**Cite This:**

*J. Chem. Theory Comput.*2023, 19, 19, 6796-6804

# Estimating Free Energy Barriers for Heterogeneous Catalytic Reactions with Machine Learning Potentials and Umbrella IntegrationClick to copy article linkArticle link copied!

- Sina StockerSina StockerFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, GermanyMore by Sina Stocker
- Hyunwook JungHyunwook JungFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, GermanyMore by Hyunwook Jung
- Gábor CsányiGábor CsányiEngineering Laboratory, University of Cambridge, Cambridge CB2 1PZ, United KingdomMore by Gábor Csányi
- C. Franklin GoldsmithC. Franklin GoldsmithFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, GermanySchool of Engineering, Brown University, Providence, Rhode Island 02912, United StatesMore by C. Franklin Goldsmith
- Karsten ReuterKarsten ReuterFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, GermanyMore by Karsten Reuter
- Johannes T. Margraf
*****Johannes T. MargrafFritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany*****Email: [email protected]More by Johannes T. Margraf

## Abstract

Predicting the rate constants of elementary reaction steps is key for the computational modeling of catalytic processes. Within transition state theory (TST), this requires an accurate estimation of the corresponding free energy barriers. While sophisticated methods for estimating free energy differences exist, these typically require extensive (biased) molecular dynamics simulations that are computationally prohibitive with the first-principles electronic structure methods that are typically used in catalysis research. In this contribution, we show that machine-learning (ML) interatomic potentials can be trained in an automated iterative workflow to perform such free energy calculations at a much reduced computational cost as compared to a direct density functional theory (DFT) based evaluation. For the decomposition of CHO on Rh(111), we find that thermal effects are substantial and lead to a decrease in the free energy barrier, which can be vanishingly small, depending on the DFT functional used. This is in stark contrast to previously reported estimates based on a harmonic TST approximation, which predicted an increase in the barrier at elevated temperatures. Since CHO is the reactant of the putative rate limiting reaction step in syngas conversion on Rh(111) and essential for the selectivity toward oxygenates containing multiple carbon atoms (C_{2+} oxygenates), our results call into question the reported mechanism established by microkinetic models.

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### License Summary*

You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:

Creative Commons (CC): This is a Creative Commons license.

Attribution (BY): Credit must be given to the creator.

*Disclaimer

This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.

### License Summary*

You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:

Creative Commons (CC): This is a Creative Commons license.

Attribution (BY): Credit must be given to the creator.

*Disclaimer

This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.

## I. Introduction

*e.g*., via Transition Path Sampling, (7) Metadynamics, (8) or Umbrella Sampling. (9,10)

*e.g*., to study the binding affinities of drug candidates to certain enzymes. Here, computationally efficient empirical force fields are available so that extensive sampling is not an insurmountable issue. Unfortunately, this is not the case in heterogeneous catalysis, where the surface of a solid catalyst must be accurately modeled. This requires the use of computationally expensive first-principles methods like density functional theory (DFT) with the consequence that rigorous free energy calculations are rarely performed in this context.

*e.g.*, with the Climbing Image Nudged Elastic Band (CI-NEB) approach and related methods. (11)

_{2}) to higher oxygenates like ethanol and acetaldehyde with appreciable selectivity. (18−21) We focus on CHO because it is the reactant in the putative rate limiting step for ethanol and acetaldehyde synthesis, according to some microkinetic models. (19) Furthermore, the relative formation rates of CHO and COH ultimately determine the selectivity for the C

_{2+}oxygenates.

## II. Methods

### II.1. Umbrella Integration

*w*

_{i}is the

*i*th biasing potential with a spring constant

*k*, which restrains the sampling around the window center

*ξ*

_{i}. ξ′(

**R**) is a function that maps the coordinates of system

**R**to the collective variable ξ, which can be an interatomic distance, angle, coordination number, or more complex function of the atomic coordinates. Note that ξ can, in principle, be higher dimensional, although we only consider the 1D case herein. The biasing potential restrains simulations to a region in phase space close to

*ξ*

_{i}, which is referred to as the

*i*th window.

*F*with respect to ξ. (10,22,23) To this end, one merely needs the mean value of ξ (

*ξ̅*

_{i}) for each biased ensemble:

*k*is sufficiently large, so the main remaining source of uncertainty is the statistical error on

*ξ̅*

_{i}. The FES can then be obtained by integrating $\frac{\partial F}{\partial \xi}$. Stecher et al. showed that this can be done in an uncertainty aware fashion using Gaussian Process Regression (GPR) and we follow this approach herein. (27) All UI simulations below are performed with the atomic simulation environment (ASE) and a Langevin thermostat. (28)

### II.2. Gaussian Approximation Potentials

### II.3. Density Functional Theory

^{surf}dispersion correction (35) were used, as implemented in the full-potential numerical atomic orbital code FHI-aims. (36) Here, light integration settings and a tier-1 basis set were used, as is usually done for

*ab initio*MD simulations. On the other hand, the BEEF-vdW (37) functional was used, as implemented in the plane-wave code QuantumEspresso, using ultrasoft pseudopotentials and a kinetic energy cutoff of 500 eV for orbitals and 5000 eV for the density. (38) Note that the revPBE setup was used in the iterative training scheme, while the BEEF-vdW potential was subsequently trained in the same configurations. In the following, all figures show revPBE-based results unless otherwise noted. All simulations were performed in a 3 × 3 × 4 Rh(111) surface slab (where the lower two slab layers were constrained during all simulations). A 4 × 4 × 1

*k*-grid was used to sample the Brillouin zone.

## III. Results

### III.1. Minimum Energy Path and Collective Variable

*d*, in Å). While these parameters would in principle form adequate CVs for this reaction, the computational effort for free energy calculations rises substantially with each dimension that is considered. We therefore first define an effective one-dimensional CV.

*d*and θ. This reveals that the reaction first proceeds by a gradual decrease of

*d*and increase of θ, until the transition state is reached. Subsequently, θ further increases, until the product geometry is obtained.

*d*and θ, connecting the reactant minimum configuration and the transition state. Here, the units of the parameters are chosen to render the overall CV unit-less. This CV is plotted as a gray line in Figure 2, with the projection of each NEB image indicated by the dotted lines and diamonds. Note that any parallel line in this plot effectively corresponds to the same CV. This shows that all NEB images are well separated on this scale, indicating that ξ is a suitable reaction coordinate. For the following free energy calculations, 50 evenly spaced biasing potentials are defined in the range ξ = −0.2–0.85, with a spring constant

*k*= 50 eV.

### III.2. Potential Training and Validation

### III.3. Free Energy Calculations

^{surf}and BEEF+vdW levels are shown in Figure 4, along with the PESs obtained with NEB calculations.

^{surf}level, indicating that CHO is not a stable intermediate at 523 K at all. At the BEEF-vdW level, a small barrier of 0.13 eV remains. Figure 4 also shows the free energy derivatives, as defined in eq 2. This shows that the GAP-based MD simulations provide good coverage of the CV range. More importantly, the derivatives display no discontinuities, which would point to lack of convergence or broken ergodicity.

### III.4. Rate Constants

*k*. The most common framework for computing

*k*from first-principles is Transition State Theory (TST). In this context, the rate constant is defined via the Eyring equation as

*G*is the free energy barrier. One can illustrate the importance of thermal effects on rates by plugging in the potential energy barrier Δ

*E*instead of the free energy barrier. At the BEEF-vdW level the corresponding rates differ by a factor of 85, i.e., by almost 2 orders of magnitude.

*Q*

_{IS}and

*Q*

_{TS}:

*N*vibrational modes and

*ν*

_{i}is the frequency of mode

*i*.

*k*

_{H,class}and

*k*

_{H,quant}. According to the correspondence principle, the classical and quantum models should yield equivalent results in the high-temperature limit. At which temperature this limit is reached in practice depends on the specific vibrational frequencies of the system, however. This is illustrated in Figure 5, where the ratios of the quantum and classical rate constants are plotted as a function of temperature. This reveals that

*k*

_{H,quant}exceeds

*k*

_{H,class}by a factor of 1.5 to 2 at 523 K, depending on the DFT functional. While this is a relatively small difference given that rate constants tend to vary by several orders of magnitude in catalytic reaction networks, quantum nuclear effects are clearly not negligible for this reaction.

*k*

_{UI}). These are shown in Figure 6, revealing that the classical, fully anharmonic description of the free energy barrier obtained with UI yields significantly larger rate constants than both the classical and quantum HA. Indeed, the enhancement from

*k*

_{H,class}to

*k*

_{UI}is much larger than the enhancement from

*k*

_{H,class}to

*k*

_{H,quant}(30 and 5-fold, for BEEF-vdW and revPBE+vdW

^{surf}, respectively).

*E*into eq 3 (the dotted lines in Figure 6). To estimate the combined effect of (anharmonic) thermal and quantum effects, the Pitzer–Gwinn (PG) approximation for the partition functions can be used. (41) To this end, we assume that

^{12}s

^{–1}(BEEF-vdW) and 9 × 10

^{12}s

^{–1}(revPBE+vdW

^{surf}). These rate constants can be understood more intuitively in terms of the half-lives ${\tau}_{1/2}$ of CHO they imply. These are 550 and 80 fs for BEEF-vdW and revPBE+vdW

^{surf}, respectively. Under these conditions, CHO decomposition is thus hardly a rare event.

*E*enter eq 4 exponentially while the partition functions are part of the prefactor, the accuracy of DFT transition state energetics has been a prime focus in computational catalysis methods development. (42) Our results indicate that thermal effects can be equally important for certain reactions.

### III.5. Harmonic Free Energy Corrections

^{surf}are indicated as stars in the central plot. An appealing feature of these harmonic free energy corrections is that they can be decomposed into physically interpretable contributions, namely, the integrated heat capacity

*C*

_{vib}

^{0→T}, the entropic contribution −

*TS*

_{vib}, and the zero point vibrational energy (ZPVE). These contributions to the barrier are shown in Table 1.

Contribution | revPBE+vdW^{surf} | BEEF-vdW |
---|---|---|

C_{vib}^{0→T} | –16 | –18 |

–ΔTS_{vib} | 25 | 16 |

ΔZPVE | –60 | –74 |

Sum | –51 | –76 |

^{a}

The final line is the overall correction. All values are given in meV.

*C*

_{vib}

^{0→T}and −

*TS*

_{vib}) have small and compensating effects on the barrier, with the entropic contributions to the barrier being positive and of similar magnitude to the negative contributions of the integrated heat capacity. This is in stark contrast to the UI predictions, which exclusively cover thermal effects and lead to a much stronger decrease in the barrier.

^{–1}, however, so that they would not be considered to be particularly pathological (see SI). Nevertheless, the PES obviously displays considerable anharmonicity. This is likely related to the small reaction barrier and the small geometric changes between the initial and transition states. As a consequence, application of the HA cannot be recommended in such situations.

### III.6. Density Functional Comparison

^{surf}dispersion correction. Specifically, the DFT reaction barrier was recomputed using single point calculations with different functionals and dispersion corrections at the BEEF-vdW and revPBE+vdW

^{surf}initial and transition state geometries (see Figure 7). Here, we considered the pure PBE and revPBE functionals as well as PBE with both the vdW

^{surf}and conventional Tkatchenko–Scheffler dispersion corrections (see the SI for details). This reveals revPBE+vdW

^{surf}to be something of an outlier (see the SI for the individual barriers of each functional).

^{surf}results discussed above represent the upper and lower bounds of the expected barrier within the scope of GGA DFT. Overall, the qualitative behavior of both functionals is analogous, in that the inclusion of thermal effects, anharmonicity, and nuclear quantum effects all lead to a significant increase in the predicted rate constants. In terms of the absolute rates we can conclude that the BEEF-vdW numbers are likely more reliable, though they may be slightly overestimating the barrier.

### III.7. Limitations

## IV. Conclusions

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00541.

Detailed description of the GAP model hyperparameters, training procedure, vibrational frequencies and density functional differences (PDF)

## Terms & Conditions

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

## Acknowledgments

S.S. gratefully acknowledges Wenbin Xu for the support with the Quantum Espresso calculations.

