<i>Ab initio</i> instanton rate theory made efficient using Gaussian process regression

Laude, Gabriel; Calderini, Danilo; Tew, David P.; Richardson, Jeremy O.

doi:10.1039/c8fd00085a

Cited by 67 publications

(95 citation statements)

References 82 publications

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“…In all previous studies [21][22][23][24][25][26][27][28][29][30], the GP models of PES were constructed with a fixed kernel function, such as one of the kernel functions (3) - (5). In the present work, we follow…”

Section: Composite Kernels For Gp Models Of Pesmentioning

confidence: 99%

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Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Dai

Krems

2020

J. Chem. Theory Comput.

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Gaussian process regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential energy points, so does the numerical difficulty of training and evaluating GP models. Here, we demonstrate an approach to improve the accuracy of global PES without increasing the number of energy points. The present work reports four important results. First, we show that the selection of the best kernel function for GP models of PES can be automated using the Bayesian information criterion as a model selection metric.Second, we demonstrate that GP models of PES trained by a small number of energy points can be significantly improved by iteratively increasing the complexity of GP kernels. The composite kernels thus obtained maximize the accuracy of GP models for a given distribution of potential energy points. Third, we show that the accuracy of the GP models of PES with composite kernels can be further improved by varying the training point distributions. Fourth, we show that GP models with composite kernels can be used for physical extrapolation of PES. We illustrate the approach by constructing the six-dimensional PES for H 3 O + . For the interpolation problem, we show that this algorithm produces a global six-dimensional PES for H 3 O + in the energy range between zero and 21, 000 cm −1 with the root mean square error 65.8 cm −1 using only 500 randomly selected ab initio points as input. To illustrate extrapolation, we produce the PES at high energies using the energy points at low energies as input. We show that one can obtain an accurate global fit of the PES extending to 21, 000 cm −1 based on 1500 potential energy points at energies below 10, 000 cm −1 . arXiv:1907.08717v1 [physics.chem-ph]

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Section: Composite Kernels For Gp Models Of Pesmentioning

confidence: 99%

“…The present work reports several significant results. We first consider the interpolation problem, as in previous work [18][19][20][21][22][23][24][25][26][27][28][29][30], and show that the accuracy of the resulting GP models of the PES can be significantly enhanced by increasing the complexity of GP model kernels.…”

Section: Introductionmentioning

confidence: 97%

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Dai

Krems

2020

J. Chem. Theory Comput.

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“…These have been successfully applied to computing minimum-energy pathways 59 and recently also to instanton calculations. 60,61 Techniques developed for increasing the efficiency of path-integral molecular dynamics could conceivably also be employed in instanton calculations. In particular, the use of higher-order discretization schemes 62 and ring-polymer contraction 63,64 has not yet been fully explored.…”

Section: B Implementation Of Ab Initio Instanton Theorymentioning

confidence: 99%

Perspective: Ring-polymer instanton theory

Richardson

2018

The Journal of Chemical Physics

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124

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Since the earliest explorations of quantum mechanics, it has been a topic of great interest that quantum tunneling allows particles to penetrate classically insurmountable barriers. Instanton theory provides a simple description of these processes in terms of dominant tunneling pathways. Using a ring-polymer discretization, an efficient computational method is obtained for applying this theory to compute reaction rates and tunneling splittings in molecular systems. Unlike other quantum-dynamics approaches, the method scales well with the number of degrees of freedom, and for many polyatomic systems, the method may provide the most accurate predictions which can be practically computed. Instanton theory thus has the capability to produce useful data for many fields of low-temperature chemistry including spectroscopy, atmospheric and astrochemistry, as well as surface science. There is however still room for improvement in the efficiency of the numerical algorithms, and new theories are under development for describing tunneling in nonadiabatic transitions.

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“…31,37 Since the Hessians are not needed for the propagation of the classical trajectory, additional speed-up is achieved through parallel computation of the Hessians after the full trajectory is known. Note that other Hessian approximations, such as the Hessian update schemes [38][39][40] and Gaussian process regression 41,42 have been developed in the context of ab initio simulations. The considerable cost of multiple Hessian evaluations has also inspired various semiclassical approximations, 43 including the prefactor-free, 22 adiabatic, 44,45 harmonic, 43 and "poor person's" 46 variations of the Herman-Kluk propagator.…”

Section: Hessian Interpolationmentioning

confidence: 99%

Single-Hessian thawed Gaussian approximation

Begušić

Cordova

Vaníček

2019

The Journal of Chemical Physics

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To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all points along an anharmonic classical trajectory is approximated by a constant matrix. The spectra obtained with this approximation are compared with the exact quantum spectra of a one-dimensional Morse potential and with the experimental spectra of ammonia and quinquethiophene. In all cases, the single-Hessian version performs almost as well as the much more expensive on-the-fly ab initio thawed Gaussian approximation and significantly better than the global harmonic schemes. Remarkably, unlike the thawed Gaussian approximation, the proposed method conserves energy exactly, despite the time dependence of the corresponding effective Hamiltonian, and, in addition, can be mapped to a higher-dimensional time-independent classical Hamiltonian system.We also provide a detailed comparison with several related approximations used for accelerating prefactor calculations in semiclassical simulations.

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Ab initio instanton rate theory made efficient using Gaussian process regression

Cited by 67 publications

References 82 publications

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with Composite Kernels

Perspective: Ring-polymer instanton theory

Single-Hessian thawed Gaussian approximation

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