Long range induction and dispersion interactions between Hartree-Fock subsystems

Abstract

A consistent perturbation theory of long range induction interactions between two subsystems described in the Hartree-Fock approximation is presented. For the wavefunction of the interacting system represented by the Hartree product of the subsystem Hartree-Fock wavefunctions (the HHF approximation) the resulting perturbation equations are shown to be precisely equivalent to those of the coupled Hartree-Fock perturbation theory. In contrast to some earlier proposals concerning the calculation of induction energies the present treatment provides the HF level of accuracy for each of the two interacting subsystems.

The non-perturbative solutions of the induction energy problem are then used to build a variation scheme for the calculation of intra- and inter-subsystem correlation effects. By using different partition schemes for the total hamiltonian the functionals derived for the second-order inter-subsystem correlation energy represent either the uncoupled or the coupled pair schemes. In the lowest order with respect to induction interactions they are equivalent to the corresponding ordinary second-order dispersion energy functionals.

The structure of the perturbed wavefunctions is analysed and it is shown that in order to obtain the whole of the induction effects one has to take into account some portion of intra- and inter-subsystem double excitations which can be expressed in the ‘unlinked’ form. Also some computational aspects of the theory presented in this paper are discussed.