compared to as many parallel classical mol. dynamics simulations of the same length or to a single one lasting 450 ns. A direct comparison between the various simulations has been possible thanks to the implementation of the weighted histogram anal. method, by which conformations simulated with modified force-field parameters can be assigned different wts. Interatom, inter-residue distances in the structural ensembles obtained with the authors' novel replica exchange approach and by classical MD simulations compare equally well with those derived from NMR data. Rare events, such as unfolding and refolding, occur with reasonable statistical frequency. Visiting of conformations characterized by very small Boltzmann wts. is also possible. Despite their low probability, such regions of the conformational space may play an important role in the search for local potential-energy min. and in dynamically controlled functions.
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      Wang, L.; Friesner, R. A.; Berne, B. J. Replica Exchange with Solute Scaling: A More Efficient Version of Replica Exchange with Solute Tempering (REST2). J. Phys. Chem. B 2011, 115 (30), 9431– 9438,  DOI: 10.1021/jp204407d
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      Replica Exchange with Solute Scaling: A More Efficient Version of Replica Exchange with Solute Tempering (REST2)
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      A small change in the Hamiltonian scaling in Replica Exchange with Solute Tempering (REST) is found to improve its sampling efficiency greatly, esp. for the sampling of aq. protein solns. in which there are large-scale solute conformation changes. Like the original REST (REST1), the new version (which the authors call REST2) also bypasses the poor scaling with system size of the std. Temp. Replica Exchange Method (TREM), reducing the no. of replicas (parallel processes) from what must be used in TREM. This redn. is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the no. of explicit water mols. in the system. For proof of concept, REST2 is compared with TREM and with REST1 for the folding of the trpcage and β-hairpin in water. The comparisons confirm that REST2 greatly reduces the no. of CPUs required by regular replica exchange and greatly increases the sampling efficiency over REST1. This method reduces the CPU time required for calcg. thermodn. avs. and for the ab initio folding of proteins in explicit water.
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      Recent developments in path integral methodol. have significantly reduced the computational expense of including quantum mech. effects in the nuclear motion in ab initio mol. dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calcns. and path integral mol. dynamics, i-PI can also be used to perform classical mol. dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water.
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      Progress in the at.-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interat. forces that work by either solving the electronic structure problem explicitly, or by computing accurate approxns. of the soln. and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodn. ensemble, and to est. the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck assocd. with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interat. potentials and forces calcd. by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral mol. dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivs.
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      Vannay, L.; Meyer, B.; Petraglia, R.; Sforazzini, G.; Ceriotti, M.; Corminboeuf, C. Analyzing Fluxional Molecules Using DORI. J. Chem. Theory Comput. 2018, 14 (5), 2370– 2379,  DOI: 10.1021/acs.jctc.7b01176
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      Analyzing Fluxional Molecules Using DORI
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      Journal of Chemical Theory and Computation (2018), 14 (5), 2370-2379CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The D. Overlap Region Indicator (DORI) is a d.-based scalar field that reveals covalent bonding patterns and non-covalent interactions in the same value range. This work goes beyond the traditional static quantum chem. use of scalar fields and illustrates the suitability of DORI for analyzing geometrical and electronic signatures in highly fluxional mol. systems. Examples include a dithiocyclophane, which possesses multiple local min. with differing extents of π-stacking interactions and a temp. dependent rotation of a mol. rotor, where the descriptor is employed to capture fingerprints of CH-π and π-π interactions. Finally, DORI serves to examine the fluctuating π-conjugation pathway of a photochromic torsional switch (PTS). Attention is also placed on post-processing the large amt. of generated data and juxtaposing DORI with a data-driven low-dimensional representation of the structural landscape.
