Targeted Transferable Machine-Learned Potential for Linear Alkanes Trained on C14H30 and Tested for C4H10 to C30H62

Given the great importance of linear alkanes in fundamental and applied research, an accurate machine-learned potential (MLP) would be a major advance in computational modeling of these hydrocarbons. Recently, we reported a novel, many-body permutationally invariant model that was trained specifically for the 44-atom hydrocarbon C14H30 on roughly 250,000 B3LYP energies (Qu, C.; Houston, P. L.; Allison, T.; Schneider, B. I.; Bowman, J. M. J. Chem. Theory Comput. 2024, 20, 9339-9353). Here, we demonstrate the accuracy of the transferability of this potential for linear alkanes ranging from butane C4H10 up to C30H62. Unlike other approaches for transferability that aim for universal applicability, the present approach is targeted for linear alkanes. The mean absolute error (MAE) for energy ranges from 0.26 kcal/mol for butane and rises to 0.73 kcal/mol for C30H62 over the energy range up to 80 kcal/mol for butane and 600 kcal/mol for C30H62. These values are unprecedented for transferable potentials and indicate the high performance of a targeted transferable potential. The conformational barriers are shown to be in excellent agreement with high-level ab initio calculations for pentane, the largest alkane for which such calculations have been reported. Vibrational power spectra of C30H62 from molecular dynamics calculations are presented and briefly discussed. Finally, the evaluation time for the potential is shown to vary linearly with the number of atoms.

New Algorithms to Generate Permutationally Invariant Polynomials and Fundamental Invariants for Potential Energy Surface Fitting

Symmetric functions, such as Permutationally Invariant Polynomials (PIPs) and Fundamental Invariants (FIs), are effective and concise descriptors for incorporating permutation symmetry into neural network (NN) potential energy surface (PES) fitting. The traditional algorithm for generating such symmetric polynomials has a factorial time complexity of N!, where N is the number of identical atoms, posing a significant challenge to applying symmetric polynomials as descriptors of NN PESs for larger systems, particularly with more than 10 atoms. Herein, we report a new algorithm which has only linear time complexity for identical atoms. It can tremendously accelerate generation process of symmetric polynomials for molecular systems. The proposed algorithm is based on graph connectivity analysis following the action of the generation set of molecular permutational group. For instance, in the case of calculating the invariant polynomials for a 15-atom molecule, such as tropolone, our algorithm is approximately 2 million times faster than the previous method. The efficiency of the new algorithm can be further enhanced with increasing molecular size and number of identical atoms, making the FI-NN approach feasible for systems with over 10 atoms and high symmetry demands.

Automated potential energy surface development and quasi-classical dynamics for the F- + SiH3I system

We report a potential energy surface (PES) development for the F- + SiH3I system to study its gas-phase reactions through quasi-classical dynamics simulations. The PES is represented by a full-dimensional permutationally invariant polynomial fitted to composite coupled cluster energy points obtained at the ManyHF-[CCSD-F12b + BCCD(T) - BCCD]/aug-cc-pVTZ(-PP) level of theory. The development was automated by Robosurfer, which samples the configurational space, manages ab initio calculations, and iteratively extends the fitting set. When selecting the ab initio method, we address two types of electronic structure calculation issues: first, the gold standard CCSD(T)-F12b is prone to occasional breakdown due to the perturbative (T) contribution, whereas CCSD-F12b + BCCD(T) - BCCD, with the Brueckner (T) term, is more robust; second, the underlying Hartree-Fock calculation may not always converge to the global minimum, resulting in highly erroneous energies. To mitigate this, we employed ManyHF, configuring the Hartree-Fock calculations with multiple initial guess orbitals and selecting the solution with the lowest energy. According to the simulations, the title system exhibits exceptionally high and diverse reactivity. We observe two dominant product formations: SN2 and proton abstraction. Moreover, SiH2F- + HI, SiHFI- + H2, SiH2FI + H-, SiH2 + FHI-, SiH2 + HF + I-, and SiHF + H2 + I- formations are found at lower probabilities. We differentiated inversion and retention for SN2, both being significant throughout the entire collision energy range. Opacity- and excitation functions are reported, and the details of the atomistic dynamics are visually examined via trajectory animations.

