Molecular Potential Energy Surfaces by Interpolation

Collins, Michael A.

doi:10.1007/3-540-44864-0_17

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…Various techniques exist to construct surrogate PESs, such as modified Shepard interpolation, − permutationally invariant polynomials, − ,− interpolative moving least squares, − Gaussian processes, , neural networks (nn-PES), − and the finite-element method . Most of these methods are primarily concerned with constructing a full PES as a function of 3 N – 6 internal coordinates representing bond lengths, bond angles, and torsion angles.…”

Section: Introductionmentioning

confidence: 99%

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

Morrow

Kwon

Kelley

et al. 2021

J. Chem. Theory Comput.

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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.

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Section: Introductionmentioning

confidence: 99%

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

Morrow

Kwon

Kelley

et al. 2021

J. Chem. Theory Comput.

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“…[31,32] Another broad class of ML methods instead looks at the configuration of the entire system and predicts the energy gradients of all the atoms in the system at once. These types of ML often use linear interpolation [33,34,35,36,37], reproducing kernel interpolation [38,39,40,41,42,43], or kernel ridge regression. [44,45] The molecular systems that serve as proof of concepts in those ML developments are mostly close-to-optimal structures, for example, oscillations of atoms in metal or vibrations of molecules at a relatively high temperature (up to 500 K).…”

Section: Introductionmentioning

confidence: 99%

Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

Fujioka¹,

Sun²

2021

Preprint

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Ab initio molecular dymamics (AIMD) simulation studies are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of the ab initio energy gradient calculations needed for AIMD, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been employed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called interpolating moving ridge regression (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and the predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. The method is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

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“…As a result, more efficient methods to obtain information about the PES are required. The force field methods, which represent the potential energy as a sum of different contributions with empirical function forms, are widely used on simulations of biomolecules and polymers. − ,,,− However, improving the accuracy of force field parameters to match the experimental and ab initio MD results is, for some cases, hard to achieve because of the limitation of functional form that describes different types of interactions and the requirement for parameters to be transferrable among different systems. − To efficiently carry out reliable MD simulations in these situations, different approaches have been developed to approximate the PES of a specified system, including, but not limited to, the modified Shepard interpolation method developed by Collins, − permutationally invariant potential energy surface by linear least-square fitting developed by Braams and Bowman, ,,− neural network approaches, − Gaussian process, , and finite element method. − The size of a system that can be treated by these full-dimensional PES (f-PES) MD methods is very limited because the computational cost increases rapidly with the increase of degrees of freedom (dofs).…”

Section: Introductionmentioning

confidence: 99%

Molecular Dynamics Simulations on Relaxed Reduced-Dimensional Potential Energy Surfaces

2019

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Molecular dynamics (MD) simulations with full-dimensional potential energy surfaces (PESs) obtained from high-level ab initio calculations are frequently used to model reaction dynamics of small molecules (i.e., molecules with up to 10 atoms). Construction of full-dimensional PESs for larger molecules is, however, not feasible since the number of ab initio calculations required grows rapidly with the increase of dimension. Only a small number of coordinates are often essential for describing the reactivity of even very large systems, and reduced-dimensional PESs with these coordinates can be built for reaction dynamics studies. While analytical methods based on transition-state theory framework are well established for analyzing the reduced-dimensional PESs, MD simulation algorithms capable of generating trajectories on such surfaces are more rare. In this work, we present a new MD implementation that utilizes the relaxed reduced-dimensional PES for standard microcanonical (NVE) and canonical (NVT) MD simulations. The method is applied to the pyramidal inversion of a NH3 molecule. The results from the MD simulations on a reduced, three-dimensional PES are validated against the ab initio MD simulations, as well as MD simulations on full-dimensional PES and experimental data.

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Molecular Potential Energy Surfaces by Interpolation

Cited by 7 publications

References 18 publications

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

Molecular Dynamics Simulations on Relaxed Reduced-Dimensional Potential Energy Surfaces

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