Generalization of Brillouin theorem for the non-relativistic electronic Schr\"odinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions

TL;DR

This paper generalizes the Brillouin theorem for the non-relativistic electronic Hamiltonian with a coupling parameter, enabling improved configuration interaction calculations by modifying the SCF algorithm to relax previous restrictions.

Contribution

It extends the Brillouin theorem to include a coupling strength parameter and modifies the SCF procedure to facilitate CI calculations without traditional restrictions.

Findings

Modified SCF algorithm supports CI calculations at different coupling strengths.

The approach removes restrictions imposed by the original Brillouin theorem.

Provides a practical method for basis set generation in electronic structure calculations.

Abstract

The Brillouin theorem has been generalized for the extended non-relativistic electronic Hamiltonian (Hkin+ Hne+ aHee) in relation to coupling strength parameter (a), as well as for the configuration interactions (CI) formalism in this respect. For a computation support, we have made a particular modification of the SCF part in the Gaussian package: essentially a single line was changed in an SCF algorithm, wherein the operator rij-1 was overwritten as 1/rij to a/rij, and a was used as input. The case a=0 generates an orto-normalized set of Slater determinants which can be used as a basis set for CI calculations for the interesting physical case a=1, removing the known restriction by Brillouin theorem with this trick. The latter opens a door from the theoretically interesting subject of this work toward practice.