Based on the locally projected molecular orbitals, the third and fourth order perturbation corrections for the molecular interaction within the single excitations are evaluated, and the calculated interaction energies are compared with the counterpoise (CP) corrected interaction energy of the Hartree-Fock level of theory. It is demonstrated that the third order calculation is a practical and powerful method to obtain the binding energy almost equal to the CP corrected energy. It requires only one more two-electron integral handling after the LPMO calculation, which is faster than a usual super-molecule HF calculation. For the perturbation expansion, the absolutely local excited orbitals are determined. For small basis sets, it is shown that the partial delocalization of the absolutely local excited orbitals is a compromizing technique to take into account the charge-transfer contribution without reintroducing a large basis set superposition error.