Leveraging Enhanced, Recursively Stratified Sampled Monte Carlo Integration for Accurate Molecular Partition Functions*

Accurate molecular thermodynamics predictions are important for the modeling of atmospheric, industrial, and combustion processes. Most state-of-the-art methods handle thermodynamic contributions from the motions of nuclei using approximate partition functions calculated from high-quality electronic models. Configuration Integral Monte Carlo Integration (CIMCI) [1] instead calculates full partition functions via numerical integrations over all phase space, usually of a coarser electronic model. However, state-of-the-art Monte Carlo (MC) integration techniques like MISER [2] and VEGAS [3] proved to be insufficient for CIMCI, so new enhancements were developed. These include support for multiple parallel integrations over the same phase space, a pair of improved variants of MISER (PMISER and RMISER) that allow pre-sampling results to be included in final results, and a more mathematically rigorous way to predict sub-region variances when performing stratified sampling recursively the way MISER does. Preliminary benchmarking shows efficiency gains equivalent to what one would get from a ca. 9x to 100x increase in sampling budget. While these were mainly created for CIMCI, MC integration's widespread use means many more applications can also benefit.

References:

[1] G. Rath et al., J. Chem. Inf. Mod. 61 (12), 5853 (2021).

[2] W. H. Press et al., Comp. in Phys. 4, 190 (1990).

[3] G. P. Lepage, No. CLNS-447 Cornell Univ. Lab. Nucl. Stud., 1980-03 (1980).