In order to derive the second-order exchange corrections in a S 4 approximation one shall insert the overlap expansion (3) of the permutation operator P into the equation (74) in a similar manner as was done in the section III A. Then by truncating the expansion only to terms consisting of up to 4 overlap integrals and performing an order-by-order analysis, one obtains an expression for the second-order exchange corrections in the S 4 approximation.