Using Density Matrix Quantum Monte Carlo for Calculating Exact-on-Average Energies for ab Initio Hamiltonians in a Finite Basis Set.

We here apply the recently developed initiator density matrix quantum Monte Carlo (i-DMQMC) to a variety of 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. In order to explore the applicability of i-DMQMC for molecular systems, we choose to study a recently developed test set by Rubenstein and co-workers: Be, H2O, and H10 at near-equilibrium and stretched geometries. We find that, for Be and H2O, i-DMQMC delivers energies with submillihartree 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, estimates the difference in canonical versus grand canonical energies. We close with two discussions: one of simulation settings (initiator error, the interaction picture, and different basis sets), and another of energy difference calculations in the form of specific heat capacity and ionization potential calculations.