Fitting Potential Energy Surfaces Research Articles

Masked pretraining strategy for neural potentials

We propose a masked pretraining method for Graph Neural Networks (GNNs) to improve their performance on fitting potential energy surfaces, particularly in water and small organic molecule systems. GNNs are pretrained by recovering the spatial information of masked-out atoms from molecules selected with certain ratios and then transferred and fine-tuned on atomic force fields. Through such pretraining, GNNs learn meaningful prior about the structural and underlying physical information of molecule systems that are useful for downstream tasks. With comprehensive experiments and ablation studies, we show that the proposed method improves both the accuracy and convergence speed of GNNs compared to their counterparts trained from scratch or with other pretraining techniques. This approach showcases its potential to enhance the performance and data efficiency of GNNs in fitting molecular force fields.

Performance Comparisons of NequIP and DPMD Machine Learning Interatomic Potentials for Tobermorites

Machine Learning Interatomic Potentials (MLIPs) present a significant advancement in fitting molecular potential energy surfaces and predicting molecular crystal structures and mechanical properties by closely approximating first-principles (FP) calculations results while substantially reducing computational time. In this work, utilizing datasets derived from FP calculations, neural equivariant interatomic potentials (NequIP) and Deep Potential Molecular Dynamics (DPMD) was implemented to develop MLIPs for tobermorite 9, 11, 14 Å. The accuracy and efficiency of NequIP and DPMD were assessed by predicting energies and forces as well as performing molecular dynamics (MD) simulations. The findings indicate that NequIP closely fits the results of FP calculations, with both accuracy and efficiency improved by 1∼2 orders of magnitude compared to the DPMD. This demonstrates that MLIPs developed through NequIP for tobermorites have the capacity to enhance the capability of large-scale molecular dynamics simulations.

Quantum dynamics studies on reactive scattering of Cl with rotationally excited H[formula omitted

In this work, extensive multi-configurational time-dependent Hartree (MCTDH) calculations in conjugation with the neural-network (NN) fitted potential energy surface (Science, 347 (2015), 60) were launched to study dynamics of Cl reacting with rotationally excited H2. Due to its direct abstraction mechanism, Cl + H2→ HCl + H in the ground state has no clear reaction resonances, which is well reproduced Here. For the reaction of Cl with H2 in rotationally excited states, the reactive probabilities are enhanced due to a Polanyi-like rule for rotationally excited states. Such Polanyi-like rule can be interpreted through the similar way as for the cases of vibrationally excited states. Moreover, distinctive resonances peaks are investigated for these cases implying a model for generating a quasi-bound rotation state. Similar to the chemical bond softening model for the vibrationally excited cases, a probable model is proposed in this work.

SpaiNN: equivariant message passing for excited-state nonadiabatic molecular dynamics.

Excited-state molecular dynamics simulations are crucial for understanding processes like photosynthesis, vision, and radiation damage. However, the computational complexity of quantum chemical calculations restricts their scope. Machine learning offers a solution by delivering high-accuracy properties at lower computational costs. We present SpaiNN, an open-source Python software for ML-driven surface hopping nonadiabatic molecular dynamics simulations. SpaiNN combines the invariant and equivariant neural network architectures of SchNetPack with SHARC for surface hopping dynamics. Its modular design allows users to implement and adapt modules easily. We compare rotationally-invariant and equivariant representations in fitting potential energy surfaces of multiple electronic states and properties arising from the interaction of two electronic states. Simulations of the methyleneimmonium cation and various alkenes demonstrate the superior performance of equivariant SpaiNN models, improving accuracy, generalization, and efficiency in both training and inference.

Fast and accurate excited states predictions: machine learning and diabatization.

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

A potential energy surface of spectroscopic accuracy for a lithium ion–hydrogen clusters

We develop a systematic approach to optimize training set sizes for neural networks when fitting ab initio potential energy surfaces. We use the approach to construct several spectroscopic quality potential energy surfaces for [Li(H2)n]+, n=1−9. Ground state properties are computed for all the systems and for selected isotopologues. The nuclear quantum effects, produce relatively small zero point energy fractions of the classical binding energy. Evaporating a hydrogen molecule from the pentamer requires 2280 K of energy when the zero point energy contribution is included, making the aggregate thermodynamically stable below 200 K.