HF Trimer: A New Full-Dimensional Potential Energy Surface and Rigorous 12D Quantum Calculations of Vibrational States

HF trimer, as the smallest and the lightest cyclic hydrogen-bonded (HB) cluster, has long been a favorite prototype system for spectroscopic and theoretical investigations of the structure, energetics, spectroscopy, and dynamics of hydrogen-bond networks. Recently, rigorous quantum 12D calculations of the coupled intra- and intermolecular vibrations of this fundamental HB trimer (J. Chem. Phys. 2023, 158, 234109) were performed, employing an older ab initio-based many-body potential energy surface (PES). While the theoretical results were found to be in reasonably good agreement with the available spectroscopic data, it was also evident that it is highly desirable to develop a more accurate 12D PES of HF trimer. Motivated by this, here we report a new, and the first fully ab initio 12D PES of this paradigmatic system. Approximately 42,540 geometries were sampled and calculated at the level of CCSD(T)-F12a/AVTZ. The permutationally invariant polynomial-neural network based Δ-machine learning approach (J. Phys. Chem. Lett. 2022, 13, 4729) was employed to perform cost-efficient calculations of the basis-set-superposition error (BSSE) correction. By strategically selecting data points, this approach facilitated the construction of a high-precision PES with BSSE correction, while requiring only a minimal number of BSSE value computations. The fitting error of the final PES is only 0.035 kcal/mol. To assess its performance, the 12D fully coupled quantum calculations of excited intra- and intermolecular vibrational states of HF trimer are carried out using the rigorous methodology developed by us earlier. The results are found to be in a significantly better agreement with the available spectroscopic data than those obtained with the previously existing semiempirical 12D PES.

DFT-Based Permutationally Invariant Polynomial Potentials Capture the Twists and Turns of C14H30

Hydrocarbons are ubiquitous as fuels, solvents, lubricants, and as the principal components of plastics and fibers, yet our ability to predict their dynamical properties is limited to force-field mechanics. Here, we report two machine-learned potential energy surfaces (PESs) for the linear 44-atom hydrocarbon C14H30 using an extensive data set of roughly 250,000 density functional theory (DFT) (B3LYP) energies for a large variety of configurations, obtained using MM3 direct-dynamics calculations at 500, 1000, and 2500 K. The surfaces, based on Permutationally Invariant Polynomials (PIPs) and using both a many-body expansion approach and a fragmented-basis approach, produce precise fits for energies and forces and also produce excellent out-of-sample agreement with direct DFT calculations for torsional and dihedral angle potentials. Going beyond precision, the PESs are used in molecular dynamics calculations that demonstrate the robustness of the PESs for a large range of conformations. The many-body PIPs PES, although more compute intensive than the fragmented-basis one, is directly transferable for other linear hydrocarbons.

Δ-Machine Learning to Elevate DFT-Based Potentials and a Force Field to the CCSD(T) Level Illustrated for Ethanol

Progress in machine learning has facilitated the development of potentials that offer both the accuracy of first-principles techniques and vast increases in the speed of evaluation. Recently, Δ-machine learning has been used to elevate the quality of a potential energy surface (PES) based on low-level, e.g., density functional theory (DFT) energies and gradients to close to the gold-standard coupled cluster level of accuracy. We have demonstrated the success of this approach for molecules, ranging in size from H3O+ to 15-atom acetyl-acetone and tropolone. These were all done using the B3LYP functional. Here, we investigate the generality of this approach for the PBE, M06, M06-2X, and PBE0 + MBD functionals, using ethanol as the example molecule. Linear regression with permutationally invariant polynomials is used to fit both low-level and correction PESs. These PESs are employed for standard RMSE analysis for training and test data sets, and then general fidelity tests such as energetics of stationary points, normal-mode frequencies, and torsional potentials are examined. We achieve similar improvements in all cases. Interestingly, we obtained significant improvement over DFT gradients where coupled cluster gradients were not used to correct the low-level PES. Finally, we present some results for correcting a recent molecular mechanics force field for ethanol and comment on the possible generality of this approach.