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      Assessment of Approximate Methods for Anharmonic Free Energies
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      Journal of Chemical Theory and Computation (2019), 15 (11), 5845-5857CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Quant. evaluations of the thermodn. properties of materials - most notably their stability, as measured by the free energy - must take into account the role of thermal and zero-point energy fluctuations. While these effects can easily be estd. within a harmonic approxn., corrections arising from the anharmonic nature of the interat. potential are often crucial and require computationally costly path integral simulations. Consequently, different approx. frameworks for computing affordable ests. of the anharmonic free energies have been developed over the years. Understanding which of the approxns. involved are justified for a given system, and therefore choosing the most suitable method, is complicated by the lack of comparative benchmarks. To facilitate this choice we assess the accuracy and efficiency of some of the most commonly used approx. methods - the independent mode framework, the vibrational SCF and self-consistent phonons - by comparing the anharmonic correction to the Helmholtz free energy against ref. path integral calcns. These benchmarks are performed for a diverse set of systems, ranging from simple quasi-harmonic solids to flexible mol. crystals with freely-rotating units. Our results suggest that for simple solids such as allotropes of carbon these methods yield results that are in excellent agreement with the ref. calcns., at a considerably lower computational cost. For more complex mol. systems such as polymorphs of ice and paracetamol the methods do not consistently provide a reliable approxn. of the anharmonic correction. Despite substantial cancellation of errors when comparing the stability of different phases, we do not observe a systematic improvement over the harmonic approxn. even for relative free-energies. Our results suggest that efforts towards obtaining computationally-feasible anharmonic free-energies for flexible mol. solids should therefore be directed towards reducing the expense of path integral methods.
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      Conformational Behavior of Cinchonidine in Different Solvents: A Combined NMR and ab Initio Investigation
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      The conformation of cinchonidine in soln. has been investigated by NMR techniques as well as theor. Three conformers of cinchonidine are shown to be substantially populated at room temp., Closed(1), Closed(2), and Open(3), with the latter being the most stable in apolar solvents. The stability of the closed conformers relative to that of Open(3), however, increases with solvent polarity. In polar solvents the three conformers have similar energy. The relationship between relative energies and the dielec. const. of the solvent is not linear but resembles the form of an Onsager function. Ab initio and d. functional reaction field calcns. using cavity shapes detd. by an isodensity surface are in good agreement with expt. for solvents which do not show strong specific interaction with cinchonidine. The role of the conformational behavior of cinchonidine is illustrated using the example of the platinum-catalyzed enantioselective hydrogenation of ketopantolactone in different solvents.
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      Huang, M.; Dissanayake, T.; Kuechler, E.; Radak, B. K.; Lee, T. S.; Giese, T. J.; York, D. M. A Multidimensional B-Spline Correction for Accurate Modeling Sugar Puckering in QM/MM Simulations. J. Chem. Theory Comput. 2017, 13 (9), 3975– 3984,  DOI: 10.1021/acs.jctc.7b00161
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      A Multidimensional B-Spline Correction for Accurate Modeling Sugar Puckering in QM/MM Simulations
      Huang, Ming; Dissanayake, Thakshila; Kuechler, Erich; Radak, Brian K.; Lee, Tai-Sung; Giese, Timothy J.; York, Darrin M.
      Journal of Chemical Theory and Computation (2017), 13 (9), 3975-3984CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The computational efficiency of approx. quantum mech. methods allows their use for the construction of multidimensional reaction free energy profiles. It has recently been demonstrated that quantum models based on the NDDO approxn. have difficulty modeling deoxyribose and ribose sugar ring puckers and thus limit their predictive value in the study of RNA and DNA systems. A method has been introduced in our previous work to improve the description of the sugar puckering conformational landscape that uses a multidimensional B-spline correction map (BMAP correction) for systems involving intrinsically coupled torsion angles. This method greatly improved the adiabatic potential energy surface profiles of DNA and RNA sugar rings relative to high-level ab initio methods even for highly problematic NDDO-based models. In the present work, a BMAP correction is developed, implemented, and tested in mol. dynamics simulations using the AM1/d-PhoT semiempirical Hamiltonian for biol. phosphoryl transfer reactions. Results are presented for gas-phase adiabatic potential energy surfaces of RNA transesterification model reactions and condensed-phase QM/MM free energy surfaces for nonenzymic and RNase A-catalyzed transesterification reactions. The results show that the BMAP correction is stable, efficient, and leads to improvement in both the potential energy and free energy profiles for the reactions studied, as compared with ab initio and exptl. ref. data. Exploration of the effect of the size of the quantum mech. region indicates the best agreement with exptl. reaction barriers occurs when the full CpA dinucleotide substrate is treated quantum mech. with the sugar pucker correction.
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