Extension of the atom by atom scheme of counterpoise method and presentation of its new advantages

In this paper, for the first time, we want to clearly show that two types of binding energies, cited here as interaction energies (IEs) and stabilization energies (SEs), may need different values of basis set superposition error (BSSE) corrections. We also report the first calculation of the BSSE correction for the strain energies (E_S) of supermolecular systems. For this purpose, the known atom by atom scheme of the counterpoise method was extended to mathematically show that the values of BSSE for IE versus SE of a defined system can be really different. Then the IE and SE values of some AB and ABC supermolecules were corrected for BSSE, calculated through the full counterpoise method (CPⁿ) versus its atom by atom scheme (CP^aa). The data confirmed that the CP^aa accurately gives the different BSSE values for IE versus SE when there is a noticeable difference between the values of these energies. In the above case, the CPⁿ method that gives a single value of BSSE for both IE and SE is not a suitable choice for correcting the SE values.