Effects of many-electron atom polarization in electron-hole formalism

As is known [1], for odd number of electrons the Hartree Fock method of self-consistent field gives the equation, calculation with which help is connected to a problem of diagonalizing a matrix Lagrange multiplier. It results to possible noncommutativity of a Fock operator with the operator density matrix (a projector on subspace of orbitals for electron in a atomic core) and, hence, to absence of an interpretation of the Fock operator as a Hamiltonian for single-particle state [2], [3], [4]. The method of pseudo-potential allows to interpret diagonal elements of the Lagrange multiplier in a Hartree Fock equation as the energy of single-particle state. However, a pseudo-valent orbital constructed by the method appears so compressed one, that results to very underestimated lengths of chemical bonds in comparison with experiments [5], [6]. It, seemingly, is stipulated by the incorrect description of polarization effects in an atom as in the method of pseudo-potential one uses approximation of spherically symmetric unexcited atomic core (”frozen” core). Therefore, at the last time in the ”ab initio” calculations fulfilled the pseudo-potential is utilized only within the limits of core, supplementing with the phenomenological potential describing polarization of the core in the classical way [7], [8]. Although, for example, for halogen dimers a relativistic calculation taking into account the dipole polarizability of atomic cores gives lengths of chemical bounds matching satisfactory with experiment data, the found binding energy is underestimated with respect to its real value [9], [10], [11]. Obviously, it is due to the fact that the correct quantum description of polarization of an atom is possible, if one assumes the existence of quasiparticle exitations for the spherically symmetric core. The goal of this paper is to develop a self-consistent method allowing to calculate effects of core polarization in a field of valent electron within the framework of secondary quantized electron-”hole” formalizm.