Pfaffian pairing wave functions in electronic structure quantum Monte Carlo

TL;DR

This paper explores the use of pfaffian pairing wave functions in quantum Monte Carlo calculations, demonstrating high accuracy in correlation energy recovery and improvements in fermion node descriptions for atoms and molecules.

Contribution

It introduces pfaffian pairing wave functions for quantum Monte Carlo and shows their effectiveness in capturing correlation energies and improving fermion nodes.

Findings

Pfaffian wave functions recover about 95% of correlation energy.

Multi-pfaffian wave functions further improve energy recovery.

Pfaffians significantly enhance fermion node descriptions.

Abstract

We investigate the accuracy of trial wave function for quantum Monte Carlo based on pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-pfaffian pairing wave functions. We show that a small number of pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.