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

No Headache for PIPs: A PIP Potential for Aspirin Runs Much Faster and with Similar Precision Than Other Machine-Learned Potentials

Assessments of machine-learning (ML) potentials are an important aspect of the rapid development of this field. We recently reported an assessment of the linear-regression permutationally invariant polynomial (PIP) method for ethanol, using the widely used (revised) rMD17 data set. We demonstrated that the PIP approach outperformed numerous other methods, e.g., ANI, PhysNet, sGDML, and p-KRR, with respect to precision and notably with respect to speed [Houston et al., J. Chem. Phys. 2022, 156, 044120]. Here, we extend this assessment to the 21-atom aspirin molecule, using the rMD17 data set, with a focus on the speed of evaluation. Both energies and forces are used for training, and the precision of several PIPs is examined for both. Normal mode frequencies, the methyl torsional potential, and 1d vibrational energies for an OH stretch are presented. We show that the PIP approach achieves the level of precision obtained from other ML methods, e.g., atom-centered neural network methods, linear regression ACE, and kernel methods, as reported by Kovács et al. in J. Chem. Theory Comput. 2021, 17, 7696-7711. More significantly, we show that the PIP PESs run much faster than all other ML methods, whose timings were evaluated in that paper. We also show that the PIP PES extrapolates well enough to describe several internal motions of aspirin, including an OH stretch.

Construction of a Mode-Combination Hamiltonian under the Grid-Based Representation for the Quantum Dynamics of OH + HO2 → O2 + H2O

In this work, a systematic construction framework on a mode-combination Hamiltonian operator of a typical polyatomic reaction, OH + HO2 → O2 + H2O, is developed. First, a set of Jacobi coordinates are employed to construct the kinetic energy operator (KEO) through the polyspherical approach ( Phys. Rep. 2009, 484, 169). Second, due to the multiconfigurational electronic structure of this system, a non-adiabatic potential energy surface (PES) is constructed where the first singlet and triplet states are involved with spin-orbital coupling. To improve the training database, the training set of random energy data was optimized through a popular iterative optimization approach with extensive trajectories. Here, we propose an automatic trajectory method, instead of the classical trajectory on a crude PES, where the gradients are directly computed by the present ab initio calculations. Third, on the basis of the training set, the potential function is directly constructed in the canonical polyadic decomposition (CPD) form ( J. Chem. Theory Comput. 2021, 17, 2702-2713) which is helpful in propagating the nuclear wave function under the grid-based representation. To do this, the Gaussian process regression (GPR) approach for building the CPD form, called the CPD-GPR method ( J. Phys. Chem. Lett. 2022, 13, 11128-11135) is adopted where we further revise CPD-GPR by introducing the mode-combination (mc) scheme leading to the present CPD-mc-GPR approach. Constructing the full-dimension non-adiabatic Hamiltonian operator with mode combination, as test calculations, the nuclear wave function is propagated to preliminarily compute the reactive probability of OH + HO2 → O2 + H2O where the reactants are prepared in vibrational ground states and in the first triplet electronic state.

Flexible DMRG-Based Framework for Anharmonic Vibrational Calculations

We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general, high-dimensional model representations of potential energy surfaces. For this purpose, we extend the vDMRG framework to support vibrational Hamiltonians expressed in the so-called n-mode second-quantization formalism. The resulting n-mode vDMRG method offers full flexibility with respect to both the functional form of the PES and the choice of the single-particle basis set. We leverage this framework to apply, for the first time, vDMRG based on an anharmonic modal basis set optimized with the vibrational self-consistent field algorithm on an on-the-fly constructed PES. We also extend the n-mode vDMRG framework to include excited-state-targeting algorithms in order to efficiently calculate anharmonic transition frequencies. We demonstrate the capabilities of our novel n-mode vDMRG framework for methyloxirane, a challenging molecule with 24 coupled vibrational modes.

Machine Learning Interatomic Potentials for Reactive Hydrogen Dynamics at Metal Surfaces Based on Iterative Refinement of Reaction Probabilities

The reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction design, but studying dynamics at surfaces is computationally challenging due to the complex electronic structure at interfaces and the high sensitivity of dynamics to reaction barriers. In addition, ab initio molecular dynamics, based on density functional theory, is too computationally demanding to accurately predict reactive sticking or desorption probabilities, as it requires averaging over tens of thousands of initial conditions. High-dimensional machine learning-based interatomic potentials are starting to be more commonly used in gas-surface dynamics, yet robust approaches to generate reliable training data and assess how model uncertainty affects the prediction of dynamic observables are not well established. Here, we employ ensemble learning to adaptively generate training data while assessing model performance with full uncertainty quantification (UQ) for reaction probabilities of hydrogen scattering on different copper facets. We use this approach to investigate the performance of two message-passing neural networks, SchNet and PaiNN. Ensemble-based UQ and iterative refinement allow us to expose the shortcomings of the invariant pairwise-distance-based feature representation in the SchNet model for gas-surface dynamics.

