The difference in the degree of localization between the LFMO and NBO basis sets, and its effects on the energy partitions

The LFMO (localized fragment molecular orbital) and NBO (natural bond orbital) basis sets are constructed. In the LFMO basis set, the σ and π systems are completely separated out, and each LFMO is absolutely localized on its own fragment. But, an NBO is only concentrated on its own fragment when it is expressed as the linear combination of AOs. Afterwards, the Morokum's SCF energy partition and the NBO energetic analysis are performed, over each of the LFMO and NBO basis sets, for the molecules in order to calculate their vertical resonance energy (ΔEV). As shown by the theoretical data presented in this work, ΔEV for molecule C6B6H6 is always destabilizing when it is obtained from the NBO energetic analysis over each of the LFMO and NBO basis sets, and the π interaction between fragments has no effect on the energy of the σ system (ΔEσ=0). But, the values of ΔEV, over the LFMO and NBO basis sets, are rather different. In the case of the Morokuma's SCF energy partition, however, ΔEσ≠0 due to the electron coupling between the π and σ systems. As a result, ΔEV for molecule C6B6H6 become stabilizing, and ΔEV obtained from the Morokuma's energy partition over the NBO basis set is greater in the absolute value than that over the LFMO basis set, indicating that the difference, in the degree of the localization, between the LFMO and NBO basis sets has a great effect on the electron coupling. In molecule C12H6, the vertical resonance energy ΔEV, obtained from the NBO energetic analysis over each of the LFMO and NBO basis set, is always stabilizing. On the contrary, ΔEV, obtained from the Morokum's energy partition over the NBO basis set, is stabilizing, but that, over the LFMO basis set, is destabilizing. According to the 4N+2 rule, the NBO basis set is unreasonable for the energy partition, and the NBO energetic analysis is unable to provide molecule with an reliable ΔEV because it neglects the strong coupling between the π and σ systems.