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(Elsevier Inc.)Research on zeolite-catalyzed methanol-to-hydrocarbons (MTH) conversion has long been concerned with the mechanism of the reaction between methanol and alkenes. Two pathways were debated: (1) the stepwise, proceeding through a surface-methoxy intermediate and (2) the concerted, in which the alkenes react directly with methanol. This work addresses the debate through micro-kinetic modeling based on d. functional theory calcns. of both pathways, as well as expts. employing temporal anal. of products to study the kinetics of the stepwise pathway for alkenes in H-ZSM-22 zeolite. The model predicts the stepwise pathway to prevail at typical MTH reaction temps., due to a higher entropy loss in the concerted as compared to the stepwise pathway. The entropy difference results from intermediate release of water in the stepwise pathway. These findings lead one to suggest that the stepwise pathway should also be considered when modeling MTH conversion in other zeolites.**15**Deringer, V. L.; Bartók, A. P.; Bernstein, N.; Wilkins, D. M.; Ceriotti, M.; Csányi, G. Gaussian Process Regression for Materials and Molecules.*Chem. Rev.*2021,*121*, 10073– 10141, DOI: 10.1021/acs.chemrev.1c00022Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhslyhs7rN&md5=012f2943caea3b785a70be9ad4acf5cbGaussian Process Regression for Materials and MoleculesDeringer, Volker L.; Bartok, Albert P.; Bernstein, Noam; Wilkins, David M.; Ceriotti, Michele; Csanyi, GaborChemical Reviews (Washington, DC, United States) (2021), 121 (16), 10073-10141CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chem. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interat. potentials, or force fields, in the Gaussian Approxn. Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodol. aspects of ref. data generation, representation and regression, as well as the question how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chem. and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodol. in the years to come.**16**Behler, J. Four Generations of High-Dimensional Neural Network Potentials.*Chem. Rev.*2021,*121*, 10037– 10072, DOI: 10.1021/acs.chemrev.0c00868Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXntlersL8%253D&md5=bde19a281c99afeb6348e2b6581bb610Four Generations of High-Dimensional Neural Network PotentialsBehler, JoergChemical Reviews (Washington, DC, United States) (2021), 121 (16), 10037-10072CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small mol. systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems contg. thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodol. of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent at. energy contributions; second, the description of the at. environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the ref. electronic structure data sets by active learning. In third-generation HDNNPs, in addn., long-range interactions are included employing environment-dependent partial charges expressed by at. neural networks. In fourth-generation HDNNPs, which are just emerging, in addn., nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.**17**Behler, J.; Csányi, G. Machine learning potentials for extended systems: a perspective.*Eur. Phys. J. B*2021,*94*, 142, DOI: 10.1140/epjb/s10051-021-00156-1Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsFylsbjN&md5=6fc466cc5c9769e0f7e3a353e9b4bac7Machine learning potentials for extended systems: a perspectiveBehler, Joerg; Csanyi, GaborEuropean Physical Journal B: Condensed Matter and Complex Systems (2021), 94 (7), 142CODEN: EPJBFY; ISSN:1434-6028. (Springer)Abstr.: In the past two and a half decades machine learning potentials have evolved from a special purpose soln. to a broadly applicable tool for large-scale atomistic simulations. By combining the efficiency of empirical potentials and force fields with an accuracy close to first-principles calcns. they now enable computer simulations of a wide range of mols. and materials. In this perspective, we summarize the present status of these new types of models for extended systems, which are increasingly used for materials modeling. There are several approaches, but they all have in common that they exploit the locality of at. properties in some form. Long-range interactions, most prominently electrostatic interactions, can also be included even for systems in which non-local charge transfer leads to an electronic structure that depends globally on all at. positions. Remaining challenges and limitations of current approaches are discussed. Graphic Abstr.: [graphic not available: see fulltext].**18**Bwoker, M. On the mechanism of ethanol synthesis on rhodium.*Catal. Today*1992,*15*, 77– 100, DOI: 10.1016/0920-5861(92)80123-5Google ScholarThere is no corresponding record for this reference.**19**Yang, N.; Medford, A. J.; Liu, X.; Studt, F.; Bligaard, T.; Bent, S. F.; Nørskov, J. K. Intrinsic Selectivity and Structure Sensitivity of Rhodium Catalysts for C2+Oxygenate Production.*J. Am. Chem. Soc.*2016,*138*, 3705– 3714, DOI: 10.1021/jacs.5b12087Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslKlsL0%253D&md5=ec6bf6812e71ffa3beae527bc808e306Intrinsic Selectivity and Structure Sensitivity of Rhodium Catalysts for C2+ Oxygenate ProductionYang, Nuoya; Medford, Andrew J.; Liu, Xinyan; Studt, Felix; Bligaard, Thomas; Bent, Stacey F.; Noerskov, Jens K.Journal of the American Chemical Society (2016), 138 (11), 3705-3714CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Synthesis gas (CO + H2) conversion is a promising route to converting coal, natural gas, or biomass into synthetic liq. fuels. Rhodium has long been studied as it is the only elemental catalyst that has demonstrated selectivity to ethanol and other C2+ oxygenates. However, the fundamentals of syngas conversion over rhodium are still debated. In this work a microkinetic model is developed for conversion of CO and H2 into methane, ethanol, and acetaldehyde on the Rh (211) and (111) surfaces, chosen to describe steps and close-packed facets on catalyst particles. The model is based on DFT calcns. using the BEEF-vdW functional. The mean-field kinetic model includes lateral adsorbate-adsorbate interactions, and the BEEF-vdW error estn. ensemble is used to propagate error from the DFT calcns. to the predicted rates. The model shows the Rh(211) surface to be ∼6 orders of magnitude more active than the Rh(111) surface, but highly selective toward methane, while the Rh(111) surface is intrinsically selective toward acetaldehyde. A variety of Rh/SiO2 catalysts are synthesized, tested for catalytic oxygenate prodn., and characterized using TEM. The exptl. results indicate that the Rh(111) surface is intrinsically selective toward acetaldehyde, and a strong inverse correlation between catalytic activity and oxygenate selectivity is obsd. Furthermore, iron impurities are shown to play a key role in modulating the selectivity of Rh/SiO2 catalysts toward ethanol. The exptl. observations are consistent with the structure-sensitivity predicted from theory. This work provides an improved at.-scale understanding and new insight into the mechanism, active site, and intrinsic selectivity of syngas conversion over rhodium catalysts and may also guide rational design of alloy catalysts made from more abundant elements.**20**Ulissi, Z. W.; Medford, A. J.; Bligaard, T.; Nørskov, J. K. To address surface reaction network complexity using scaling relations machine learning and DFT calculations.*Nat. Commun.*2017,*8*, 14621, DOI: 10.1038/ncomms14621Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czjtFamuw%253D%253D&md5=bde19b4dcb6abce90b2ea7ab073e1c6eTo address surface reaction network complexity using scaling relations machine learning and DFT calculationsUlissi Zachary W; Norskov Jens K; Medford Andrew J; Bligaard ThomasNature communications (2017), 8 (), 14621 ISSN:.Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries. We present a framework for optimization under uncertainty for heterogeneous catalysis reaction networks using surrogate models that are trained on the fly. The surrogate model is constructed by teaching a Gaussian process adsorption energies based on group additivity fingerprints, combined with transition-state scaling relations and a simple classifier for determining the rate-limiting step. The surrogate model is iteratively used to predict the most important reaction step to be calculated explicitly with computationally demanding electronic structure theory. Applying these methods to the reaction of syngas on rhodium(111), we identify the most likely reaction mechanism. Propagating uncertainty throughout this process yields the likelihood that the final mechanism is complete given measurements on only a subset of the entire network and uncertainty in the underlying density functional theory calculations.**21**Deimel, M.; Prats, H.; Seibt, M.; Reuter, K.; Andersen, M. Selectivity Trends and Role of Adsorbate–Adsorbate Interactions in CO Hydrogenation on Rhodium Catalysts.*ACS Catal.*2022,*12*, 7907– 7917, DOI: 10.1021/acscatal.2c02353Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFejtL7F&md5=7fb6ccfe0d7f35c7f72e2cf80d6be558Selectivity Trends and Role of Adsorbate-Adsorbate Interactions in CO Hydrogenation on Rhodium CatalystsDeimel, Martin; Prats, Hector; Seibt, Michael; Reuter, Karsten; Andersen, MieACS Catalysis (2022), 12 (13), 7907-7917CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)Predictive-quality computational modeling of heterogeneously catalyzed reactions has emerged as an important tool for the anal. and assessment of activity and activity trends. In contrast, more subtle selectivities and selectivity trends still pose a significant challenge to prevalent microkinetic modeling approaches that typically employ a mean-field approxn. (MFA). Here, we focus on CO hydrogenation on Rh catalysts with the possible products methane, acetaldehyde, ethanol, and water. This reaction has already been subjected to a no. of exptl. and theor. studies with conflicting views on the factors controlling activity and selectivity toward the more valuable higher oxygenates. Using accelerated first-principles kinetic Monte Carlo simulations and explicitly and systematically accounting for adsorbate-adsorbate interactions through a cluster expansion approach, we model the reaction on the low-index Rh(111) and stepped Rh(211) surfaces. We find that the Rh(111) facet is selective toward methane, while the Rh(211) facet exhibits a similar selectivity toward methane and acetaldehyde. This is consistent with the exptl. selectivity obsd. for larger, predominantly (111)-exposing Rh nanoparticles and resolves the discrepancy with earlier first-principles MFA microkinetic work that found the Rh(111) facet to be selective toward acetaldehyde. While the latter work tried to approx. account for lateral interactions through coverage-dependent rate expressions, our anal. demonstrates that this fails to sufficiently capture concomitant correlations among the adsorbed reaction intermediates that crucially det. the overall selectivity.**22**Kästner, J.; Thiel, W. Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: “Umbrella integration.*J. Chem. Phys.*2005,*123*, 144104, DOI: 10.1063/1.2052648Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFCnu7fM&md5=99a753fdcc7653c220980c35cca37d78Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration"Kastner, Johannes; Thiel, WalterJournal of Chemical Physics (2005), 123 (14), 144104/1-144104/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a method to analyze biased mol.-dynamics and Monte Carlo simulations, also known as umbrella sampling. In the limiting case of a strong bias, this method is equiv. to thermodn. integration. It employs only quantities with easily controllable equilibration and greatly reduces the statistical errors compared to the std. weighted histogram anal. method. We show the success of our approach for two examples, one analytic function, and one biol. system.**23**Kästner, J.; Thiel, W. Analysis of the statistical error in umbrella sampling simulations by umbrella integration.*J. Chem. Phys.*2006,*124*, 234106, DOI: 10.1063/1.2206775Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmsVWntr4%253D&md5=6e7f306bef4c578434c14436d25a4f10Analysis of the statistical error in umbrella sampling simulations by umbrella integrationKastner, Johannes; Thiel, WalterJournal of Chemical Physics (2006), 124 (23), 234106/1-234106/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Umbrella sampling simulations, or biased mol. dynamics, can be used to calc. the free-energy change of a chem. reaction. We investigate the sources of different sampling errors and derive approx. expressions for the statistical errors when using harmonic restraints and umbrella integration anal. This leads to generally applicable rules for the choice of the bias potential and the sampling parameters. Numerical results for simulations on an anal. model potential are presented for validation. While the derivations are based on umbrella integration anal., the final error est. is evaluated from the raw simulation data, and it may therefore be generally applicable as indicated by tests using the weighted histogram anal. method.**24**Roux, B. The calculation of the potential of mean force using computer simulations.*Comput. Phys. Commun.*1995,*91*, 275– 282, DOI: 10.1016/0010-4655(95)00053-IGoogle Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXps1Wrt7o%253D&md5=c5f038741fdc5765d3df4a07f37ec804The calculation of the potential of mean force using computer simulationsRoux, BenoitComputer Physics Communications (1995), 91 (1-3), 275-82CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)The problem of unbiasing and combining the results of umbrella sampling calcns. is reviewed. The weighted histogram anal. method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with mol. dynamics simulations of the alanine dipeptide for one- and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.**25**Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method.*J. Comput. Chem.