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

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. A...

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Veröffentlicht in:The Journal of chemical physics 2023-06, Vol.158 (21)
Hauptverfasser: Van Benschoten, William Z., Weiler, Laura, Smith, Gabriel J., Man, Songhang, DeMello, Taylor, Shepherd, James J.
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container_issue 21
container_start_page
container_title The Journal of chemical physics
container_volume 158
creator Van Benschoten, William Z.
Weiler, Laura
Smith, Gabriel J.
Man, Songhang
DeMello, Taylor
Shepherd, James J.
description 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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subjects Configuration interaction
Density
Entropy
finite electronic temperature
free energy calculations
full configuration interaction
Gaussian process
INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Machine learning
Numerical integration
Regression models
Specific heat
thermodynamic properties
title 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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