Accurate fundamental invariant-neural network representation of ab initio potential energy surfaces

Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry.

Global Neural Network Potential with Explicit Many-Body Functions for Improved Descriptions of Complex Potential Energy Surface

The high dimensional machine learning potential (MLP) that has developed rapidly in the past decade represents a giant step forward in large-scale atomic simulation for complex systems. The long-range interaction and the poor description of chemical reactions are typical problems of high dimensional MLP, which are mainly caused by the poor structure discrimination of the atom-centered ML model. Herein, we propose a low-cost neural-network-based MLP architecture for fitting global potential energy surface data, namely, G-MBNN, that can offer improved energy and force resolution on a complex potential energy surface. In G-MBNN, a set of many-body energy terms based on the local atomic environment are explicitly included in computing the total energy─the total energy of the system is written as the sum of atomic energy and many-body energy contributions. These extra many-body energy terms are computationally low-cost and, importantly, can provide easy access to delicate energy terms in complex systems such as very short repulsion, long-range attractions, and sensitive angular-dependent covalent interactions. We implement G-MBNN in the LASP code and demonstrate the improved accuracy of the new framework in representative systems, including ternary-element energy materials LiCoOx, TiO2 with defects, and a series of organic reactions.

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on ab initio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated ab initio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

Neural network potential energy surfaces and dipole moment surfaces for SO2(H2O) and SO2(H2O)2 complexes

Full-dimensional, ab initio-based many-body potential energy surfaces and dipole moment surfaces constructed using the neural network method for SO2(H2O)n (n = 1,2) complexes are reported. The database of the SO2 1-body PES, SO2(H2O) 2-body PES and SO2(H2O)2 3-body PES consists of 11 952, 79 882 and 84 159 ab initio energies, respectively. All 1-body energies were calculated at the CCSD(T)/CBS(AVTZ:AVQZ) level and all 2,3-body energies were calculated at the DSD-PBEP86/AVTZ level. The database of DMSs is the same as that of PESs and all dipole moments were calculated at the MP2/AVTZ level. Harmonic frequencies and dissociation energies of SO2(H2O) and SO2(H2O)2 were calculated on these PESs and compared with ab initio results to examine the fidelity of these PESs.

Reaction mechanism - explored with the unified reaction valley approach

One of the ultimate goals of chemistry is to understand and manipulate chemical reactions, which implies the ability to monitor the reaction and its underlying mechanism at an atomic scale. In this article, we introduce the Unified Reaction Valley Approach (URVA) as a tool for elucidating reaction mechanisms, complementing existing computational procedures. URVA combines the concept of the potential energy surface with vibrational spectroscopy and describes a chemical reaction via the reaction path and the surrounding reaction valley traced out by the reacting species on the potential energy surface on their way from the entrance to the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting species is registered by a change in the normal vibrational modes spanning the reaction valley and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction, with curvature minima reflecting minimal change and curvature maxima indicating the location of important chemical events such as bond breaking/formation, charge polarization and transfer, rehybridization, etc. A decomposition of the path curvature into internal coordinate components or other coordinates of relevance for the reaction under consideration, provides comprehensive insight into the origin of the chemical changes taking place. After giving an overview of current experimental and computational efforts to gain insight into the mechanism of a chemical reaction and presenting the theoretical background of URVA, we illustrate how URVA works for three diverse processes, (i) [1,3] hydrogen transfer reactions; (ii) α-keto-amino inhibitor for SARS-CoV-2 Mpro; (iii) Rh-catalyzed cyanation. We hope that this article will inspire our computational colleagues to add URVA to their repertoire and will serve as an incubator for new reaction mechanisms to be studied in collaboration with our experimental experts in the field.

Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development

Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.

Positioning of grid points for spanning potential energy surfaces-How much effort is really needed?

The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related.

