Systematic reduction of sign errors in many-body calculations of atoms and molecules

TL;DR

This paper demonstrates that the self-healing diffusion Monte Carlo (SHDMC) method is an accurate, robust, and scalable approach for calculating ground states of atoms and molecules, effectively reducing sign errors.

Contribution

The paper shows that SHDMC systematically converges to the ground state, achieves near chemical accuracy for N2, and can find nodal surfaces for large systems like C20.

Findings

SHDMC converges systematically to the ground-state wave function.

SHDMC achieves near chemical accuracy for N2 binding energies.

SHDMC can find nodal surfaces for systems as large as C20.

Abstract

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf 79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an accurate and robust method for calculating the ground state of atoms and molecules. By direct comparison with accurate configuration interaction results for the oxygen atom we show that SHDMC converges systematically towards the ground-state wave function. We present results for the challenging N$_2$ molecule, where the binding energies obtained via both energy minimization and SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that SHDMC is robust enough to find the nodal surface for systems at least as large as C$_{20}$ starting from random coefficients. SHDMC is a linear-scaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.