An artificial neural network potential for uranium metal at low pressures

Based on machine learning, the high-dimensional fitting of potential energy surfaces under the framework of first principles provides density-functional accuracy of atomic interaction potential for high-precision and large-scale simulation of alloy materials. In this paper, we obtained the high-dimensional neural network (NN) potential function of uranium metal by training a large amount of first-principles calculated data. The lattice constants of uranium metal with different crystal structures, the elastic constants, and the anisotropy of lattice expansion of alpha-uranium obtained based on this potential function are highly consistent with first-principles calculation or experimental data. In addition, the calculated formation energy of vacancies in alpha- and beta-uranium also matches the first-principles calculation. The calculated site of the most stable self-interstitial and its formation energy is in good agreement with the findings from density functional theory (DFT) calculations. These results show that our potential function can be used for further large-scale molecular dynamics simulation studies of uranium metal at low pressures, and provides the basis for further construction of potential model suitable for a wide range of pressures.

Pbqff: Push-Button Quartic Force Fields.

pbqff is an open-source program for fully automating the production of quartic force fields (QFFs) and their corresponding anharmonic spectroscopic data. Rather than being a monolithic piece of code, it consists of several key modules including a generic interface to quantum chemistry codes and, notably, queuing systems; a molecular point group symmetry library; an internal-to-Cartesian coordinate conversion module; a module for the ordinary least-squares fitting of potential energy surfaces; and an improved second-order rotational and vibrational perturbation theory package for asymmetric and symmetric tops that handles type-1 and -2 Fermi resonances, Fermi resonance polyads, and Coriolis resonances. All of these pieces are written in Rust, a modern, safe, and performant programming language that has much to offer for scientific programming. This work introduces pbqff and its surrounding ecosystem, in addition to reporting new anharmonic vibrational data for c-(C)C3H2 and describing how the components of pbqff can be leveraged in other projects.

Artificial neural networks and their utility in fitting potential energy curves and surfaces and related problems

Artificial neural networks and their utility in fitting potential energy curves and surfaces and related problems

The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces.

Kernel-based methods, including Gaussian process regression (GPR) and generally kernel ridge regression, have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family, such as Gaussian-like kernels (basis functions), are often used which allow imparting to them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry. We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.

Optimization of hyperparameters of Gaussian process regression with the help of а low-order high-dimensional model representation: application to a potential energy surface

Gaussian process regression (GPR) has been finding an increased use in computational chemistry, including for applications where high accuracy of machine learning is required, such as potential energy surfaces or functionals for density functional theory. The quality of a GPR model critically depends on the choice of hyperparameters of the kernel. When the data are sparse, optimization of the hyperparameters by the commonly used methods such as maximum likelihood estimation (MLE) criterion can lead to overfitting. We show that choosing hyperparameters (in this case, the kernel length parameter and the regularization parameter) based on a criterion of the completeness of the basis in the corresponding linear regression problem is superior to MLE. We show that this is facilitated by the use of high-dimensional model representation (HDMR) whereby a low-order HDMR representation can provide reliable reference functions and allow generating large synthetic test data sets needed for basis parameter optimization even when the original data are few. This is expected to be particularly useful when fitting potential energy surfaces where a sufficiently low-order HDMR can provide a good approximation. An example of a 15-dimensional PES of UF6 is presented.

Adaptive fitting of potential energy surfaces of small to medium-sized molecules in sum-of-product form: Application to vibrational spectroscopy.

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting rely on energies only and can be used for re-fitting existing analytic potential energy surfaces in the sum-of-product form or for direct fits from ab initio computations. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based on ab initio computations at the coupled-cluster single double and perturbative triples-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg multi-configurational time dependent Hartree package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules in terms of accuracy, including resulting vibrational states, required number of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

Six-dimensional state-to-state quantum dynamics of H2/D2 scattering from Cu(100): Validity of site-averaging model

Six-dimensional quantum dynamics calculations for the state-to-state scattering of H2/D2 on the rigid Cu(100) surface have been carried out using a time-dependent wave packet approach, based on an accurate neural network potential energy surface fit for thousands of density functional theory data computed with the optPBE-vdW density functional. The present results are compared with previous theoretical and experimental ones regarding to the rovibrationally (in)elastic scattering of H2 and D2 from Cu(100). In particular, we test the validity of the site-averaging approximation in this system by which the six-dimensional (in)elastic scattering probabilities are compared with the weighted average of four-dimensional results over fifteen fixed sites. Specifically, the site-averaging model reproduces vibrationally elastic scattering probabilities quite well, though less well for vibrationally inelastic results at high energies. These results support the use of the site-averaging model to reduce computational costs in future investigations on the state-to-state scattering dynamics of heavy diatomic or polyatomic molecules from metal surfaces, where full-dimensional calculations are too expensive.

