LCAO Molecular Orbital Computation of Resonance Energies of Benzene and Butadiene, with General Analysis of Theoretical Versus Thermochemical Resonance Energies

Abstract

The decrease in π_x‐electron energy for the change from a Kekulé to a proper benzene structure is computed purely theoretically by the method of antisymmetrized products of MO's (molecular orbitals), in LCAO approximation, using Slater 2pπ_x AO's (atomic orbitals) of effective charge 3.18, and assuming a carbon‐carbon distance of 1.39A. The result (73.1 kcal/mole) is a theoretical value for the gross (vertical) resonance energy of benzene taken for constant C–C distances of 1.39A. In order to make a comparison with the net or ordinary empirical resonance energy, several corrections to the latter are required. The principal one is for the ``compression energy'' required to compress the single and stretch the double bonds of the Kekulé structure from normal single and double‐bond distances to 1.39A. The others (not hitherto clearly recognized) involve hyperconjugation and related effects. The corrections are discussed and their magnitudes estimated, but a reliable value can be obtained only for the compression energy. Allowing for this alone, the computed net resonance energy is 36.5 kcal. This agrees, within the uncertainties due to the omitted correction terms, with the value (41.8 kcal) of the ``observed'' resonance energy Δ based on thermochemical data. Here Δ is the departure of the actual heat of formation ΔH_f⁰ of benzene from the value given by a standard formula for nonresonating hydrocarbons. A new standard formula containing corrections for the mutual effects of neighboring carbon‐carbon bonds is given; this is of interest also for itself, and its significance is briefly discussed. The analysis given in the paper serves to clarify hitherto existing obscurities in what is meant by ``resonance energy.'' An analysis of the nature and significance of ``nonresonating'' structures (like for example Kekulé benzene) is also included, using He₂, 1,3 butadiene, and benzene as examples. Repulsion terms in the LCAO MO theory occur for nonresonating structures, which appear to be the counterpart of exchange repulsions of the valence‐bond theory. When resonance occurs, it more or less overcomes these repulsions. The gross resonance energies of cis‐ and trans−1,3‐butadiene are computed by the same method. For transbutadiene, the computed value corrected for compression is 3.7 kcal/mole, while the ``observed'' thermochemical value Δ is 6.5.