A correction method for the pair density to get close to the ground state one

TL;DR

This paper introduces a correction method for the pair density that improves the approximation of the ground state in quantum systems, validated by numerical tests on a neon atom.

Contribution

The method optimizes the pair density to be variationally best within an extended search region, maintaining N-representability and satisfying the virial relation.

Findings

Reduces the root-mean-square error of energies by 69.7%.

Validated on neon atom with improved accuracy.

No additional heavy calculations required.

Abstract

We present a correction method for the pair density (PD) to get close to the ground state one. The PD is corrected to be a variationally-best PD within the search region that is extended by adding the uniformly-scaled PDs to its elements. The corrected PD is kept N-representable and satisfies the virial relation rigorously. The validity of the present method is confirmed by numerical calculations of neon atom. It is shown that the root-mean-square error of the electron-electron interaction and external potential energies, which is a good benchmark for the error of the PD, is reduced by 69.7% without additional heavy calculations.