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

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, H 2 O, and H 10 at near-equilibrium and stretched geometries. We find that, for Be and H 2 O, i-DMQMC delivers energies which are sub-millihartree accuracy when compared with finite temperature FCI. For H 2 O and both geometries of

The sign problem in density matrix quantum Monte Carlo

“…In a recent study, we showed that the density matrix quantum Monte Carlo (DMQMC) method could be applied to molecular systems, extending it beyond original applications to model systems in condensed matter physics. 1 The use of finite temperature electronic structure methods are becoming increasingly important in applications such as plasmonic catalysis, 2,3 the study of planetary interiors, 4 and solid-state materials 5 , where the temperature dependence is key in obtaining physical and chemical properties, such as phase diagrams and excitation energies. The inclusion of temperature in quantum chemistry methods is difficult because at finite temperatures, more than one state is often occupied, increasing the difficulty of solving the Schrodinger equation.…”

“…The development of the initiator approximation in DMQMC achieved a similar outcome allowing for our previous work on the uniform electron gas and ab initio molecular systems. 1,34 Subsequently, there were also a wide variety of FCIQMC or FCIQMC-like methods developments which are beyond the scope of this work to review in detail. [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] Large scale implementations of the FCIQMC method and related methods have also been developed and these papers review current challenges and developments for the interested reader.…”

Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble

“…62 This will enable the study of low temperature Bose and Bose-Fermi condensates 62 as well as superconductors 91 with the high accuracy typical of AFQMC techniques. In addition, our algorithm will enable apples-to-apples, canonical ensemble comparisons between FT-AFQMC and other canonical ensemble finite temperature electronic structure techniques, such as Density Matrix QMC 92 and finite temperature coupled cluster approaches, [18][19][20][21] for the first time. Some of these comparisons will necessitate generalizing our formalism to arbitrary ab initio Hamiltonians, which is an ongoing effort.…”

Piecewise Interaction Picture Density Matrix Quantum Monte Carlo

“…After being developed to use the initiator approach, 65 which was also adapted from the groundstate FCIQMC version 66 , IP-DMQMC benchmarked the warm dense electron gas alongside path integral Monte Carlo approaches to obtain a finite-temperature local density approximation functional. [67][68][69] In addition to these successes, IP-DMQMC showed promise in initial applications to molecular systems 70 and its sign problem showed to be similar to that of FCIQMC. 71 In this work we seek to extend IP-DMQMC by continuing the simulation after the target inverse temperature is reached.…”