On the correlation energy of pi-electrons in planar hydrocarbons

We considered the nondynamical E(ND)(pi) anti dynamical E(D)(pi) correlatio n energies of pi electrons in a wide variety of planar hydrocarbons. The fo rmer 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)(pi) was sensitive to the bas is set. It is also found that the ab initio E(ND)(pi) and E(D)(pi) values f ollow very simple additivity rules, which allow fairly good estimates of th e nondynamical and dynamical correlation effects of it electrons simply by counting the carbon and hydrogen atoms. Small deviations from the additivit y of E(D)(pi) 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. Non dynamical correlation E(ND)(pi) exhibits even more pronounced deviations fr om the additivity in the systems characterized by a pi -electron delocaliza tion larger than that in linear polyenes. A novel electrostatics + correlat ion 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 (V-ee) inte ractions and the nondynamical correlation are much more favorable in cyclob utadiene'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 inc rease in the nuclear repulsion (V-nn), which is higher by 86.8 kcal/mol tha n in the GS. Consequently, the propensity of CBD to assume a rectangular ge ometry in the GS occurs inter alia because of a dramatic relief in the nucl ear repulsion. The opposite is the case in the GS of benzene, where the dom inating V-ne in the regular hexagon prevails over an increase in V-ee and V -nn repulsions caused by the D-6h formation. Intriguing and counterintutiti ve results are obtained by comparing the E(ND)(pi) of the CBD(GS) and benze ne with those of corresponding linear polyenes. The E(ND)rr of the CBD(GS) is higher by 86.8 kcal/mol than that of the 1,3-butadiene, whereas the E(ND )(pi) of benzene is lower by 5.71 than that of hexatriene tin kcal/mol). Th e (anti)aromatic (de)stabilization of CBD and benzene relative to 1,3-butad iene is 40.7 and 28.4 kcal/mol, respectively. The V-ne attraction in both c ompounds is appreciably higher (i.e., less favorable) than that in the refe rence molecule, 1,3-butadiene. However, this is overcompensated in benzene by more advantageous V-ee and V-nn terms, but it is not the case for CBD. T his difference makes benzene exoaromatic and CBD exoantiaromatic.