Restricted geometry optimization: a different way to estimate stabilization energies for aromatic molecules of various types.

At RHF, MPn, and DFT levels, a procedure of geometry optimization under the restrictions of pi-orbital interactions (GOR) was developed, thus providing a conjugated molecule with the following two types of localized reference geometries: a "GL" geometry where all double bonds are localized, and n different "GE-n" geometries, in each of which only two double bonds were permitted to conjugate. Interestingly, the molecular energy differences between the corresponding pairs of GE-n and GL geometries were found to be additive in each of the acyclic polyenes, and these were not additive for benzene. As a result, an extra stabilization energy (ESE) value of -39.0 kcal/mol was found in benzene. Afterward, GOR was applied to benzene- and furan-like species, strained aromatic molecules, and substituted benzenes, and the calculated ESEs for these molecules were found to be in reasonable ranges. The GOR can isolate a specific group from other groups, and it has several special functions. First, with regard to the substituent effect, the ESE difference between substituted benzene and benzene can be partitioned into conjugative and inductive parts. Second, the behavior of strained aromatic molecules can be ascertained from the roles of their resonance interactions, strained-induced bond localization (SIBL), and inductive effects, indicating that it is resonance interactions, rather than SIBL, which are responsible for localizing double bonds. Emphatically, it is the GL and GE-n geometries of aromatic molecules, rather than nonaromatic compounds, which can be used as the reference structures for calculating ESE. Particularly, these localized geometries are no longer arbitrary.