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The congruent transformation of the electronic Hamiltonian is developed toaddress the electron correlation problem in many-electron systems. The centralstrategy presented in this method is to perform transformation on theelectronic Hamiltonian for approximate removal of the Coulomb singularity. Theprinciple difference between the present method and the transcorrelated methodof Handy and Boys is that the congruent transformation preserves the Hermitianproperty of the Hamiltonian. The congruent transformation is carried out usingexplicitly correlated functions and the optimum correlated transformHamiltonian is obtained by performing a search over a set of transformationfunctions. The ansatz of the transformation functions are selected tofacilitate analytical evaluation of all the resulting integrals. The groundstate energy is obtained variationally by performing a full configurationinteraction (FCI) calculation on the congruent transformed Hamiltonian.Computed results on well-studied benchmark systems show that for the identicalbasis functions, the energy from the congruent transformed Hamiltonian issignificantly lower than the conventional FCI calculations. Since the number ofconfiguration state functions in the FCI calculation increases rapidly with thesize of the 1-particle basis set, the results indicate that the congruenttransformed Hamiltonian provides a viable alternative to obtain FCI qualityenergy using a smaller underlying 1-particle basis set.

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