*1992,*13*, 1011– 1021, DOI: 10.1002/jcc.540130812Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK38XmtVynsrs%253D&md5=5b2ad7410198f03025708a37c0fbe89dThe weighted histogram analysis method for free-energy calculations on biomolecules. I. The methodKumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.**26**Hub, J. S.; De Groot, B. L.; Van der Spoel, D. g_wham─A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates.*J. Chem. Theory Comput.*2010,*6*, 3713– 3720, DOI: 10.1021/ct100494zGoogle Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsVegu7bI&md5=c798afe576b97471e29040069e434028g_wham: A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation EstimatesHub, Jochen S.; de Groot, Bert L.; van der Spoel, DavidJournal of Chemical Theory and Computation (2010), 6 (12), 3713-3720CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The Weighted Histogram Anal. Method (WHAM) is a std. technique used to compute potentials of mean force (PMFs) from a set of umbrella sampling simulations. Here, the authors present a new WHAM implementation, termed g_wham, which is distributed freely with the GROMACS mol. simulation suite. G_wham ests. statistical errors using the technique of bootstrap anal. Three bootstrap methods are supported: (i) bootstrapping new trajectories based on the umbrella histograms, (ii) bootstrapping of complete histograms, and (iii) Bayesian bootstrapping of complete histograms, i.e., bootstrapping via the assignment of random wts. to the histograms. Because methods ii and iii consider only complete histograms as independent data points, these methods do not require the accurate calcn. of autocorrelation times. The authors demonstrate that, given sufficient sampling, bootstrapping new trajectories allows for an accurate error est. In the presence of long autocorrelations, however, (Bayesian) bootstrapping of complete histograms yields a more reliable error est., whereas bootstrapping of new trajectories may underestimate the error. In addn., the authors emphasize that the incorporation of autocorrelations into WHAM reduces the bias from limited sampling, in particular, when computing periodic PMFs in inhomogeneous systems such as solvated lipid membranes or protein channels.**27**Stecher, T.; Bernstein, N.; Csányi, G. Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression.*J. Chem. Theory Comput.*2014,*10*, 4079– 4097, DOI: 10.1021/ct500438vGoogle Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFyrurnI&md5=2f0cafb9fd30566efcbf7a359092b1ffFree Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process RegressionStecher, Thomas; Bernstein, Noam; Csanyi, GaborJournal of Chemical Theory and Computation (2014), 10 (9), 4079-4097CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost redn. to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant addnl. computation. A software implementation is made available on www.libatoms.org.**28**Hjorth Larsen, A.; Jørgen Mortensen, J.; Blomqvist, J.; Castelli, I. E.; Christensen, R.; Dułak, M.; Friis, J.; Groves, M. N.; Hammer, B.; Hargus, C.; Hermes, E. D.; Jennings, P. C.; Bjerre Jensen, P.; Kermode, J.; Kitchin, J. R.; Leonhard Kolsbjerg, E.; Kubal, J.; Kaasbjerg, K.; Lysgaard, S.; Bergmann Maronsson, J.; Maxson, T.; Olsen, T.; Pastewka, L.; Peterson, A.; Rostgaard, C.; Schiøtz, J.; Schütt, O.; Strange, M.; Thygesen, K. S.; Vegge, T.; Vilhelmsen, L.; Walter, M.; Zeng, Z.; Jacobsen, K. W. The atomic simulation environment─a Python library for working with atoms.*J. Phys.: Condens. Matter*2017,*29*, 273002, DOI: 10.1088/1361-648X/aa680eGoogle Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czpt1aksw%253D%253D&md5=c242d7e905c308340d613ade7adfcadfThe atomic simulation environment-a Python library for working with atomsHjorth Larsen Ask; Jorgen Mortensen Jens; Blomqvist Jakob; Castelli Ivano E; Christensen Rune; Dulak Marcin; Friis Jesper; Groves Michael N; Hammer Bjork; Hargus Cory; Hermes Eric D; Jennings Paul C; Bjerre Jensen Peter; Kermode James; Kitchin John R; Leonhard Kolsbjerg Esben; Kubal Joseph; Kaasbjerg Kristen; Lysgaard Steen; Bergmann Maronsson Jon; Maxson Tristan; Olsen Thomas; Pastewka Lars; Peterson Andrew; Rostgaard Carsten; Schiotz Jakob; Schutt Ole; Strange Mikkel; Thygesen Kristian S; Vegge Tejs; Vilhelmsen Lasse; Walter Michael; Zeng Zhenhua; Jacobsen Karsten WJournal of physics. Condensed matter : an Institute of Physics journal (2017), 29 (27), 273002 ISSN:.The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.**29**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*, 136403, DOI: 10.1103/PhysRevLett.104.136403Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXkt1Kqur8%253D&md5=0a468458554e85413b53816c082419f2Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the ElectronsBartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, GaborPhysical 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.**30**Bartók, A. P.; Kondor, R.; Csányi, G. On representing chemical environments.*Phys. Rev. B*2013,*87*, 184115, DOI: 10.1103/PhysRevB.87.184115Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXpvFClu7Y%253D&md5=f7739275562b8e77d4532f00da8814fbOn representing chemical environmentsBartok, Albert P.; Kondor, Risi; Csanyi, GaborPhysical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.**31**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*, e1701816, DOI: 10.1126/sciadv.1701816Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVWgsbjP&md5=e996f3746c995ed0304f33762f7da713Machine learning unifies the modeling of materials and moleculesBartok, Albert P.; De, Sandip; Poelking, Carl; Bernstein, Noam; Kermode, James R.; Csanyi, Gabor; Ceriotti, MicheleScience 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.**32**Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals.*Phys. Rev. B*1999,*59*, 7413– 7421, DOI: 10.1103/PhysRevB.59.7413Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXjtlOgtA%253D%253D&md5=5a79706aa2b3d959686cf4e425d21a6aImproved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionalsHammer, B.; Hansen, L. B.; Norskov, J. K.Physical Review B: Condensed Matter and Materials Physics (1999), 59 (11), 7413-7421CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)A simple formulation of a generalized gradient approxn. for the exchange and correlation energy of electrons has been proposed by J. Perdew et al. (1996). Subsequently, Y. Zhang and W. Wang (1998) have shown that a slight revision of the Perdew-Burke-Ernzerhof (PBE) functional systematically improves the atomization energies for a large database of small mols. In the present work, we show that the Zhang and Yang functional (revPBE) also improves the chemisorption energetics of atoms and mols. on transition-metal surfaces. Our test systems comprise at. and mol. adsorption of oxygen, CO, and NO on Ni(100), Ni(111), Rh(100), Pd(100), and Pd(111) surfaces. As the revPBE functional may locally violate the Lieb-Oxford criterion, we further develop an alternative revision of the PBE functional, RPBE, which gives the same improvement of the chemisorption energies as the revPBE functional at the same time as it fulfills the Lieb-Oxford criterion locally.**33**Wellendorff, J.; Silbaugh, T. L.; Garcia-Pintos, D.; Nørskov, J. K.; Bligaard, T.; Studt, F.; Campbell, C. T. A benchmark database for adsorption bond energies to transition metal surfaces and comparison to selected DFT functionals.*Surf. Sci.*2015,*640*, 36– 44, DOI: 10.1016/j.susc.2015.03.023Google Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtlGmu70%253D&md5=d0bb91c519e55f69afd96b0af7d345e1A benchmark database for adsorption bond energies to transition metal surfaces and comparison to selected DFT functionalsWellendorff, Jess; Silbaugh, Trent L.; Garcia-Pintos, Delfina; Noerskov, Jens K.; Bligaard, Thomas; Studt, Felix; Campbell, Charles T.Surface Science (2015), 640 (), 36-44CODEN: SUSCAS; ISSN:0039-6028. (Elsevier B.V.)A literature collection of exptl. adsorption energies over late transition metal surfaces is presented for systems where the authors believe that the energy measurements are particularly accurate, and the at.-scale adsorption geometries are particularly well established. This could become useful for benchmarking theor. methods for calcg. adsorption processes. The authors compare the exptl. results to six commonly used electron d. functionals, including some (RPBE, BEEF-vdW) which were specifically developed to treat adsorption processes. The comparison shows that there is ample room for improvements in the theor. descriptions.**34**Zhang, Y.; Yang, W. Comment on “Generalized Gradient Approximation Made Simple.*Phys. Rev. Lett.*1998,*80*, 890– 890, DOI: 10.1103/PhysRevLett.80.890Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXlsV2itg%253D%253D&md5=d14c7fc06fe200788f4192a00dca0730Comment on "Generalized Gradient Approximation Made Simple"Zhang, Yingkai; Yang, WeitaoPhysical Review Letters (1998), 80 (4), 890CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)A Comment on the Letter by John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. 77, 3865 (1996). The authors of the Letter offer a Reply.**35**Ruiz, V. G.; Liu, W.; Tkatchenko, A. Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces.*Phys. Rev. B*2016,*93*, 035118, DOI: 10.1103/PhysRevB.93.035118Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsVKmu7vF&md5=3b2a2d9fee8adf7df94ccd03d69534b2Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfacesRuiz, Victor G.; Liu, Wei; Tkatchenko, AlexandrePhysical Review B (2016), 93 (3), 035118/1-035118/17CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)Modeling the adsorption of atoms and mols. on surfaces requires efficient electronic-structure methods that are able to capture both covalent and noncovalent interactions in a reliable manner. In order to tackle this problem, we have developed a method within d.-functional theory (DFT) to model screened van der Waals interactions (vdW) for atoms and mols. on surfaces (the so-called DFT+vdWsurf method). The relatively high accuracy of the DFT+vdWsurf method in the calcn. of both adsorption distances and energies, as well as the high degree of its reliability across a wide range of adsorbates, indicates the importance of the collective electronic effects within the extended substrate for the calcn. of the vdW energy tail. We examine in detail the theor. background of the method and assess its performance for adsorption phenomena including the physisorption of Xe on selected close-packed transition metal surfaces and 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) on Au(111). We also address the performance of DFT+vdWsurf in the case of non-close-packed surfaces by studying the adsorption of Xe on Cu(110) and the interfaces formed by the adsorption of a PTCDA monolayer on the Ag(111), Ag(100), and Ag(110) surfaces. We conclude by discussing outstanding challenges in the modeling of vdW interactions for studying at. and mol. adsorbates on inorg. substrates.**36**Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab initio molecular simulations with numeric atom-centered orbitals.*Comput. Phys. Commun.*2009,*180*, 2175– 2196, DOI: 10.1016/j.cpc.2009.06.022Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtFGhurnI&md5=41ce9f9e42041605710733dc1f7818a5Ab initio molecular simulations with numeric atom-centered orbitalsBlum, Volker; Gehrke, Ralf; Hanke, Felix; Havu, Paula; Havu, Ville; Ren, Xinguo; Reuter, Karsten; Scheffler, MatthiasComputer Physics Communications (2009), 180 (11), 2175-2196CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)We describe a complete set of algorithms for ab initio mol. simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of mol. and materials properties from quantum-mech. first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute "ab initio mol. simulations" (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on d.-functional theory (DFT) in the local and semilocal (generalized gradient) approxns., but an extension to hybrid functionals, Hartree-Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio mol. dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calcn. to range from qual. tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs.**37**Wellendorff, J.; Lundgaard, K. T.; Møgelhøj, A.; Petzold, V.; Landis, D. D.; Nørskov, J. K.; Bligaard, T.; Jacobsen, K. W. Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation.*Phys. Rev. B*2012,*85*, 235149, DOI: 10.1103/PhysRevB.85.235149Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFehtbzM&md5=480585065c88766af6a7cd221c366e71Density functionals for surface science: exchange-correlation model development with Bayesian error estimationWellendorff, Jess; Lundgaard, Keld T.; Moegelhoej, Andreas; Petzold, Vivien; Landis, David D.; Noerskov, Jens K.; Bligaard, Thomas; Jacobsen, Karsten W.Physical Review B: Condensed Matter and Materials Physics (2012), 85 (23), 235149/1-235149/23CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)A methodol. for semiempirical d. functional optimization, using regularization and cross-validation methods from machine learning, is developed. We demonstrate that such methods enable well-behaved exchange-correlation approxns. in very flexible model spaces, thus avoiding the overfitting found when std. least-squares methods are applied to high-order polynomial expansions. A general-purpose d. functional for surface science and catalysis studies should accurately describe bond breaking and formation in chem., solid state physics, and surface chem., and should preferably also include van der Waals dispersion interactions. Such a functional necessarily compromises between describing fundamentally different types of interactions, making transferability of the d. functional approxn. a key issue. We investigate this trade-off between describing the energetics of intramol. and intermol., bulk solid, and surface chem. bonding, and the developed optimization method explicitly handles making the compromise based on the directions in model space favored by different materials properties. The approach is applied to designing the Bayesian error estn. functional with van der Waals correlation (BEEF-vdW), a semilocal approxn. with an addnl. nonlocal correlation term. Furthermore, an ensemble of functionals around BEEF-vdW comes out naturally, offering an est. of the computational error. An extensive assessment on a range of data sets validates the applicability of BEEF-vdW to studies in chem. and condensed matter physics. Applications of the approxn. and its Bayesian ensemble error est. to two intricate surface science problems support this.