  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.
