Variational solution of congruent transformed Hamiltonian for many-electron systems using full configuration interaction calculation

TL;DR

This paper introduces a variational method using a congruent transformed Hamiltonian with explicit correlation functions, enabling more accurate FCI calculations with smaller basis sets for many-electron systems.

Contribution

The paper develops a Hermitian congruent transformation approach with explicit correlation functions, improving FCI energy calculations by reducing basis set size requirements.

Findings

Transformed Hamiltonian yields lower energies than conventional FCI.

Method maintains Hermitian property, ensuring physical validity.

Enables FCI-quality results with smaller basis sets.

Abstract

The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation functions are selected to facilitate analytical evaluation of all the resulting integrals. The ground state energy is obtained variationally by performing a full configuration interaction (FCI) calculation on the congruent transformed Hamiltonian. Computed results on well-studied benchmark systems show that for the identical basis functions, the energy from the congruent transformed Hamiltonian is significantly lower than the conventional FCI calculations. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the 1-particle basis set, the results indicate that the congruent transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying 1-particle basis set.