**38**Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; De Gironcoli, S.; Delugas, P.; Distasio, R. A.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Küçükbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la Roza, A.; Paulatto, L.; Poncé, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S. Advanced capabilities for materials modelling with Quantum Espresso.*J. Phys.: Condens. Matter*2017,*29*, 465901, DOI: 10.1088/1361-648X/aa8f79Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXntF2hsr0%253D&md5=17e46e5ac155b511f12deaeff078cc6dAdvanced capabilities for materials modelling with QUANTUM ESPRESSOGiannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; de Gironcoli, S.; Delugas, P.; Di Stasio, R. A., Jr.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Kucukbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la-Roza, A.; Paulatto, L.; Ponce, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S.Journal of Physics: Condensed Matter (2017), 29 (46), 465901/1-465901/30CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)QUANTUM ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on d.-functional theory, d.-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. QUANTUM ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.**39**Hermes, E.; Sargsyan, K.; Najm, H.; Zádor, J. Sella, an open-source automation-friendly molecular saddle point optimizer.*ChemRxiv*, DOI: 10.26434/chemrxiv-2022-44r17 , 2022.Google ScholarThere is no corresponding record for this reference.**40**Stocker, S.; Gasteiger, J.; Becker, F.; Günnemann, S.; Margraf, J. T. How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?.*Mach. Learn.: Sci. Technol.*2022,*3*, 045010, DOI: 10.1088/2632-2153/ac9955Google ScholarThere is no corresponding record for this reference.**41**Pitzer, K. S.; Gwinn, W. D. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops.*J. Chem. Phys.*1942,*10*, 428– 440, DOI: 10.1063/1.1723744Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaH38XjsVKktQ%253D%253D&md5=b5a443a174b204773051bea5b1dacf3dEnergy levels and thermodynamic functions for molecules with internal rotation. I. Rigid frame with attached topsPitzer, Kenneth S.; Gwinn, Wm. D.Journal of Chemical Physics (1942), 10 (), 428-40CODEN: JCPSA6; ISSN:0021-9606.Math.**42**Mallikarjun Sharada, S.; Bligaard, T.; Luntz, A. C.; Kroes, G.-J.; Nørskov, J. K. SBH10: A Benchmark Database of Barrier Heights on Transition Metal Surfaces.*J. Phys. Chem. C*2017,*121*, 19807– 19815, DOI: 10.1021/acs.jpcc.7b05677Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXht1OhtL3E&md5=b6349339058cc3295452a6d0a0dbd190SBH10: A Benchmark Database of Barrier Heights on Transition Metal SurfacesMallikarjun Sharada, Shaama; Bligaard, Thomas; Luntz, Alan C.; Kroes, Geert-Jan; Noerskov, Jens K.Journal of Physical Chemistry C (2017), 121 (36), 19807-19815CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)While the performance of d. functional approxns. (DFAs) for gas phase reaction energetics has been extensively benchmarked, their reliability for activation barriers on surfaces is not fully understood. The primary reason for this is the absence of well-defined, chem. accurate benchmark databases for chem. on surfaces. We present a database of 10 surface barrier heights for dissocn. of small mols., SBH10, based on carefully chosen refs. from mol. beam scattering, laser assisted associative desorption, and thermal expts. Our benchmarking study compares the performance of a dispersion-cor. generalized gradient approxn. (GGA-vdW), BEEF-vdW, a meta-GGA, MS2, and a screened hybrid functional, HSE06. In stark contrast to gas phase reactions for which GGAs systematically underestimate barrier heights and hybrids tend to be most accurate, the BEEF-vdW functional dets. barriers accurately to within 0.14 eV of expts., while MS2 and HSE06 underestimate barrier heights on surfaces. Higher accuracy of BEEF-vdW stems from the fact that the functional is trained on chemisorption systems, and transition states for dissocn. on surfaces closely resemble the final, chemisorbed states. Therefore, a functional that can describe chemisorption accurately can also reliably predict barrier heights on surfaces.**43**Caro, M. A. Parametrization of the Tkatchenko-Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid water.*arXiv*, 1704.00761v2, 2017.Google ScholarThere is no corresponding record for this reference.**44**Hörmann, L.; Jeindl, A.; Hofmann, O. T. Reproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111).*J. Chem. Phys.*2020,*153*, 104701, DOI: 10.1063/5.0020736Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB38bpt1Sntg%253D%253D&md5=ce54bd80fcce5cfb3ab1302c60c03fcaReproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111)Hormann Lukas; Jeindl Andreas; Hofmann Oliver TThe Journal of chemical physics (2020), 153 (10), 104701 ISSN:.Molecular adsorption at organic/metal interfaces depends on a range of mechanisms: covalent bonds, charge transfer, Pauli repulsion, and van der Waals (vdW) interactions shape the potential energy surface (PES), making it key to understanding organic/metal interfaces. Describing such interfaces with density functional theory requires carefully selecting the exchange correlation (XC) functional and vdW correction scheme. To explore the reproducibility of the PES with respect to the choice of method, we present a benchmark of common local, semi-local, and non-local XC functionals in combination with various vdW corrections. We benchmark these methods using perylene-tetracarboxylic dianhydride on Ag(111), one of the most frequently studied organic/metal interfaces. For each method, we determine the PES using a Gaussian process regression algorithm, which requires only about 50 density functional theory calculations as input. This allows a detailed analysis of the PESs' features, such as the positions and energies of minima and saddle points. Comparing the results from different combinations of XC functionals and vdW corrections enables us to identify trends and differences between the approaches. PESs for different computation methods are in qualitative agreement but also display significant quantitative differences. In particular, the lateral positions of adsorption geometries agree well with experiment, while adsorption heights, energies, and barriers show larger discrepancies.**45**Dietschreit, J. C. B.; Diestler, D. J.; Hulm, A.; Ochsenfeld, C.; Gómez-Bombarelli, R. From free-energy profiles to activation free energies.*J. Chem. Phys.*2022,*157*, 084113, DOI: 10.1063/5.0102075Google Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xit1aqu77P&md5=f44ef862ecbdfca27c22d362b5425313From free-energy profiles to activation free energiesDietschreit, Johannes C. B.; Diestler, Dennis J.; Hulm, Andreas; Ochsenfeld, Christian; Gomez-Bombarelli, RafaelJournal of Chemical Physics (2022), 157 (8), 084113CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Given a chem. reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the "free-energy" analog of the min. potential energy path and to take the activation free energy, ΔF‡RP, as the difference between the max. at the transition state and the min. at R. We show that this approxn. can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different ΔF‡RP. We derive an exact expression for the activation free energy that avoids this ambiguity. We find ΔF‡RP to be a combination of the probability of the system being in the reactant state, the probability d. on the dividing surface, and the thermal de Broglie wavelength assocd. with the transition. We apply our formalism to simple analytic models and realistic chem. systems and show that the FEP-based approxn. applies only at low temps. for CVs with a small effective mass. Most chem. reactions occur on complex, high-dimensional PES that cannot be treated anal. and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, ΔF‡RP is quite sensitive. (c) 2022 American Institute of Physics.**46**Goldsmith, C. F.; Harding, L. B.; Georgievskii, Y.; Miller, J. A.; Klippenstein, S. J. Temperature and Pressure-Dependent Rate Coefficients for the Reaction of Vinyl Radical with Molecular Oxygen.*J. Phys. Chem. A*2015,*119*, 7766– 7779, DOI: 10.1021/acs.jpca.5b01088Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXosVChu7c%253D&md5=b67e6beeafea086707b70824de8ca65fTemperature and Pressure-Dependent Rate Coefficients for the Reaction of Vinyl Radical with Molecular OxygenGoldsmith, C. Franklin; Harding, Lawrence B.; Georgievskii, Yuri; Miller, James A.; Klippenstein, Stephen J.Journal of Physical Chemistry A (2015), 119 (28), 7766-7779CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)State-of-the-art calcns. of the C2H3O2 potential energy surface are presented. A new method is described for computing the interaction potential for R + O2 reactions. The method, which combines accurate detn. of the quartet potential along the doublet min. energy path with multireference calcns. of the doublet/quartet splitting, decreases the uncertainty in the doublet potential and thence the rate consts. by more than a factor of 2. The temp.- and pressure-dependent rate coeffs. are computed using variable reaction coordinate transition-state theory, variational transition-state theory, and conventional transition-state theory, as implemented in a new RRKM/ME code. The main bimol. product channels are CH2O + HCO at lower temps. and CH2CHO + O at higher temps. Above 10 atm, the collisional stabilization of CH2CHOO directly competes with these two product channels. CH2CHOO decomps. primarily to CH2O + HCO. The next two most significant bimol. products are OCHCHO + H and 3CHCHO + OH, and not C2H2 + HO2. C2H3 + O2 will be predominantly chain branching above 1700 K. Uncertainty anal. is presented for the two most important transition states. The uncertainties in these two barrier heights result in a significant uncertainty in the temp. at which CH2CHO + O overtakes all other product channels.**47**Markland, T. E.; Ceriotti, M. Nuclear quantum effects enter the mainstream.*Nat. Rev. Chem.*2018,*2*, 0109, DOI: 10.1038/s41570-017-0109Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtVyksbfP&md5=39796515dbe165f548d032683cf76049Nuclear quantum effects enter the mainstreamMarkland, Thomas E.; Ceriotti, MicheleNature Reviews Chemistry (2018), 2 (3), 0109CODEN: NRCAF7; ISSN:2397-3358. (Nature Research)A review. Atomistic simulations of chem., biol. and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mech. behavior of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approxn. could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, esp. when systems contg. light atoms are treated using current state-of-the-art descriptions of chem. interactions. Over the past decade, this realization has spurred a series of methodol. advances that have dramatically reduced the cost of including these important phys. effects in the structure and dynamics of chem. systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of mol. simulations. These advances have led to new insights into phenomena that are relevant to different areas of science - from biochem. to condensed matter - and open the door to many exciting future opportunities.**48**Pavošević, F.; Culpitt, T.; Hammes-Schiffer, S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method.*Chem. Rev.*2020,*120*, 4222– 4253, DOI: 10.1021/acs.chemrev.9b00798Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXmvVClt7Y%253D&md5=f22e85887a6343405537ecdfbb83943aMulticomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear-Electronic Orbital MethodPavosevic, Fabijan; Culpitt, Tanner; Hammes-Schiffer, SharonChemical Reviews (Washington, DC, United States) (2020), 120 (9), 4222-4253CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. In multicomponent quantum chem., more than one type of particle is treated quantum mech. with either d. functional theory or wave function based methods. In particular, the nuclear-electronic orbital (NEO) approach treats specified nuclei, typically hydrogen nuclei, on the same level as the electrons. This approach enables the incorporation of nuclear quantum effects, such as nuclear delocalization, anharmonicity, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects directly into quantum chem. calcns. Such effects impact optimized geometries, mol. vibrational frequencies, reaction paths, isotope effects, and dynamical simulations. Multicomponent d. functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) achieve an optimal balance between computational efficiency and accuracy for computing ground and excited state properties, resp. Multicomponent wave function based methods, such as the coupled cluster singles and doubles (NEO-CCSD) method for ground states and the equation-of-motion counterpart (NEO-EOM-CCSD) for excited states, attain similar accuracy without requiring any parametrization and can be systematically improved but are more computationally expensive. Variants of the orbital-optimized perturbation theory (NEO-OOMP2) method achieve nearly the accuracy of NEO-CCSD for ground states with significantly lower computational cost. Addnl. approaches for computing excited electronic, vibrational, and vibronic states include the delta SCF (NEO-ΔSCF), complete active space SCF (NEO-CASSCF), and nonorthogonal CI methods. Multireference methods are particularly important for describing hydrogen tunneling processes. Other types of multicomponent systems, such as those contg. electrons and positrons, have also been studied within the NEO framework. The NEO approach allows the incorporation of nuclear quantum effects and non-Born-Oppenheimer effects for specified nuclei into quantum chem. calcns. in an accessible and computationally efficient manner.

