Why doubly excited determinants govern configuration interaction calculations of electron correlations

TL;DR

This paper demonstrates that in configuration interaction calculations of electron correlations, doubly excited determinants are the dominant contributors, with determinants of odd excitation number being negligible, supported by mathematical explanation.

Contribution

It reveals that doubly excited determinants govern electron correlation calculations and provides a mathematical rationale for their dominance over odd excitation determinants.

Findings

Doubly excited determinants are the primary contributors in CI calculations.

Determinants with an odd number of excitations are negligible.

Mathematical explanation supports the dominance of doubly excited determinants.

Abstract

Computational evidence shows that, when using natural orbitals to study (dynamical and non-dynamical) electron correlation, determinants with an odd number of excitations play a negligible role. Instead, doubly excited determinants rule the rostrum in this kind of configuration interaction calculations. We explain mathematically why it must be so.