Cumulant-based calculations of the correlation energy in a molecule

TL;DR

This paper introduces cumulant-based methods for calculating the correlation energy in molecules, using Lanczos tridiagonalization to generate a convergent correction sequence without storing the full wave function.

Contribution

It presents a novel approach combining cumulants and Lanczos tridiagonalization for efficient correlation energy calculations in molecular systems.

Findings

Sequence of corrections converges to the ground state energy

Method avoids storing the many-electron wave function

Cumulant-based approach is effective for molecular energy calculations

Abstract

The problem of constructing a guaranteed convergent sequence of corrections to the Hartree--Fock ground state energy of a molecule without storing the many-electron wave function is considered. Several methods based on cumulants are considered and it is shown that such a sequence is obtained by Lanczos tridiagonalization, in which the elements of the tridiagonal matrix are calculated through cumulants.