Based on calculations carried out for selected test systems, it can be seen that the S 4 approximation leads to a significant improvement in the relative errors of the first-order exchange and second-order exchange-induction energies. The improvement in the values obtained for the second-order exchange-dispersion is also present, although relatively smaller in most cases. An exception to this is the ethylene dimer (Figure ), where the improvement in the exchange-dispersion errors compared between the S 2 and S 4 approximations is more than noticeable. For two of the complexes studied in this work, namely Ar-H 2 O (Figure ) and ethylene dimer, it has been observed that the values of exchange corrections calculated in the S 4 approximation for the distances greater than the equilibrium distance can reproduce For the Be-NH 3 complex (Figure ), the most significant relative errors were observed among the selected systems. A possible reason for this may be the very small equilibrium distance of only 1.79 Å compared to the other systems studied. Since the exchange energy drops exponentially with the intermolecular distance R, the values of the exchange correction were generally larger than for other systems. Moreover, the validity of both the S 2 and S 4 approximations decreases with the intermolecular distance R. These two effects combined may explain the observed values of the relative errors for the Be-NH 3 system. The addition of S 4 terms in this system changes the energy in the equilibrium distance by over . 83.45 milihartrees, which exceeds 12.5 times the absolute value of the interaction energy from CCSD. For the complexes with water molecules, the addition of S 4 terms changes the energy in the equilibrium distance between 13.04% of the E int (CCSD) absolute value for the Mg-H 2 O to 0.09% for Ar-H 2 O, whereas for Be-H 2 O, the S 4 terms constitute 1.29% of the E int (CCSD) absolute value in the equilibrium distance. For the ethylene dimer in the equilibrium distance, the addition of the S 4 in the exchange energy results in the change of 0.24% of the E int (CCSD) energy. As can be seen in Table , a few percent of the total exchange in each case (which is a typical value for the S 2 approximation) is often a sizeable contribution to SAPT error. In particular, the induction and exchange-induction effects cancel out to a large degree, and if the extent of cancellation is not adequate, the overall error can be huge compared to the well depth. The importance of theory beyond S 2 is even