Perturbation theory for the density matrix in the MO LCAO method

The problem of calculating the density matrix of perturbed electron shells in complex molecules has been solved in the MO LCAO molecular orbital linear combination atomic orbitals] approximation. Considering the electron interaction in correcting the density matrix in each order of the perturbation theory yields one matrix equation uniquely defining the correction. This equation is formulated as an ordinary, linear nonhomogeneous system with respect to the individual matrix elements; this provided the possibility of establishing the convergence region of the self-consistent method. The solution of this system is accomplished by the method of steepest descent which, as has been shown, is always convergent in this case. It was established that just as in the conventional perturbation theory, the (2i + 1)th correction for the energy in terms of the Hartree-Fock method may be expressed by a correction of the density matrix not exceeding the i-th order. Detailed expressions are presented up to the eighth energy correction.