A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H3C-C-OH)

We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H₃C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH₃ (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function u_LR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO₂-He including the CO₂ antisymmetric vibration Q₃ and the six-dimensional IPES of the H₂O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H₂O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Mind the GAP: quantifying the breakdown of the linear vibronic coupling Hamiltonian

Excited state dynamics play a critical role across a broad range of scientific fields. Importantly, the highly non-equilibrium nature of the states generated by photoexcitation means that excited state simulations should usually include an accurate description of the coupled electronic-nuclear motion, which often requires solving the time-dependent Schrödinger equation (TDSE). One of the biggest challenges for these simulations is the requirement to calculate the PES over which the nuclei evolve. An effective approach for addressing this challenge is to use the approximate linear vibronic coupling (LVC) Hamiltonian, which enables a model potential to be parameterised using relatively few quantum chemistry calculations. However, this approach is only valid provided there are no large amplitude motions in the excited state dynamics. In this paper we introduce and deploy a metric, the global anharmonicity parameter (GAP), which can be used to assess the accuracy of an LVC potential. Following its derivation, we illustrate its utility by applying it to three molecules exhibiting different rigidity in their excited states.

WS22 database, Wigner Sampling and geometry interpolation for configurationally diverse molecular datasets

Multidimensional surfaces of quantum chemical properties, such as potential energies and dipole moments, are common targets for machine learning, requiring the development of robust and diverse databases extensively exploring molecular configurational spaces. Here we composed the WS22 database covering several quantum mechanical (QM) properties (including potential energies, forces, dipole moments, polarizabilities, HOMO, and LUMO energies) for ten flexible organic molecules of increasing complexity and with up to 22 atoms. This database consists of 1.18 million equilibrium and non-equilibrium geometries carefully sampled from Wigner distributions centered at different equilibrium conformations (either at the ground or excited electronic states) and further augmented with interpolated structures. The diversity of our datasets is demonstrated by visualizing the geometries distribution with dimensionality reduction as well as via comparison of statistical features of the QM properties with those available in existing datasets. Our sampling targets broader quantum mechanical distribution of the configurational space than provided by commonly used sampling through classical molecular dynamics, upping the challenge for machine learning models.

Δ-Machine Learned Potential Energy Surfaces and Force Fields

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

Semiclassical and VSCF/VCI Calculations of the Vibrational Energies of trans- and gauche-Ethanol Using a CCSD(T) Potential Energy Surface

A recent full-dimensional Δ-Machine learning potential energy surface (PES) for ethanol is employed in semiclassical and vibrational self-consistent field (VSCF) and virtual-state configuration interaction (VCI) calculations, using MULTIMODE, to determine the anharmonic vibrational frequencies of vibration for both the trans and gauche conformers of ethanol. Both semiclassical and VSCF/VCI energies agree well with the experimental data. We find significant mixing between the VSCF basis states due to Fermi resonances between bending and stretching modes. The same effects are also accurately described by the full-dimensional semiclassical calculations. These are the first high-level anharmonic calculations using a PES, in particular a "gold-standard" CCSD(T) one.

Quantum Calculations on a New CCSD(T) Machine-Learned Potential Energy Surface Reveal the Leaky Nature of Gas-Phase Trans and Gauche Ethanol Conformers

Ethanol is a molecule of fundamental interest in combustion, astrochemistry, and condensed phase as a solvent. It is characterized by two methyl rotors and trans (anti) and gauche conformers, which are known to be very close in energy. Here we show that based on rigorous quantum calculations of the vibrational zero-point state, using a new ab initio potential energy surface (PES), the ground state resembles the trans conformer, but substantial delocalization to the gauche conformer is present. This explains experimental issues about identification and isolation of the two conformers. This “leak” effect is partially quenched when deuterating the OH group, which further demonstrates the need for a quantum mechanical approach. Diffusion Monte Carlo and full-dimensional semiclassical dynamics calculations are employed. The new PES is obtained by means of a Δ-machine learning approach starting from a pre-existing low level density functional theory surface. This surface is brought to the CCSD(T) level of theory using a relatively small number of ab initio CCSD(T) energies. Agreement between the corrected PES and direct ab initio results for standard tests is excellent. One- and two-dimensional discrete variable representation calculations focusing on the trans–gauche torsional motion are also reported, in reasonable agreement with experiment.

