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; James J Shepherd

doi:10.48550/arxiv.2305.07081

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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

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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

William Z Van Benschoten, Laura Weiler, Gabriel J Smith, Songhang Man, Taylor DeMello and James J Shepherd

ArXiv.org

05/11/2023

DOI: 10.48550/arxiv.2305.07081

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https://doi.org/10.48550/arXiv.2305.07081View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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 whose 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.

Details

Title: Subtitle: Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
Creators: William Z Van Benschoten
Laura Weiler
Gabriel J Smith
Songhang Man
Taylor DeMello
James J Shepherd
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2305.07081
ISSN: 2331-8422
Language: English
Date posted: 05/11/2023
Academic Unit: Chemistry
Record Identifier: 9984410796402771

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