Valence non-Lewis density as an approach to describe and measure aromaticity of organic and inorganic molecules.

Based on the linear combination of atomic orbital-molecular orbital by the natural bond orbitals (NBO) theory, the attractive donor-acceptor superposition interaction between filled (Lewis-type) and vacant (non-Lewis-type) orbitals provide a general mechanism for quantal energy lowering. This interaction has a direct impact on the quantity of the second-order stabilization energy. Therefore, the valence non-Lewis density (VNLD) index, the electron density of unoccupied valence nonbonding and antibonding orbitals, is introduced as an approach to describe and measure aromaticity. This index is based on the frontier orbital concept. To investigate the validity of the proposed aromaticity index, we selected several test sets of organic and inorganic molecules such as different ring sizes in cyclic and heterocyclic hydrocarbons, and all-metal and semimetal clusters, and compared our findings with previous aromaticity analysis. According to the results, VNLD values are well correlated and anticipated the order of aromaticity with the formerly introduced criteria. Furthermore, VNLD reveals that the rings with π-sextet electrons localized in a ring are more aromatic than the other rings, thus, it is in line with Clar's rule. Our proposed aromaticity index has advantages such as, easy to obtain from NBO analysis, and does not require reference molecules which made it more applicable for realizing the aromaticity order in many organic and inorganic compounds.