On the Correlation Energy of π-Electrons in Planar Hydrocarbons

Abstract

We considered the nondynamical E(ND)π and dynamical E(D)π correlation energies of π electrons in a wide variety of planar hydrocarbons. The former could be conveniently calculated within the CASSCF formalism by using modest basis sets. The dynamical part of the correlation energy was studied with the CASPT2 method. It appeared that E(D)π was sensitive to the basis set. It is also found that the ab initio E(ND)π and E(D)π values follow very simple additivity rules, which allow fairly good estimates of the nondynamical and dynamical correlation effects of π electrons simply by counting the carbon and hydrogen atoms. Small deviations from the additivity of E(D)π are found in benzene (2.1 kcal/mol), naphthalene (3.3 kcal/mol), and cyclobutadiene (−3.0 kcal/mol), indicating that some care has to be exercised in applying the additivity rules to (anti)aromatic molecules. Nondynamical correlation E(ND)π exhibits even more pronounced deviations from the additivity in the systems characterized by a π-electron delocalization larger than that in linear polyenes. A novel electrostatics + correlation interpretation of (anti)aromaticity is introduced which sheds new light on an old but central problem of chemistry. It is also suggested that endo- and exoaromaticity should be distinguished. An interesting result of the present calculations is that the Hartree−Fock electron−electron (Vee) interactions and the nondynamical correlation are much more favorable in cyclobutadiene's (CBD's) transition structure (TS) than in its ground state (GS). It appears, however, that the overwhelming effect in the CBD(TS) is an increase in the nuclear repulsion (Vnn), which is higher by 86.8 kcal/mol than in the GS. Consequently, the propensity of CBD to assume a rectangular geometry in the GS occurs inter alia because of a dramatic relief in the nuclear repulsion. The opposite is the case in the GS of benzene, where the dominating Vne in the regular hexagon prevails over an increase in Vee and Vnn repulsions caused by the D6h formation. Intriguing and counterintutitive results are obtained by comparing the E(ND)π of the CBD(GS) and benzene with those of corresponding linear polyenes. The E(ND)π of the CBD(GS) is higher by 8 kcal/mol than that of the 1,3-butadiene, whereas the E(ND)π of benzene is lower by 5.7 than that of hexatriene (in kcal/mol). The (anti)aromatic (de)stabilization of CBD and benzene relative to 1,3-butadiene is 40.7 and 28.4 kcal/mol, respectively. The Vne attraction in both compounds is appreciably higher (i.e., less favorable) than that in the reference molecule, 1,3-butadiene. However, this is overcompensated in benzene by more advantageous Vee and Vnn terms, but it is not the case for CBD. This difference makes benzene exoaromatic and CBD exoantiaromatic.