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## References

This article references 48 other publications.

**1**Roberts, M. Birth of the catalytic concept (1800–1900).*Catal. Lett.*2000,*67*, 1– 4, DOI: 10.1023/A:1016622806065There is no corresponding record for this reference.**2**Eyring, H. The Activated Complex in Chemical Reactions.*J. Chem. Phys.*1935,*3*, 107– 115, DOI: 10.1063/1.17496042https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaA2MXhs1Sksw%253D%253D&md5=48a4a9fa845d5bbafe3b249b9eb7b28eStatistical Mechanical Treatment of the Activated Complex in Chemical ReactionsEyring, HenryJournal of Chemical Physics (1935), 3 (), 107-15CODEN: JCPSA6; ISSN:0021-9606.A possible error in Eyring's recent calcns. of abs. reaction rates due to the short life and consequent unsharp quantization of the activated complex is noted. The existence of this error is made more probable by a consideration of the target area required by Eyring's equations at low temps. There is no doubt that his treatment becomes asymptotically correct at high temps.**3**Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. Current Status of Transition-State Theory.*J. Phys. Chem.*1996,*100*, 12771– 12800, DOI: 10.1021/jp953748q3https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xkt1ansr8%253D&md5=5663e2f23815cdc1c0bbb6bbb91adabeCurrent Status of Transition-State TheoryTruhlar, Donald G.; Garrett, Bruce C.; Klippenstein, Stephen J.Journal of Physical Chemistry (1996), 100 (31), 12771-12800CODEN: JPCHAX; ISSN:0022-3654. (American Chemical Society)A review with 843 refs.; we present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodol. for calcns. on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both exptl. and other theor. dynamical approxns.**4**Bruix, A.; Margraf, J. T.; Andersen, M.; Reuter, K. First-principles-based multiscale modelling of heterogeneous catalysis.*Nat. Catal.*2019,*2*, 659– 670, DOI: 10.1038/s41929-019-0298-34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXht1KksLrN&md5=942697c42dde038094f929e5b91f639fFirst-principles-based multiscale modelling of heterogeneous catalysisBruix, Albert; Margraf, Johannes T.; Andersen, Mie; Reuter, KarstenNature Catalysis (2019), 2 (8), 659-670CODEN: NCAACP; ISSN:2520-1158. (Nature Research)A review. First-principles-based multiscale models are ever more successful in addressing the wide range of length and time scales over which material-function relationships evolve in heterogeneous catalysis. They provide invaluable mechanistic insight and allow screening of vast materials spaces for promising new catalysts - in silico and at predictive quality. Here, we briefly review methodol. cornerstones of existing approaches and highlight successes and ongoing developments. The biggest challenge is to overcome presently largely static couplings between the descriptions at the various scales to adequately treat the dynamic and adaptive nature of working catalysts. On the road towards a higher structural, mechanistic and environmental complexity, it is, in particular, the fusion with machine learning methodol. that promises rapid advances in the years to come.**5**Nørskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H. Towards the computational design of solid catalysts.*Nat. Chem.*2009,*1*, 37– 46, DOI: 10.1038/nchem.1215https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXktlSlur8%253D&md5=cdd7bfafd022c7b538deed1446836f20Towards the computational design of solid catalystsNorskov, J. K.; Bligaard, T.; Rossmeisl, J.; Christensen, C. H.Nature Chemistry (2009), 1 (1), 37-46CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)A review; over the past decade the theor. description of surface reactions has undergone a radical development. Advances in d. functional theory mean it is now possible to describe catalytic reactions at surfaces with the detail and accuracy required for computational results to compare favorably with expts. Theor. methods can be used to describe surface chem. reactions in detail and to understand variations in catalytic activity from one catalyst to another. Here, we review the first steps towards using computational methods to design new catalysts. Examples include screening for catalysts with increased activity and catalysts with improved selectivity. We discuss how, in the future, such methods may be used to engineer the electronic structure of the active surface by changing its compn. and structure.**6**Margraf, J. T.; Jung, H.; Scheurer, C.; Reuter, K. Exploring Catalytic Reaction Networks with Machine Learning.*Nat. Catal.*2023,*6*, 112– 121, DOI: 10.1038/s41929-022-00896-yThere is no corresponding record for this reference.**7**Dellago, C.; Bolhuis, P. G.; Csajka, F. S.; Chandler, D. Transition path sampling and the calculation of rate constants.*J. Chem. Phys.*1998,*108*, 1964– 1977, DOI: 10.1063/1.4755627https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXkvFChsQ%253D%253D&md5=4bb2f7b8316dbb4526be81bd24083814Transition path sampling and the calculation of rate constantsDellago, Christoph; Bolhuis, Peter G.; Csajka, Felix S.; Chandler, DavidJournal of Chemical Physics (1998), 108 (5), 1964-1977CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We have developed a method to study transition pathways for rare events in complex systems. The method can be used to det. rate consts. for transitions between stable states by turning the calcn. of reactive flux correlation functions into the computation of an isomorphic reversible work. In contrast to previous dynamical approaches, the method relies neither on prior knowledge nor on explicit specification of transition states. Rather, it provides an importance sampling from which transition states can be characterized statistically. A simple model is analyzed to illustrate the methodol.**8**Bussi, G.; Laio, A. Using metadynamics to explore complex free-energy landscapes.*Nat. Rev. Phys.*2020,*2*, 200– 212, DOI: 10.1038/s42254-020-0153-0There is no corresponding record for this reference.**9**Torrie, G. M.; Valleau, J. P. Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid.*Chem. Phys. Lett.*1974,*28*, 578– 581, DOI: 10.1016/0009-2614(74)80109-09https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2MXnslyjtQ%253D%253D&md5=4cdfeafc8c3bfc6bf08e50d8448b75f4Monte-Carlo free energy estimates using non-Boltzmann sampling. Application to the subcritical Lennard-Jones fluidTorrie, Glenn M.; Valleau, John P.Chemical Physics Letters (1974), 28 (4), 578-81CODEN: CHPLBC; ISSN:0009-2614.A Monte Carlo technique is presented for estn. of the free energies of fluids by sampling on distributions designed for this purpose, rather than on the usual Boltzmann distribution. As an illustration of its use, the free energy of a Lennard-Jones fluid in the liq.-vapour coexistence region was estd. by relating it to that of the inverse-12 (soft sphere) fluid, which itself shows no condensation.**10**Kästner, J. Umbrella sampling.*Wiley Interdiscip. Rev. Comput. Mol. Sci.*2011,*1*, 932– 942, DOI: 10.1002/wcms.66There is no corresponding record for this reference.**11**Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths.*J. Chem. Phys.*2000,*113*, 9901– 9904, DOI: 10.1063/1.132967211https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXosFagurc%253D&md5=3899b9e2e9e3eb74009987d96623f018A climbing image nudged elastic band method for finding saddle points and minimum energy pathsHenkelman, Graeme; Uberuaga, Blas P.; Jonsson, HannesJournal of Chemical Physics (2000), 113 (22), 9901-9904CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A modification of the nudged elastic band method for finding min. energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring consts. are used to increase the d. of images near the top of the energy barrier to get an improved est. of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir(111) and H2 on Si(100) using plane wave based d. functional theory are presented.**12**Andersen, M.; Cingolani, J. S.; Reuter, K. Ab Initio Thermodynamics of Hydrocarbons Relevant to Graphene Growth at Solid and Liquid Cu Surfaces.*J. Phys. Chem. C*2019,*123*, 22299– 22310, DOI: 10.1021/acs.jpcc.9b0564212https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsF2nurzP&md5=29a764a2dabfcfd779e690aefcc532bcAb Initio Thermodynamics of Hydrocarbons Relevant to Graphene Growth at Solid and Liquid Cu SurfacesAndersen, Mie; Cingolani, Juan Santiago; Reuter, KarstenJournal of Physical Chemistry C (2019), 123 (36), 22299-22310CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Using ab initio thermodn., the stability of a wide range of hydrocarbon adsorbates under various chem. vapor deposition (CVD) conditions (temp., methane and hydrogen pressures) used in exptl. graphene growth protocols at solid and liq. Cu surfaces has been explored. At the employed high growth temps. around the m.p. of Cu, we find that commonly used thermodn. models such as the harmonic oscillator model may no longer be accurate. Instead, we account for the translational and rotational mobility of adsorbates using a recently developed hindered translator and rotator model or a two-dimensional ideal gas model. The thermodn. considerations turn out to be crucial for explaining exptl. results and allow us to improve and extend the findings of earlier theor. studies regarding the role of hydrogen and hydrocarbon species in CVD. In particular, we find that smaller hydrocarbons will completely dehydrogenate under most CVD conditions. For larger clusters, our results show that metal-terminated and hydrogen-terminated edges have very similar stabilities. While both cluster types might thus form during the expt., we show that the low binding strength of clusters with hydrogen-terminated edges could result in instability toward desorption.**13**Bajpai, A.; Mehta, P.; Frey, K.; Lehmer, A. M.; Schneider, W. F. Benchmark First-Principles Calculations of Adsorbate Free Energies.*ACS Catal.*2018,*8*, 1945– 1954, DOI: 10.1021/acscatal.7b0343813https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhsFGqu7o%253D&md5=d6b5782ac827c9ac8ffc5a023d7c1234Benchmark First-Principles Calculations of Adsorbate Free EnergiesBajpai, Anshumaan; Mehta, Prateek; Frey, Kurt; Lehmer, Andrew M.; Schneider, William F.ACS Catalysis (2018), 8 (3), 1945-1954CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)Adsorbate free energies are fundamental quantities in the microkinetic modeling of catalytic reactions. In first-principles modeling, finite-temp. free energies are generally obtained by combining d. functional theory energies with std. approx. models, such as the harmonic oscillator, the hindered translator, or the two-dimensional ideal gas. In this work, we calc. accurate free energies directly from first-principles potential energy surfaces combined with exact quantum mech. solns. for the translational energy states to benchmark the reliability of common approxns. Through a series of case studies of monat. adsorbates on metal surfaces, we show that no one free energy model performs satisfactorily in all cases. Moreover, even combinations of different approxns. sometimes deviate significantly from the free energies calcd. by our first-principles approach. Using observations from these case studies, we discuss how a full quantum mech. approach can be extended to calc. accurate free energies for arbitrary adsorbate potential energy surfaces at computational cost similar to std. models.**14**Brogaard, R. Y.; Henry, R.; Schuurman, Y.; Medford, A. J.; Moses, P. G.; Beato, P.; Svelle, S.; Nørskov, J. K.; Olsbye, U. Methanol-to-hydrocarbons conversion: The alkene methylation pathway.*J. Catal.*2014,*314*, 159– 169, DOI: 10.1016/j.jcat.2014.04.00614https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXotVyqt7g%253D&md5=95e79589a85ed6a73147246fe1fb6458Methanol-to-hydrocarbons conversion: The alkene methylation pathwayBrogaard, Rasmus Y.; Henry, Reynald; Schuurman, Yves; Medford, Andrew J.; Moses, Poul Georg; Beato, Pablo; Svelle, Stian; Noerskov, Jens K.; Olsbye, UnniJournal of Catalysis (2014), 314 (), 159-169CODEN: JCTLA5; ISSN:0021-9517. (Elsevier Inc.)Research on zeolite-catalyzed methanol-to-hydrocarbons (MTH) conversion has long been concerned with the mechanism of the reaction between methanol and alkenes. Two pathways were debated: (1) the stepwise, proceeding through a surface-methoxy intermediate and (2) the concerted, in which the alkenes react directly with methanol. This work addresses the debate through micro-kinetic modeling based on d. functional theory calcns. of both pathways, as well as expts. employing temporal anal. of products to study the kinetics of the stepwise pathway for alkenes in H-ZSM-22 zeolite. The model predicts the stepwise pathway to prevail at typical MTH reaction temps., due to a higher entropy loss in the concerted as compared to the stepwise pathway. The entropy difference results from intermediate release of water in the stepwise pathway. These findings lead one to suggest that the stepwise pathway should also be considered when modeling MTH conversion in other zeolites.**15**Deringer, V. L.; Bartók, A. P.; Bernstein, N.; Wilkins, D. M.; Ceriotti, M.; Csányi, G. Gaussian Process Regression for Materials and Molecules.*Chem. Rev.*2021,*121*, 10073– 10141, DOI: 10.1021/acs.chemrev.1c0002215https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhslyhs7rN&md5=012f2943caea3b785a70be9ad4acf5cbGaussian Process Regression for Materials and MoleculesDeringer, Volker L.; Bartok, Albert P.; Bernstein, Noam; Wilkins, David M.; Ceriotti, Michele; Csanyi, GaborChemical Reviews (Washington, DC, United States) (2021), 121 (16), 10073-10141CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chem. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interat. potentials, or force fields, in the Gaussian Approxn. Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodol. aspects of ref. data generation, representation and regression, as well as the question how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chem. and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodol. in the years to come.**16**Behler, J. Four Generations of High-Dimensional Neural Network Potentials.*Chem. Rev.*2021,*121*, 10037– 10072, DOI: 10.1021/acs.chemrev.0c0086816https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXntlersL8%253D&md5=bde19a281c99afeb6348e2b6581bb610Four Generations of High-Dimensional Neural Network PotentialsBehler, JoergChemical Reviews (Washington, DC, United States) (2021), 121 (16), 10037-10072CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small mol. systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems contg. thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodol. of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent at. energy contributions; second, the description of the at. environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the ref. electronic structure data sets by active learning. In third-generation HDNNPs, in addn., long-range interactions are included employing environment-dependent partial charges expressed by at. neural networks. In fourth-generation HDNNPs, which are just emerging, in addn., nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.**17**Behler, J.; Csányi, G. Machine learning potentials for extended systems: a perspective.*Eur. Phys. J. B*2021,*94*, 142, DOI: 10.1140/epjb/s10051-021-00156-117https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsFylsbjN&md5=6fc466cc5c9769e0f7e3a353e9b4bac7Machine learning potentials for extended systems: a perspectiveBehler, Joerg; Csanyi, GaborEuropean Physical Journal B: Condensed Matter and Complex Systems (2021), 94 (7), 142CODEN: EPJBFY; ISSN:1434-6028. (Springer)Abstr.: In the past two and a half decades machine learning potentials have evolved from a special purpose soln. to a broadly applicable tool for large-scale atomistic simulations. By combining the efficiency of empirical potentials and force fields with an accuracy close to first-principles calcns. they now enable computer simulations of a wide range of mols. and materials. In this perspective, we summarize the present status of these new types of models for extended systems, which are increasingly used for materials modeling. There are several approaches, but they all have in common that they exploit the locality of at. properties in some form. Long-range interactions, most prominently electrostatic interactions, can also be included even for systems in which non-local charge transfer leads to an electronic structure that depends globally on all at. positions. Remaining challenges and limitations of current approaches are discussed. Graphic Abstr.: [graphic not available: see fulltext].**18**Bwoker, M. On the mechanism of ethanol synthesis on rhodium.*Catal. Today*1992,*15*, 77– 100, DOI: 10.1016/0920-5861(92)80123-5There is no corresponding record for this reference.**19**Yang, N.; Medford, A. J.; Liu, X.; Studt, F.; Bligaard, T.; Bent, S. F.; Nørskov, J. K. Intrinsic Selectivity and Structure Sensitivity of Rhodium Catalysts for C2+Oxygenate Production.*J. Am. Chem. Soc.*2016,*138*, 3705– 3714, DOI: 10.1021/jacs.5b1208719https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslKlsL0%253D&md5=ec6bf6812e71ffa3beae527bc808e306Intrinsic Selectivity and Structure Sensitivity of Rhodium Catalysts for C2+ Oxygenate ProductionYang, Nuoya; Medford, Andrew J.; Liu, Xinyan; Studt, Felix; Bligaard, Thomas; Bent, Stacey F.; Noerskov, Jens K.Journal of the American Chemical Society (2016), 138 (11), 3705-3714CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Synthesis gas (CO + H2) conversion is a promising route to converting coal, natural gas, or biomass into synthetic liq. fuels. Rhodium has long been studied as it is the only elemental catalyst that has demonstrated selectivity to ethanol and other C2+ oxygenates. However, the fundamentals of syngas conversion over rhodium are still debated. In this work a microkinetic model is developed for conversion of CO and H2 into methane, ethanol, and acetaldehyde on the Rh (211) and (111) surfaces, chosen to describe steps and close-packed facets on catalyst particles. The model is based on DFT calcns. using the BEEF-vdW functional. The mean-field kinetic model includes lateral adsorbate-adsorbate interactions, and the BEEF-vdW error estn. ensemble is used to propagate error from the DFT calcns. to the predicted rates. The model shows the Rh(211) surface to be ∼6 orders of magnitude more active than the Rh(111) surface, but highly selective toward methane, while the Rh(111) surface is intrinsically selective toward acetaldehyde. A variety of Rh/SiO2 catalysts are synthesized, tested for catalytic oxygenate prodn., and characterized using TEM. The exptl. results indicate that the Rh(111) surface is intrinsically selective toward acetaldehyde, and a strong inverse correlation between catalytic activity and oxygenate selectivity is obsd. Furthermore, iron impurities are shown to play a key role in modulating the selectivity of Rh/SiO2 catalysts toward ethanol. The exptl. observations are consistent with the structure-sensitivity predicted from theory. This work provides an improved at.-scale understanding and new insight into the mechanism, active site, and intrinsic selectivity of syngas conversion over rhodium catalysts and may also guide rational design of alloy catalysts made from more abundant elements.**20**Ulissi, Z. W.; Medford, A. J.; Bligaard, T.; Nørskov, J. K. To address surface reaction network complexity using scaling relations machine learning and DFT calculations.*Nat. Commun.*2017,*8*, 14621, DOI: 10.1038/ncomms1462120https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czjtFamuw%253D%253D&md5=bde19b4dcb6abce90b2ea7ab073e1c6eTo address surface reaction network complexity using scaling relations machine learning and DFT calculationsUlissi Zachary W; Norskov Jens K; Medford Andrew J; Bligaard ThomasNature communications (2017), 8 (), 14621 ISSN:.Surface reaction networks involving hydrocarbons exhibit enormous complexity with thousands of species and reactions for all but the very simplest of chemistries. We present a framework for optimization under uncertainty for heterogeneous catalysis reaction networks using surrogate models that are trained on the fly. The surrogate model is constructed by teaching a Gaussian process adsorption energies based on group additivity fingerprints, combined with transition-state scaling relations and a simple classifier for determining the rate-limiting step. The surrogate model is iteratively used to predict the most important reaction step to be calculated explicitly with computationally demanding electronic structure theory. Applying these methods to the reaction of syngas on rhodium(111), we identify the most likely reaction mechanism. Propagating uncertainty throughout this process yields the likelihood that the final mechanism is complete given measurements on only a subset of the entire network and uncertainty in the underlying density functional theory calculations.**21**Deimel, M.; Prats, H.; Seibt, M.; Reuter, K.; Andersen, M. Selectivity Trends and Role of Adsorbate–Adsorbate Interactions in CO Hydrogenation on Rhodium Catalysts.*ACS Catal.*2022,*12*, 7907– 7917, DOI: 10.1021/acscatal.2c0235321https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFejtL7F&md5=7fb6ccfe0d7f35c7f72e2cf80d6be558Selectivity Trends and Role of Adsorbate-Adsorbate Interactions in CO Hydrogenation on Rhodium CatalystsDeimel, Martin; Prats, Hector; Seibt, Michael; Reuter, Karsten; Andersen, MieACS Catalysis (2022), 12 (13), 7907-7917CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)Predictive-quality computational modeling of heterogeneously catalyzed reactions has emerged as an important tool for the anal. and assessment of activity and activity trends. In contrast, more subtle selectivities and selectivity trends still pose a significant challenge to prevalent microkinetic modeling approaches that typically employ a mean-field approxn. (MFA). Here, we focus on CO hydrogenation on Rh catalysts with the possible products methane, acetaldehyde, ethanol, and water. This reaction has already been subjected to a no. of exptl. and theor. studies with conflicting views on the factors controlling activity and selectivity toward the more valuable higher oxygenates. Using accelerated first-principles kinetic Monte Carlo simulations and explicitly and systematically accounting for adsorbate-adsorbate interactions through a cluster expansion approach, we model the reaction on the low-index Rh(111) and stepped Rh(211) surfaces. We find that the Rh(111) facet is selective toward methane, while the Rh(211) facet exhibits a similar selectivity toward methane and acetaldehyde. This is consistent with the exptl. selectivity obsd. for larger, predominantly (111)-exposing Rh nanoparticles and resolves the discrepancy with earlier first-principles MFA microkinetic work that found the Rh(111) facet to be selective toward acetaldehyde. While the latter work tried to approx. account for lateral interactions through coverage-dependent rate expressions, our anal. demonstrates that this fails to sufficiently capture concomitant correlations among the adsorbed reaction intermediates that crucially det. the overall selectivity.**22**Kästner, J.; Thiel, W. Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: “Umbrella integration.*J. Chem. Phys.*2005,*123*, 144104, DOI: 10.1063/1.205264822https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFCnu7fM&md5=99a753fdcc7653c220980c35cca37d78Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration"Kastner, Johannes; Thiel, WalterJournal of Chemical Physics (2005), 123 (14), 144104/1-144104/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a method to analyze biased mol.-dynamics and Monte Carlo simulations, also known as umbrella sampling. In the limiting case of a strong bias, this method is equiv. to thermodn. integration. It employs only quantities with easily controllable equilibration and greatly reduces the statistical errors compared to the std. weighted histogram anal. method. We show the success of our approach for two examples, one analytic function, and one biol. system.**23**Kästner, J.; Thiel, W. Analysis of the statistical error in umbrella sampling simulations by umbrella integration.*J. Chem. Phys.*2006,*124*, 234106, DOI: 10.1063/1.220677523https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmsVWntr4%253D&md5=6e7f306bef4c578434c14436d25a4f10Analysis of the statistical error in umbrella sampling simulations by umbrella integrationKastner, Johannes; Thiel, WalterJournal of Chemical Physics (2006), 124 (23), 234106/1-234106/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Umbrella sampling simulations, or biased mol. dynamics, can be used to calc. the free-energy change of a chem. reaction. We investigate the sources of different sampling errors and derive approx. expressions for the statistical errors when using harmonic restraints and umbrella integration anal. This leads to generally applicable rules for the choice of the bias potential and the sampling parameters. Numerical results for simulations on an anal. model potential are presented for validation. While the derivations are based on umbrella integration anal., the final error est. is evaluated from the raw simulation data, and it may therefore be generally applicable as indicated by tests using the weighted histogram anal. method.**24**Roux, B. The calculation of the potential of mean force using computer simulations.*Comput. Phys. Commun.*1995,*91*, 275– 282, DOI: 10.1016/0010-4655(95)00053-I24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXps1Wrt7o%253D&md5=c5f038741fdc5765d3df4a07f37ec804The calculation of the potential of mean force using computer simulationsRoux, BenoitComputer Physics Communications (1995), 91 (1-3), 275-82CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)The problem of unbiasing and combining the results of umbrella sampling calcns. is reviewed. The weighted histogram anal. method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with mol. dynamics simulations of the alanine dipeptide for one- and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.**25**Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method.*J. Comput. Chem.*1992,*13*, 1011– 1021, DOI: 10.1002/jcc.54013081225https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK38XmtVynsrs%253D&md5=5b2ad7410198f03025708a37c0fbe89dThe weighted histogram analysis method for free-energy calculations on biomolecules. I. The methodKumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.**26**Hub, J. S.; De Groot, B. L.; Van der Spoel, D. g_wham─A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates.*J. Chem. Theory Comput.*2010,*6*, 3713– 3720, DOI: 10.1021/ct100494z26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsVegu7bI&md5=c798afe576b97471e29040069e434028g_wham: A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation EstimatesHub, Jochen S.; de Groot, Bert L.; van der Spoel, DavidJournal of Chemical Theory and Computation (2010), 6 (12), 3713-3720CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The Weighted Histogram Anal. Method (WHAM) is a std. technique used to compute potentials of mean force (PMFs) from a set of umbrella sampling simulations. Here, the authors present a new WHAM implementation, termed g_wham, which is distributed freely with the GROMACS mol. simulation suite. G_wham ests. statistical errors using the technique of bootstrap anal. Three bootstrap methods are supported: (i) bootstrapping new trajectories based on the umbrella histograms, (ii) bootstrapping of complete histograms, and (iii) Bayesian bootstrapping of complete histograms, i.e., bootstrapping via the assignment of random wts. to the histograms. Because methods ii and iii consider only complete histograms as independent data points, these methods do not require the accurate calcn. of autocorrelation times. The authors demonstrate that, given sufficient sampling, bootstrapping new trajectories allows for an accurate error est. In the presence of long autocorrelations, however, (Bayesian) bootstrapping of complete histograms yields a more reliable error est., whereas bootstrapping of new trajectories may underestimate the error. In addn., the authors emphasize that the incorporation of autocorrelations into WHAM reduces the bias from limited sampling, in particular, when computing periodic PMFs in inhomogeneous systems such as solvated lipid membranes or protein channels.