Abstract. The electron wavefunctions for two states of the PbF molecule are calculated. For the ground state of the molecule, tensor components of the hyperfine interaction of the valence electron with the nuclear spin of Pb, electric and magnetic dipole moments and electron matrix elements of P-odd and P, T-odd interactions are calculated. In accordance with the calculation an effective spin-rotational Hamiltonian for the molecule is given. The Hamiltonian includes the parity-non-conserving terms and the interaction with the external fields. The spin-rotational spectrum of the PbF molecule is found to be rather complicated; this is connected with the large anisotropy of the hyperfine A tensor. The results of the present work can be used in planning future experiments on the search for P-odd and P, T-odd phenomena in molecules.

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A coupled perturbation theory for the antisymmetrized product of separated geminals (APSG) approximation is derived. The variational principle for the APSG wave function in an external oscillating field is employed and a set of equations of the form analogous to the normal RPA is obtained. At this level the reduced resolvent in the form of a spectral expansion is written and it is used for the evaluation of the second-order properties.

Two possible variation approximations for the exchange-correlation interaction are considered in the one-particle approach to the electronic structure theories. These approximations appear within the Super-CI procedure in the MCSCF optimization schemes. The basic formalism shows its close connection to the Green's function theory in the extended Koopmans' approach. An immediate implementation of the corresponding Super-CI Green's functions is the Møller-Plesset open-shell and quasi-degenerate perturbation expansions, and the density matrix functional theory. The relativistic formulation which is based on the relativistic extended Koopmans' approach can be used to calculate radiation corrections in frames of the conventional Feynman formalism.