Deterministic and quasi-random sampling of optimized Gaussian mixture distributions for vibronic Monte Carlo

TL;DR

This paper introduces deterministic and quasi-random sampling techniques for Gaussian mixture distributions in vibronic Monte Carlo simulations, improving efficiency and automation over traditional importance sampling methods.

Contribution

It presents a novel approach combining deterministic component selection, quasi-random sampling, and automatic GMD parameter optimization for enhanced Monte Carlo sampling.

Findings

Reduced stochastic error in partition function calculations

Automated GMD parameter optimization improves sampling efficiency

Applicable to a wide range of Monte Carlo GMD sampling problems

Abstract

It was recently shown that path integral Monte Carlo can be used to directly compute partition functions of Hamiltonians with vibronic coupling [J. Chem. Phys. 148, 194110 (2018)]. While the importance sampling Monte Carlo integration scheme was successful, it required many samples to reduce the stochastic error and suffered from the need to manually construct a sampling distribution for each system. We tackle these issues by using deterministic component selection for Gaussian mixture distributions (GMDs), introducing quasi-random numbers into the Monte Carlo sampling, and automatically optimizing the GMD parameters to obtain an improved sampling distribution. We demonstrate the effectiveness of our methods using vibronic model systems, but these methods are in principle widely applicable to general Monte Carlo sampling of GMDs.