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A second-quantization formalism for systems of interacting free elementary particles and their bound clusters is presented. A modified version of the Feynman-Goldstone diagrammatic technique is used for the classification and evaluation of individual terms appearing in this formalism. The resulting effective Hamiltonian naturally includes such processes as Coulomb and exchange interactions between bound composite particles, their breakup and recombination reactions, etc. For simplicity, a system of hydrogen atoms, protons, and electrons is studied. The method can easily be generalized to any species of composite particles.

A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.

A theory of the model Hamiltonians within the framework of Rayleigh-Schrodinger perturbation theory is elaborated. The approach of a model Hamiltonian is based on the assumption that if it is diagonalized in a chosen model space it will yield eigenvalues of the original Hamiltonian in the entire Hilbert space. The theory of the model Hamiltonians may be fruitful as a theoretical background for the study of effective Hamiltonians and as natural extension of the standard Rayleigh-Schrodinger perturbation theory.

The general diagrammatic perturbation theory for the interaction of two molecular systems treated by the extended Huckel method is elaborated.

Low-lying excitation energies are calculated by the use of the many-body quasi-degenerate Rayleigh-Schrodinger perturbation theory. An eigenvalue problem is derived for the third-order estimation of the low-lying excitation energies. The elements of the hermitian matrix appearing in this eigenvalue problem are determined up to the third order by the diagrammatic method. Some simple illustrative calculation on π-electron systems are carried out.

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.