Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

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 the approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys [Proc. R. Soc. London, Ser. A 310, 43 (1969)] 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 function is 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 congruently transformed Hamiltonian. Computed results on well-studied benchmark systems show that for identical basis functions, the energy from the congruently transformed Hamiltonian is significantly lower than that from the conventional FCI calculation. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the one-particle basis set, the results indicate that the congruently transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying one-particle basis set.