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Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
Journal article   Open access   Peer reviewed

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

William Z Van Benschoten, Laura Weiler, Gabriel J Smith, Songhang Man, Taylor DeMello and James J Shepherd
The Journal of chemical physics, Vol.158(21), 214115
06/07/2023
DOI: 10.1063/5.0150702
PMID: 37265216
url
https://www.osti.gov/servlets/purl/1993311View
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Abstract

We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

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