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High-Accuracy Molecular Simulations with Machine-Learning Potentials and Semiclassical Approximations to Quantum Dynamics

Valerii Andreichev, Jindra Dušek, Markus Meuwly, Jeremy O. Richardson

TL;DR

Various methods for constructing potential energy surfaces including transfer learning, which requires a minimal number of expensive training points, can be discussed, which can study chemical reactions at a high level but a low cost.

Abstract

Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of this workflow without any loss of accuracy. We discuss various methods for constructing potential energy surfaces including transfer learning, which requires a minimal number of expensive training points. In this way, we can study chemical reactions at a high level but a low cost. In particular, as the potentials are smooth and differentiable, they enable the use of more advanced semiclassical approximations to quantum dynamics, such as perturbatively corrected instanton theory, which can capture both tunnelling and anharmonicity.

High-Accuracy Molecular Simulations with Machine-Learning Potentials and Semiclassical Approximations to Quantum Dynamics

TL;DR

Various methods for constructing potential energy surfaces including transfer learning, which requires a minimal number of expensive training points, can be discussed, which can study chemical reactions at a high level but a low cost.

Abstract

Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of this workflow without any loss of accuracy. We discuss various methods for constructing potential energy surfaces including transfer learning, which requires a minimal number of expensive training points. In this way, we can study chemical reactions at a high level but a low cost. In particular, as the potentials are smooth and differentiable, they enable the use of more advanced semiclassical approximations to quantum dynamics, such as perturbatively corrected instanton theory, which can capture both tunnelling and anharmonicity.
Paper Structure (5 sections, 7 equations, 1 figure)

This paper contains 5 sections, 7 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Machine Learned Potential Energy Surfaces for Physical Simulations
  3. Perturbatively Corrected Instanton Theory
  4. Combining Instanton Theory with Machine-Learning Potentials
  5. Conclusions and Outlook

Figures (1)

  • Figure 1: The double-well potential $V(x) = \left( x^2/x_{\mathrm{min}}^2+1\right)^2$ is the simplest model for a system with degenerate minima which result in a tunnelling splitting $\Delta$. The lowest two energy levels $E_-$ and $E_+$ and wavefunctions $\psi_-(x)$ and $\psi_+(x)$ are shown. Additionally, an instanton trajectory with $N=1024$ beads is depicted.