**27**Stecher, T.; Bernstein, N.; Csányi, G. Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression.*J. Chem. Theory Comput.*2014,*10*, 4079– 4097, DOI: 10.1021/ct500438v27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFyrurnI&md5=2f0cafb9fd30566efcbf7a359092b1ffFree Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process RegressionStecher, Thomas; Bernstein, Noam; Csanyi, GaborJournal of Chemical Theory and Computation (2014), 10 (9), 4079-4097CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We demonstrate how the Gaussian process regression approach can be used to efficiently reconstruct free energy surfaces from umbrella sampling simulations. By making a prior assumption of smoothness and taking account of the sampling noise in a consistent fashion, we achieve a significant improvement in accuracy over the state of the art in two or more dimensions or, equivalently, a significant cost redn. to obtain the free energy surface within a prescribed tolerance in both regimes of spatially sparse data and short sampling trajectories. Stemming from its Bayesian interpretation the method provides meaningful error bars without significant addnl. computation. A software implementation is made available on www.libatoms.org.**28**Hjorth Larsen, A.; Jørgen Mortensen, J.; Blomqvist, J.; Castelli, I. E.; Christensen, R.; Dułak, M.; Friis, J.; Groves, M. N.; Hammer, B.; Hargus, C.; Hermes, E. D.; Jennings, P. C.; Bjerre Jensen, P.; Kermode, J.; Kitchin, J. R.; Leonhard Kolsbjerg, E.; Kubal, J.; Kaasbjerg, K.; Lysgaard, S.; Bergmann Maronsson, J.; Maxson, T.; Olsen, T.; Pastewka, L.; Peterson, A.; Rostgaard, C.; Schiøtz, J.; Schütt, O.; Strange, M.; Thygesen, K. S.; Vegge, T.; Vilhelmsen, L.; Walter, M.; Zeng, Z.; Jacobsen, K. W. The atomic simulation environment─a Python library for working with atoms.*J. Phys.: Condens. Matter*2017,*29*, 273002, DOI: 10.1088/1361-648X/aa680e28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czpt1aksw%253D%253D&md5=c242d7e905c308340d613ade7adfcadfThe atomic simulation environment-a Python library for working with atomsHjorth Larsen Ask; Jorgen Mortensen Jens; Blomqvist Jakob; Castelli Ivano E; Christensen Rune; Dulak Marcin; Friis Jesper; Groves Michael N; Hammer Bjork; Hargus Cory; Hermes Eric D; Jennings Paul C; Bjerre Jensen Peter; Kermode James; Kitchin John R; Leonhard Kolsbjerg Esben; Kubal Joseph; Kaasbjerg Kristen; Lysgaard Steen; Bergmann Maronsson Jon; Maxson Tristan; Olsen Thomas; Pastewka Lars; Peterson Andrew; Rostgaard Carsten; Schiotz Jakob; Schutt Ole; Strange Mikkel; Thygesen Kristian S; Vegge Tejs; Vilhelmsen Lasse; Walter Michael; Zeng Zhenhua; Jacobsen Karsten WJournal of physics. Condensed matter : an Institute of Physics journal (2017), 29 (27), 273002 ISSN:.The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.**29**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*, 136403, DOI: 10.1103/PhysRevLett.104.13640329https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXkt1Kqur8%253D&md5=0a468458554e85413b53816c082419f2Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the ElectronsBartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, GaborPhysical 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.**30**Bartók, A. P.; Kondor, R.; Csányi, G. On representing chemical environments.*Phys. Rev. B*2013,*87*, 184115, DOI: 10.1103/PhysRevB.87.18411530https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXpvFClu7Y%253D&md5=f7739275562b8e77d4532f00da8814fbOn representing chemical environmentsBartok, Albert P.; Kondor, Risi; Csanyi, GaborPhysical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.**31**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*, e1701816, DOI: 10.1126/sciadv.170181631https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVWgsbjP&md5=e996f3746c995ed0304f33762f7da713Machine learning unifies the modeling of materials and moleculesBartok, Albert P.; De, Sandip; Poelking, Carl; Bernstein, Noam; Kermode, James R.; Csanyi, Gabor; Ceriotti, MicheleScience 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.**32**Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals.*Phys. Rev. B*1999,*59*, 7413– 7421, DOI: 10.1103/PhysRevB.59.741332https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXjtlOgtA%253D%253D&md5=5a79706aa2b3d959686cf4e425d21a6aImproved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionalsHammer, B.; Hansen, L. B.; Norskov, J. K.Physical Review B: Condensed Matter and Materials Physics (1999), 59 (11), 7413-7421CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)A simple formulation of a generalized gradient approxn. for the exchange and correlation energy of electrons has been proposed by J. Perdew et al. (1996). Subsequently, Y. Zhang and W. Wang (1998) have shown that a slight revision of the Perdew-Burke-Ernzerhof (PBE) functional systematically improves the atomization energies for a large database of small mols. In the present work, we show that the Zhang and Yang functional (revPBE) also improves the chemisorption energetics of atoms and mols. on transition-metal surfaces. Our test systems comprise at. and mol. adsorption of oxygen, CO, and NO on Ni(100), Ni(111), Rh(100), Pd(100), and Pd(111) surfaces. As the revPBE functional may locally violate the Lieb-Oxford criterion, we further develop an alternative revision of the PBE functional, RPBE, which gives the same improvement of the chemisorption energies as the revPBE functional at the same time as it fulfills the Lieb-Oxford criterion locally.**33**Wellendorff, J.; Silbaugh, T. L.; Garcia-Pintos, D.; Nørskov, J. K.; Bligaard, T.; Studt, F.; Campbell, C. T. A benchmark database for adsorption bond energies to transition metal surfaces and comparison to selected DFT functionals.*Surf. Sci.*2015,*640*, 36– 44, DOI: 10.1016/j.susc.2015.03.02333https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmtlGmu70%253D&md5=d0bb91c519e55f69afd96b0af7d345e1A benchmark database for adsorption bond energies to transition metal surfaces and comparison to selected DFT functionalsWellendorff, Jess; Silbaugh, Trent L.; Garcia-Pintos, Delfina; Noerskov, Jens K.; Bligaard, Thomas; Studt, Felix; Campbell, Charles T.Surface Science (2015), 640 (), 36-44CODEN: SUSCAS; ISSN:0039-6028. (Elsevier B.V.)A literature collection of exptl. adsorption energies over late transition metal surfaces is presented for systems where the authors believe that the energy measurements are particularly accurate, and the at.-scale adsorption geometries are particularly well established. This could become useful for benchmarking theor. methods for calcg. adsorption processes. The authors compare the exptl. results to six commonly used electron d. functionals, including some (RPBE, BEEF-vdW) which were specifically developed to treat adsorption processes. The comparison shows that there is ample room for improvements in the theor. descriptions.**34**Zhang, Y.; Yang, W. Comment on “Generalized Gradient Approximation Made Simple.*Phys. Rev. Lett.*1998,*80*, 890– 890, DOI: 10.1103/PhysRevLett.80.89034https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXlsV2itg%253D%253D&md5=d14c7fc06fe200788f4192a00dca0730Comment on "Generalized Gradient Approximation Made Simple"Zhang, Yingkai; Yang, WeitaoPhysical Review Letters (1998), 80 (4), 890CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)A Comment on the Letter by John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. 77, 3865 (1996). The authors of the Letter offer a Reply.**35**Ruiz, V. G.; Liu, W.; Tkatchenko, A. Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces.*Phys. Rev. B*2016,*93*, 035118, DOI: 10.1103/PhysRevB.93.03511835https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsVKmu7vF&md5=3b2a2d9fee8adf7df94ccd03d69534b2Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfacesRuiz, Victor G.; Liu, Wei; Tkatchenko, AlexandrePhysical Review B (2016), 93 (3), 035118/1-035118/17CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)Modeling the adsorption of atoms and mols. on surfaces requires efficient electronic-structure methods that are able to capture both covalent and noncovalent interactions in a reliable manner. In order to tackle this problem, we have developed a method within d.-functional theory (DFT) to model screened van der Waals interactions (vdW) for atoms and mols. on surfaces (the so-called DFT+vdWsurf method). The relatively high accuracy of the DFT+vdWsurf method in the calcn. of both adsorption distances and energies, as well as the high degree of its reliability across a wide range of adsorbates, indicates the importance of the collective electronic effects within the extended substrate for the calcn. of the vdW energy tail. We examine in detail the theor. background of the method and assess its performance for adsorption phenomena including the physisorption of Xe on selected close-packed transition metal surfaces and 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) on Au(111). We also address the performance of DFT+vdWsurf in the case of non-close-packed surfaces by studying the adsorption of Xe on Cu(110) and the interfaces formed by the adsorption of a PTCDA monolayer on the Ag(111), Ag(100), and Ag(110) surfaces. We conclude by discussing outstanding challenges in the modeling of vdW interactions for studying at. and mol. adsorbates on inorg. substrates.**36**Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab initio molecular simulations with numeric atom-centered orbitals.*Comput. Phys. Commun.*2009,*180*, 2175– 2196, DOI: 10.1016/j.cpc.2009.06.02236https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtFGhurnI&md5=41ce9f9e42041605710733dc1f7818a5Ab initio molecular simulations with numeric atom-centered orbitalsBlum, Volker; Gehrke, Ralf; Hanke, Felix; Havu, Paula; Havu, Ville; Ren, Xinguo; Reuter, Karsten; Scheffler, MatthiasComputer Physics Communications (2009), 180 (11), 2175-2196CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)We describe a complete set of algorithms for ab initio mol. simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of mol. and materials properties from quantum-mech. first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute "ab initio mol. simulations" (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on d.-functional theory (DFT) in the local and semilocal (generalized gradient) approxns., but an extension to hybrid functionals, Hartree-Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio mol. dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calcn. to range from qual. tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs.**37**Wellendorff, J.; Lundgaard, K. T.; Møgelhøj, A.; Petzold, V.; Landis, D. D.; Nørskov, J. K.; Bligaard, T.; Jacobsen, K. W. Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation.*Phys. Rev. B*2012,*85*, 235149, DOI: 10.1103/PhysRevB.85.23514937https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFehtbzM&md5=480585065c88766af6a7cd221c366e71Density functionals for surface science: exchange-correlation model development with Bayesian error estimationWellendorff, Jess; Lundgaard, Keld T.; Moegelhoej, Andreas; Petzold, Vivien; Landis, David D.; Noerskov, Jens K.; Bligaard, Thomas; Jacobsen, Karsten W.Physical Review B: Condensed Matter and Materials Physics (2012), 85 (23), 235149/1-235149/23CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)A methodol. for semiempirical d. functional optimization, using regularization and cross-validation methods from machine learning, is developed. We demonstrate that such methods enable well-behaved exchange-correlation approxns. in very flexible model spaces, thus avoiding the overfitting found when std. least-squares methods are applied to high-order polynomial expansions. A general-purpose d. functional for surface science and catalysis studies should accurately describe bond breaking and formation in chem., solid state physics, and surface chem., and should preferably also include van der Waals dispersion interactions. Such a functional necessarily compromises between describing fundamentally different types of interactions, making transferability of the d. functional approxn. a key issue. We investigate this trade-off between describing the energetics of intramol. and intermol., bulk solid, and surface chem. bonding, and the developed optimization method explicitly handles making the compromise based on the directions in model space favored by different materials properties. The approach is applied to designing the Bayesian error estn. functional with van der Waals correlation (BEEF-vdW), a semilocal approxn. with an addnl. nonlocal correlation term. Furthermore, an ensemble of functionals around BEEF-vdW comes out naturally, offering an est. of the computational error. An extensive assessment on a range of data sets validates the applicability of BEEF-vdW to studies in chem. and condensed matter physics. Applications of the approxn. and its Bayesian ensemble error est. to two intricate surface science problems support this.**38**Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; De Gironcoli, S.; Delugas, P.; Distasio, R. A.