Full-dimensional automated potential energy surface development and dynamics for the OH + C2H6 reaction

We develop a full-dimensional analytical potential energy surface (PES) for the OH + C2H6 reaction using the Robosurfer program system, which automatically (1) selects geometries from quasi-classical trajectories, (2) performs ab initio computations using a CCSD(T)-F12/triple-zeta-quality composite method, (3) fits the energies utilizing the permutationally-invariant monomial symmetrization approach, and iteratively improves the PES via steps (1)−(3). Quasi-classical trajectory simulations on the new PES reveal that hydrogen abstraction leading to H2O + C2H5 dominates in the collision energy range of 10−50 kcal/mol. The abstraction cross sections increase and the dominant mechanism shifts from rebound (small impact parameters and backward scattering) to stripping (larger impact parameters and forward scattering) with increasing collision energy as opacity functions and scattering angle distributions indicate. The abstraction reaction clearly favors side-on OH attack over O-side and the least-preferred H-side approach, whereas C2H6 behaves like a spherical object with only slight C−C-perpendicular side-on preference. Collision energy efficiently flows into the relative translation of the products, whereas product internal energy distributions show only little collision energy dependence. H2O/C2H5 vibrational distributions slightly/significantly violate zero-point energy and are nearly independent of collision energy, whereas the rotational distributions clearly blue-shift as collision energy increases.

Adiabatic models for the quantum dynamics of surface scattering with lattice effects

In this contribution, we review models for the lattice effects in quantum dynamics calculations on surface scattering, which is important to modeling heterogeneous catalysis for achieving an interpretation of experimental measurements. Unlike dynamics models for reactions in the gas phase, those for heterogeneous reactions have to include the effects of the surface. For manageable computational costs in calculations, the effects of static surface (SS) are firstly modeled as this is simply and easily implemented. Then, the SS model has to be improved to include the effects of the flexible surface, that is the lattice effects. To do this, various surface models have been designed where the coordinates of the surface atoms are introduced in the Hamiltonian operator, especially those of the top surface atom. Based on this model Hamiltonian operator, extensive multi-dimension quantum dynamics calculations can be performed to recover the lattice effects. Here, we first review an overview of the techniques in constructing the Hamiltonian operator, which is a sum of the kinetic energy operator (KEO) and potential energy surface (PES). Since the PES containing the coordinates of the surface atoms in a cell is still expensive, the SS model is often accepted. We consider a mathematical model, called the coupled harmonic oscillator (CHO) model, to introduce the concepts of adiabatic and diabatic representations for separating the molecule and surface. Under the adiabatic model, we further introduce the expansion model where the potential function is Taylor expanded around the optimized geometry of the surface. By an expansion model truncated at the first and second order, various coupling surface models between the molecule and surface are derived. Moreover, by further and deeply understanding the adiabatic representation, an effective Hamiltonian operator is obtained by optimizing the total wave function in factorized form. By this factorized form of wave function and effective Hamiltonian operator, the geometry phase of the surface wave function is theoretically found. This theoretical prediction may be measured by carefully designing experiments. Finally, discussions on the adiabatic representation, the PES construction, and possibility of the classical-dynamics solutions are given. Based on these discussions, a simple outlook on the dynamics of photocatalytics is finally given.

The MD17 datasets from the perspective of datasets for gas-phase “small” molecule potentials

There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each molecule in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three “small” molecules, ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the potential energy surfaces (PESs) in mind: a rigorous calculation of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde, and, in the case of glycine, a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-molecule but complex chemical reactions. Finally, we introduce a new database, “QM-22,” which contains datasets of molecules ranging from 4 to 15 atoms that extend to high energies and a large span of configurations.

Current Status of the X + C2H6 [X ≡ H, F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C₂H₆ → HX + C₂H₅; X ≡ H, F(²P), Cl(²P), O(³P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(³P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.

Unconventional SN2 retention pathways induced by complex formation: High-level dynamics investigation of the NH2 - + CH3I polyatomic reaction

Investigations on the dynamics of chemical reactions have been a hot topic for experimental and theoretical studies over the last few decades. Here, we carry out the first high-level dynamical characterization for the polyatom-polyatom reaction between NH₂ ^- and CH₃I. A global analytical potential energy surface is developed to describe the possible pathways with the quasi-classical trajectory method at several collision energies. In addition to S_N2 and proton abstraction, a significant iodine abstraction is identified, leading to the CH₃ + [NH₂⋯I]^- products. For S_N2, our computations reveal an indirect character as well, promoting the formation of [CH₃⋯NH₂] complexes. Two novel dominant S_N2 retention pathways are uncovered induced by the rotation of the CH₃ fragment in these latter [CH₃⋯NH₂] complexes. Moreover, these uncommon routes turn out to be the most dominant retention paths for the NH₂ ^- + CH₃I S_N2 reaction.

