Abstract
The second order energy of an atom in an expansion in which the interelectronic interaction is treated as a perturbation can be written as a sum of certain partial sums. Each partial sum represents the contributions of the zero order states originating from a fixed excitation of one electron and an arbitrary excitation of another electron. A method for the exact analytical evaluation of a certain class of such partial sums is developed. The relevance of the method to the calculation of the correlation energies in atoms is pointed out. The advantages and the disadvantages of the method in comparison with some other methods are discussed.