Atomic-Level Features for Kinetic Monte Carlo Models of Complex Chemistry from Molecular Dynamics Simulations.

The high computational cost of evaluating atomic interactions recently motivated the development of computationally inexpensive kinetic models, which can be parameterized from molecular dynamics (MD) simulations of the complex chemistry of thousands of species or other processes and accelerate the prediction of the chemical evolution by up to four orders of magnitude. Such models go beyond the commonly employed potential energy surface fitting methods in that they are aimed purely at describing kinetic effects. So far, such kinetic models utilize molecular descriptions of reactions and have been constrained to only reproduce molecules previously observed in MD simulations. Therefore, these descriptions fail to predict the reactivity of unobserved molecules, for example, in the case of large molecules or solids. Here, we propose a new approach for the extraction of reaction mechanisms and reaction rates from MD simulations, namely, the use of atomic-level features. Using the complex chemical network of hydrocarbon pyrolysis as an example, it is demonstrated that kinetic models built using atomic features are able to explore chemical reaction pathways never observed in the MD simulations used to parameterize them, a critical feature to describe rare events. Atomic-level features are shown to construct reaction mechanisms and estimate reaction rates of unknown molecular species from elementary atomic events. Through comparisons of the model ability to extrapolate to longer simulation time scales and different chemical compositions than the ones used for parameterization, it is demonstrated that kinetic models employing atomic features retain the same level of accuracy and transferability as the use of features based on molecular species, while being more compact and parameterized with less data. We also find that atomic features can better describe the formation of large molecules enabling the simultaneous description of small molecules and condensed phases.

Application of Reaction Path Search Calculations to Potential Energy Surface Fits.

There has been significant progress in recent years in the use of machine learning techniques to model high-dimensional reactive potential energy surfaces using large-scale data obtained from ab initio electronic structure calculations. In these methods, the strategy used to gather data becomes a key issue as the molecular size increases. In this work, we examine the applicability of the reaction path search algorithm implemented in the Global Reaction Route Mapping (GRRM) code as a data-gathering approach. The electronic energies and gradients sampled by using the GRRM calculation are directly used in potential energy surface fitting to a permutationally invariant polynomial function. This simple approach was applied to the HNS and HCNO reaction systems, and we found that the fitted potential energy surfaces reasonably reproduce the features of the electronic structure calculations used in the GRRM calculations. This suggests that the GRRM sampling scheme can be used to construct an initial potential energy surface.

Spectroscopy and Scattering Studies Using Interpolated Ab Initio Potentials.

The Born-Oppenheimer potential energy surface (PES) has come a long way since its introduction in the 1920s, both conceptually and in predictive power for practical applications. Nevertheless, nearly 100 years later-despite astonishing advances in computational power-the state-of-the-art first-principles prediction of observables related to spectroscopy and scattering dynamics is surprisingly limited. For example, the water dimer, (H2O)2, with only six nuclei and 20 electrons, still presents a formidable challenge for full-dimensional variational calculations of bound states and is considered out of reach for rigorous scattering calculations. The extremely poor scaling of the most rigorous quantum methods is fundamental; however, recent progress in development of approximate methodologies has opened the door to fairly routine high-quality predictions, unthinkable 20 years ago. In this review, in relation to the workflow of spectroscopy and/or scattering studies, we summarize progress and challenges in the component areas of electronic structure calculations, PES fitting, and quantum dynamical calculations.

Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces.

The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz. The novelty of our algorithm lies in the fact that the fit is performed in terms of a direct product of a Schmidt basis, also known as natural potentials. These encode in a non-trivial way all the physics of the problem and, hence, circumvent the usual extra ad hoc and a posteriori adjustments (e.g., damping functions) of the fitted PES. Moreover, we avoid the intermediate refitting stage common to other tensor-decomposition methods, typically used in the context of nuclear quantum dynamics. The resulting SOP-FBR PES is analytical and differentiable ad infinitum. Our ansatz is fully general and can be used in combination with most (molecular) dynamics codes. In particular, it has been interfaced and extensively tested with the Heidelberg implementation of the multiconfiguration time-dependent Hartree quantum dynamical software package.