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Küçükbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la Roza, A.; Paulatto, L.; Poncé, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S. Advanced capabilities for materials modelling with Quantum Espresso.*J. Phys.: Condens. Matter*2017,*29*, 465901, DOI: 10.1088/1361-648X/aa8f7938https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXntF2hsr0%253D&md5=17e46e5ac155b511f12deaeff078cc6dAdvanced capabilities for materials modelling with QUANTUM ESPRESSOGiannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; de Gironcoli, S.; Delugas, P.; Di Stasio, R. A., Jr.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Kucukbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la-Roza, A.; Paulatto, L.; Ponce, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S.Journal of Physics: Condensed Matter (2017), 29 (46), 465901/1-465901/30CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)QUANTUM ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on d.-functional theory, d.-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. QUANTUM ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.**39**Hermes, E.; Sargsyan, K.; Najm, H.; Zádor, J. Sella, an open-source automation-friendly molecular saddle point optimizer.*ChemRxiv*, DOI: 10.26434/chemrxiv-2022-44r17 , 2022.There is no corresponding record for this reference.**40**Stocker, S.; Gasteiger, J.; Becker, F.; Günnemann, S.; Margraf, J. T. How robust are modern graph neural network potentials in long and hot molecular dynamics simulations?.*Mach. Learn.: Sci. Technol.*2022,*3*, 045010, DOI: 10.1088/2632-2153/ac9955There is no corresponding record for this reference.**41**Pitzer, K. S.; Gwinn, W. D. Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops.*J. Chem. Phys.*1942,*10*, 428– 440, DOI: 10.1063/1.172374441https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaH38XjsVKktQ%253D%253D&md5=b5a443a174b204773051bea5b1dacf3dEnergy levels and thermodynamic functions for molecules with internal rotation. I. Rigid frame with attached topsPitzer, Kenneth S.; Gwinn, Wm. D.Journal of Chemical Physics (1942), 10 (), 428-40CODEN: JCPSA6; ISSN:0021-9606.Math.**42**Mallikarjun Sharada, S.; Bligaard, T.; Luntz, A. C.; Kroes, G.-J.; Nørskov, J. K. SBH10: A Benchmark Database of Barrier Heights on Transition Metal Surfaces.*J. Phys. Chem. C*2017,*121*, 19807– 19815, DOI: 10.1021/acs.jpcc.7b0567742https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXht1OhtL3E&md5=b6349339058cc3295452a6d0a0dbd190SBH10: A Benchmark Database of Barrier Heights on Transition Metal SurfacesMallikarjun Sharada, Shaama; Bligaard, Thomas; Luntz, Alan C.; Kroes, Geert-Jan; Noerskov, Jens K.Journal of Physical Chemistry C (2017), 121 (36), 19807-19815CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)While the performance of d. functional approxns. (DFAs) for gas phase reaction energetics has been extensively benchmarked, their reliability for activation barriers on surfaces is not fully understood. The primary reason for this is the absence of well-defined, chem. accurate benchmark databases for chem. on surfaces. We present a database of 10 surface barrier heights for dissocn. of small mols., SBH10, based on carefully chosen refs. from mol. beam scattering, laser assisted associative desorption, and thermal expts. Our benchmarking study compares the performance of a dispersion-cor. generalized gradient approxn. (GGA-vdW), BEEF-vdW, a meta-GGA, MS2, and a screened hybrid functional, HSE06. In stark contrast to gas phase reactions for which GGAs systematically underestimate barrier heights and hybrids tend to be most accurate, the BEEF-vdW functional dets. barriers accurately to within 0.14 eV of expts., while MS2 and HSE06 underestimate barrier heights on surfaces. Higher accuracy of BEEF-vdW stems from the fact that the functional is trained on chemisorption systems, and transition states for dissocn. on surfaces closely resemble the final, chemisorbed states. Therefore, a functional that can describe chemisorption accurately can also reliably predict barrier heights on surfaces.**43**Caro, M. A. Parametrization of the Tkatchenko-Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid water.*arXiv*, 1704.00761v2, 2017.There is no corresponding record for this reference.**44**Hörmann, L.; Jeindl, A.; Hofmann, O. T. Reproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111).*J. Chem. Phys.*2020,*153*, 104701, DOI: 10.1063/5.002073644https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB38bpt1Sntg%253D%253D&md5=ce54bd80fcce5cfb3ab1302c60c03fcaReproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111)Hormann Lukas; Jeindl Andreas; Hofmann Oliver TThe Journal of chemical physics (2020), 153 (10), 104701 ISSN:.Molecular adsorption at organic/metal interfaces depends on a range of mechanisms: covalent bonds, charge transfer, Pauli repulsion, and van der Waals (vdW) interactions shape the potential energy surface (PES), making it key to understanding organic/metal interfaces. Describing such interfaces with density functional theory requires carefully selecting the exchange correlation (XC) functional and vdW correction scheme. To explore the reproducibility of the PES with respect to the choice of method, we present a benchmark of common local, semi-local, and non-local XC functionals in combination with various vdW corrections. We benchmark these methods using perylene-tetracarboxylic dianhydride on Ag(111), one of the most frequently studied organic/metal interfaces. For each method, we determine the PES using a Gaussian process regression algorithm, which requires only about 50 density functional theory calculations as input. This allows a detailed analysis of the PESs' features, such as the positions and energies of minima and saddle points. Comparing the results from different combinations of XC functionals and vdW corrections enables us to identify trends and differences between the approaches. PESs for different computation methods are in qualitative agreement but also display significant quantitative differences. In particular, the lateral positions of adsorption geometries agree well with experiment, while adsorption heights, energies, and barriers show larger discrepancies.**45**Dietschreit, J. C. B.; Diestler, D. J.; Hulm, A.; Ochsenfeld, C.; Gómez-Bombarelli, R. From free-energy profiles to activation free energies.*J. Chem. Phys.*2022,*157*, 084113, DOI: 10.1063/5.010207545https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xit1aqu77P&md5=f44ef862ecbdfca27c22d362b5425313From free-energy profiles to activation free energiesDietschreit, Johannes C. B.; Diestler, Dennis J.; Hulm, Andreas; Ochsenfeld, Christian; Gomez-Bombarelli, RafaelJournal of Chemical Physics (2022), 157 (8), 084113CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Given a chem. reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the "free-energy" analog of the min. potential energy path and to take the activation free energy, ΔF‡RP, as the difference between the max. at the transition state and the min. at R. We show that this approxn. can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different ΔF‡RP. We derive an exact expression for the activation free energy that avoids this ambiguity. We find ΔF‡RP to be a combination of the probability of the system being in the reactant state, the probability d. on the dividing surface, and the thermal de Broglie wavelength assocd. with the transition. We apply our formalism to simple analytic models and realistic chem. systems and show that the FEP-based approxn. applies only at low temps. for CVs with a small effective mass. Most chem. reactions occur on complex, high-dimensional PES that cannot be treated anal. and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, ΔF‡RP is quite sensitive. (c) 2022 American Institute of Physics.**46**Goldsmith, C. F.; Harding, L. B.; Georgievskii, Y.; Miller, J. A.; Klippenstein, S. J. Temperature and Pressure-Dependent Rate Coefficients for the Reaction of Vinyl Radical with Molecular Oxygen.*J. Phys. Chem. A*2015,*119*, 7766– 7779, DOI: 10.1021/acs.jpca.5b0108846https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXosVChu7c%253D&md5=b67e6beeafea086707b70824de8ca65fTemperature and Pressure-Dependent Rate Coefficients for the Reaction of Vinyl Radical with Molecular OxygenGoldsmith, C. Franklin; Harding, Lawrence B.; Georgievskii, Yuri; Miller, James A.; Klippenstein, Stephen J.Journal of Physical Chemistry A (2015), 119 (28), 7766-7779CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)State-of-the-art calcns. of the C2H3O2 potential energy surface are presented. A new method is described for computing the interaction potential for R + O2 reactions. The method, which combines accurate detn. of the quartet potential along the doublet min. energy path with multireference calcns. of the doublet/quartet splitting, decreases the uncertainty in the doublet potential and thence the rate consts. by more than a factor of 2. The temp.- and pressure-dependent rate coeffs. are computed using variable reaction coordinate transition-state theory, variational transition-state theory, and conventional transition-state theory, as implemented in a new RRKM/ME code. The main bimol. product channels are CH2O + HCO at lower temps. and CH2CHO + O at higher temps. Above 10 atm, the collisional stabilization of CH2CHOO directly competes with these two product channels. CH2CHOO decomps. primarily to CH2O + HCO. The next two most significant bimol. products are OCHCHO + H and 3CHCHO + OH, and not C2H2 + HO2. C2H3 + O2 will be predominantly chain branching above 1700 K. Uncertainty anal. is presented for the two most important transition states. The uncertainties in these two barrier heights result in a significant uncertainty in the temp. at which CH2CHO + O overtakes all other product channels.**47**Markland, T. E.; Ceriotti, M. Nuclear quantum effects enter the mainstream.*Nat. Rev. Chem.*2018,*2*, 0109, DOI: 10.1038/s41570-017-010947https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtVyksbfP&md5=39796515dbe165f548d032683cf76049Nuclear quantum effects enter the mainstreamMarkland, Thomas E.; Ceriotti, MicheleNature Reviews Chemistry (2018), 2 (3), 0109CODEN: NRCAF7; ISSN:2397-3358. (Nature Research)A review. Atomistic simulations of chem., biol. and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mech. behavior of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approxn. could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, esp. when systems contg. light atoms are treated using current state-of-the-art descriptions of chem. interactions. Over the past decade, this realization has spurred a series of methodol. advances that have dramatically reduced the cost of including these important phys. effects in the structure and dynamics of chem. systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of mol. simulations. These advances have led to new insights into phenomena that are relevant to different areas of science - from biochem. to condensed matter - and open the door to many exciting future opportunities.**48**Pavošević, F.; Culpitt, T.; Hammes-Schiffer, S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method.*Chem. Rev.*2020,*120*, 4222– 4253, DOI: 10.1021/acs.chemrev.9b0079848https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXmvVClt7Y%253D&md5=f22e85887a6343405537ecdfbb83943aMulticomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear-Electronic Orbital MethodPavosevic, Fabijan; Culpitt, Tanner; Hammes-Schiffer, SharonChemical Reviews (Washington, DC, United States) (2020), 120 (9), 4222-4253CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. In multicomponent quantum chem., more than one type of particle is treated quantum mech. with either d. functional theory or wave function based methods. In particular, the nuclear-electronic orbital (NEO) approach treats specified nuclei, typically hydrogen nuclei, on the same level as the electrons. This approach enables the incorporation of nuclear quantum effects, such as nuclear delocalization, anharmonicity, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects directly into quantum chem. calcns. Such effects impact optimized geometries, mol. vibrational frequencies, reaction paths, isotope effects, and dynamical simulations. Multicomponent d. functional theory (NEO-DFT) and time-dependent DFT (NEO-TDDFT) achieve an optimal balance between computational efficiency and accuracy for computing ground and excited state properties, resp. Multicomponent wave function based methods, such as the coupled cluster singles and doubles (NEO-CCSD) method for ground states and the equation-of-motion counterpart (NEO-EOM-CCSD) for excited states, attain similar accuracy without requiring any parametrization and can be systematically improved but are more computationally expensive. Variants of the orbital-optimized perturbation theory (NEO-OOMP2) method achieve nearly the accuracy of NEO-CCSD for ground states with significantly lower computational cost. Addnl. approaches for computing excited electronic, vibrational, and vibronic states include the delta SCF (NEO-ΔSCF), complete active space SCF (NEO-CASSCF), and nonorthogonal CI methods. Multireference methods are particularly important for describing hydrogen tunneling processes. Other types of multicomponent systems, such as those contg. electrons and positrons, have also been studied within the NEO framework. The NEO approach allows the incorporation of nuclear quantum effects and non-Born-Oppenheimer effects for specified nuclei into quantum chem. calcns. in an accessible and computationally efficient manner.

## Supporting Information

## Supporting Information

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Detailed description of the GAP model hyperparameters, training procedure, vibrational frequencies and density functional differences (PDF)

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