Mechanism and Kinetics of Methane Combustion. Part II: Potential Energy Surface for Hydrogen-Abstraction Reaction of CH4 + O(3P)

Methane combustion plays an important role in various fields such as combustion chemistry and atmospheric chemistry of the stratosphere. Highly accurate study of its initial reaction remains a key challenge. Here, through extensive studies with a state-of-the-art ab initio and neural network method, we present a potential energy surface of the O(³P) + CH₄ → OH + CH₃ reaction on the ground state 1³A and the first excited state 2³A. In this work, the energies of 10 167 points covering all important regions are obtained with state-averaged complete active space self-consistent field calculations and then fitted using the Levenberg-Marquardt algorithm with a root-mean-square error of 0.391 and 0.442 kcal/mol for the 1³A and 2³A states, respectively. This study explores the characteristics of the radical van der Waals (VdW) complex and reveals a detailed mechanism of the methane combustion initial reaction. Within the scope of this mechanism, this surface gives a fairly accurate description of the regions around the saddle point, conical intersection, and vdW wells in the entrance for efficient computational simulations. As a theoretical study on a prototypical polyatomic reaction, it is hopeful that this work will modify our understanding of the primary process in hydrocarbon combustion.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Influence of second-order saddles on reaction mechanisms

The transition state, a first-order saddle point on the potential energy surface, plays a central role in understanding the mechanism, dynamics, and rate of chemical reactions. However, we recently identified...

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Interpolation Methods for Molecular Potential Energy Surface Construction

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

A full-dimensional ab initio potential energy and dipole moment surfaces for (NH3)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) for the ammonia dimer (NH₃)₂ are reported. The database of the PES consists of 27 736 ab initio energy points and all of these points were calculated at the UCCSD(T)-F12a/AVTZ level. The PES was fitted by using the fundamental invariant neural network (FI-NN) method that satisfies the permutational symmetry of identical atoms, and the root mean square fitting error for the PES is very small as low as 0.562 meV. The geometries for the (NH₃)₂ DMS are the same as those used for the PES and are calculated at the XYG3/AVTZ level. This PES can describe a variety of internal floppy motions, including all kinds of vibrational modes no matter intermolecular or intramolecular. The CCSD(T)-PES can dissociate correctly to two NH₃ monomers, with D_e = 1135.55 cm^-1 (13.58 kJ/mol) which agrees accurately with the 13.5 ± 0.3 kJ/mol predicted by previous work.

Determination of kinetic properties in unimolecular dissociation of complex systems from graph theory based analysis of an ensemble of reactive trajectories

In this paper, we report how graph theory can be used to analyze an ensemble of independent molecular trajectories, which can react during the simulation time-length, and obtain structural and kinetic information. This method is totally general and here is applied to the prototypical case of gas phase fragmentation of protonated cyclo-di-glycine. This methodology allows us to analyze the whole set of trajectories in an automatic computer-based way without the need of visual inspection but by getting all the needed information. In particular, we not only determine the appearance of different products and intermediates but also characterize the corresponding kinetics. The use of colored graph and canonical labeling allows for the correct characterization of the chemical species involved. In the present case, the simulations consist of an ensemble of unimolecular fragmentation trajectories at constant energy such that from the rate constants at different energies, the threshold energy can also be obtained for both global and specific pathways. This approach allows for the characterization of ion-molecule complexes, likely through a roaming mechanism, by properly taking into account the elusive nature of such species. Finally, it is possible to directly obtain the theoretical mass spectrum of the fragmenting species if the reacting system is an ion as in the specific example.

Reduced-dimensional surface hopping with offline-online computations

Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm known as surface hopping. However, the computational expense of integrating the geometry on a full-dimensional PES and computing the required couplings can quickly become prohibitive as the number of atoms increases. In this work, we describe a method for surface hopping that uses only important reaction coordinates, performs all expensive evaluations of the true PESs and couplings only once before simulating dynamics (offline), and then queries the stored values during the surface hopping simulation (online). Our Python codes are freely available on GitHub. Using photodissociation of azomethane as a test case, this method is able to reproduce experimental results that have thus far eluded ab initio surface hopping studies.

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.