A general code for fitting global potential energy surfaces via CHIPR method: Direct-Fit Diatomic and tetratomic molecules

A general program to fit global adiabatic potential energy surfaces of up to tetratomic molecules to ab initio points and available spectroscopic data for simple diatomics is reported. It is based on the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) method. The final form describes all dissociating fragments and long-range/valence interactions, while obeying the system permutational symmetry. The code yields as output a Fortran 90 subroutine that readily evaluates the potential and gradient at any arbitrary geometry. Program summaryProgram title: CHIPR-4.0CPC Library link to program files:http://dx.doi.org/10.17632/8wdv87gt5x.2Licensing provisions: GPLv3Programming language: Fortran 90Journal reference of previous version: C. M. R. Rocha, A. J. C. Varandas, Comput. Phys. Commun. 247 (2020) 106913Does the new version supersede the previous version?: YesReasons for the new version: CHIPR-4.0 is a major extension of the previous CHIPR-3.0 code [1] which, besides diatomics and triatomics, also includes the possibility of fitting global adiabatic potential energy surfaces (PESs) of A4-, AB3-, A2B2-, ABC2- and ABCD-type tetratomic molecules [3]. Additionally, a new feature is that it allows the user to fine-tune ab initio diatomic curves using available spectroscopic data.Summary of revisions:• Implementation of CHIPR’s polynomial form and permutation operators for tetratomic molecules• Implementation of a direct-fit module to fine-tune ab initio potential energy curves using spectroscopic data• Automatic global minimum search on the diatomic, triatomic or tetratomic final PESs• Automatic harmonic vibrational analysis at the optimum molecular geometriesNature of problem: This version of the CHIPR code, CHIPR-4.0, provides a set of subroutines to fit global adiabatic potential energy surfaces of up to tetratomic molecules using ab initio and (for diatomics) optional fine-tuning experimental data.Solution method: CHIPR-4.0 uses the Combined-Hyperbolic-Inverse-Power-Representation (CHIPR) [2] method to interpolate and extrapolate ab initio data points.Additional comments including restrictions and unusual features: For triatomic and tetratomic fits, the user must supply subroutines containing the analytic forms defining the sum of two- and two-plus-three-bodies, respectively. These are utilized internally to calculate (from ab initio data) the corresponding three- and four-body energies to be fitted. The current version of this code is strictly based on single-sheeted analytical PESs. High-accuracy in diatomic refinements is currently limited to the 1Σ single-curve case.

Energy transfer between vibrationally excited carbon monoxide based on a highly accurate six-dimensional potential energy surface

Energy transfer between vibrational modes can be quite facile, and it has been proposed as the dominant mechanism for energy pooling in extreme environments such as nonthermal plasmas and laser cavities. To understand such processes, we perform quasi-classical trajectory studies of CO(v) + CO(v) collisions on a new full-dimensional potential energy surface fit to high-level ab initio data using a neural network method and examine the key vibrational energy transfer channels. In addition to the highly efficient CO(v + 1) + CO(v - 1) channel, there exists a significant, sometimes dominant, CO(v + 2) + CO(v - 2) channel for large v states at low collision energies. The latter is shown to stem from the substantially increased interaction between highly vibrationally excited CO, which has a much larger dipole moment than at its equilibrium bond length. Finally, the vibrational state-specific cross sections and their energy dependence on the thermal range are predicted from a limited dataset using Gaussian process regression. The relevance of these results to plasma chemistry and laser engineering and the recently observed flipping of highly vibrationally excited CO adsorbates on a cold NaCl surface is discussed.

Fitting potential energy surfaces with fundamental invariant neural network. II. Generating fundamental invariants for molecular systems with up to ten atoms

Symmetry adaptation is crucial in representing a permutationally invariant potential energy surface (PES). Due to the rapid increase in computational time with respect to the molecular size, as well as the reliance on the algebra software, the previous neural network (NN) fitting with inputs of fundamental invariants (FIs) has practical limits. Here, we report an improved and efficient generation scheme of FIs based on the computational invariant theory and parallel program, which can be readily used as the input vector of NNs in fitting high-dimensional PESs with permutation symmetry. The newly developed method significantly reduces the evaluation time of FIs, thereby extending the FI-NN method for constructing highly accurate PESs to larger systems beyond five atoms. Because of the minimum size of invariants used in the inputs of the NN, the NN structure can be very flexible for FI-NN, which leads to small fitting errors. The resulting FI-NN PES is much faster on evaluating than the corresponding permutationally invariant polynomial-NN PES.