Having developed general S 2n theories in the first-and second-order SAPT we have formulated new theory which can effectively sum up exchange energy in second-quantized formalism to infinite order in overlap matrix which exactly reproduces existing formulae for density-matrix formalism . We believe that such infinite order summation can be generalised for the higher-orders of SAPT, or SAPT with intramonomer correlation we plan to develop in the future.