Using density matrix quantum Monte Carlo for calculating exact-on-average energies for ab-initio Hamiltonians in a finite basis set

TL;DR

This paper applies initiator density matrix quantum Monte Carlo (i-DMQMC) to compute exact-on-average energies of molecules at finite temperature, demonstrating high accuracy and exploring its applicability for chemical systems.

Contribution

It introduces the application of i-DMQMC to molecular systems, achieving sub-millihartree accuracy and comparing finite temperature energies with other quantum Monte Carlo methods.

Findings

i-DMQMC achieves sub-millihartree accuracy for Be and H2O energies.

The method effectively estimates differences between canonical and grand canonical energies.

Energy difference calculations enable properties like specific heat capacity and ionization potential.

Abstract

We here apply the recently developed initiator density matrix quantum Monte Carlo (i-DMQMC) to a wide range of chemical environments using atoms and molecules in vacuum. i-DMQMC samples the exact density matrix of a Hamiltonian at finite temperature and combines the accuracy of full configuration interaction quantum Monte Carlo (FCIQMC) - full configuration interaction (FCI) or exact energies in a finite basis set - with finite temperature. By way of exploring the applicability of i-DMQMC for molecular systems, we choose to study a recently developed test set by Rubenstein and coworkers: Be, H2O, and H10 at near-equilibrium and stretched geometries. We find that, for Be and H2O, i-DMQMC delivers energies which are sub-millihartree accuracy when compared with finite temperature FCI. For H2O and both geometries of H10 we examine the difference between FT-AFQMC and i-DMQMC which in turn is an estimate of the difference in canonical versus grand canonical energies. We close with a discussion of simulation parameters (initiator error and different basis sets) and by showing energy difference calculations in the form of specific heat capacity and ionization potential calculations.