Pfaffian pairing and backflow wave functions for electronic structure quantum Monte Carlo methods

TL;DR

This paper explores pfaffian and backflow wave functions in quantum Monte Carlo methods, demonstrating their advantages in fermion node improvements and analyzing their structures for electronic systems.

Contribution

It introduces mathematical identities for pfaffians, evaluates their effectiveness in electronic structure calculations, and combines them with backflow correlations for enhanced wave functions.

Findings

Pfaffians improve fermion node descriptions over Hartree-Fock.

Linear combinations of pfaffians yield limited energy gains in molecules.

Backflow correlations enhance wave function accuracy.

Abstract

We investigate pfaffian trial wave functions with singlet and triplet pair orbitals by quantum Monte Carlo methods. We present mathematical identities and the key algebraic properties necessary for efficient evaluation of pfaffians. Following upon our previous study \cite{pfaffianprl}, we explore the possibilities of expanding the wave function in linear combinations of pfaffians. We observe that molecular systems require much larger expansions than atomic systems and linear combinations of a few pfaffians lead to rather small gains in correlation energy. We also test the wave function based on fully-antisymmetrized product of independent pair orbitals. Despite its seemingly large variational potential, we do not observe additional gains in correlation energy. We find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions and exhibit the minimal number of two nodal domains in agreement with recent results on fermion nodes topology. We analyze the nodal structure differences of Hartree-Fock, pfaffian and essentially exact large-scale configuration interaction wave functions. Finally, we combine the recently proposed form of backflow correlations \cite{drummond_bf,rios_bf} with both determinantal and pfaffian based wave functions.