Role of d-Hybridization in the Pi Molecular Orbitals of Unsaturated Hydrocarbons

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Abstract
Calculations on the 2pπu state of H2+ suggest that d‐type atomic orbitals will make appreciable contributions to the MO's of pi electrons in unsaturated molecules. A symmetry analysis shows that in planar aromatic hydrocarbons only two of the five d orbitals may hybridize with the p orbitals in pi MO systems. The coefficients of the d functions in these MO's were estimated, and their effects on the orbital energies were determined. Resonance energies, charge densities, dipole moments, hyperfine coupling constants, and bond orders were calculated from these modified orbitals, and the results were compared with experiment and with the results of simple Hückel theory. The definitions of charge densities and bond orders must be modified when d orbitals are included. The inclusion of d‐hybridization leads one to expect certain effects which are not predicted by the Hückel theory: (a) The simple Hückel theory predicts equal resonance energies for trans‐ and cis‐butadiene. Inclusion of d orbitals makes trans‐butadiene more stable than cis‐butadiene by about 700 cal. (b) Simple Hückel theory predicts that the square cyclobutadiene molecule will have no resonance stabilization. Inclusion of d orbitals produces a stabilization of about 6 kcal. (c) Simple Hückel theory predicts that phenanthrene has a zero dipole moment. Inclusion of d orbitals leads one to expect a dipole moment of 0.17 D. (d) Simple Hückel theory predicts zero spin densities at certain positions in the pyrene negative ion. Inclusion of d orbitals allows small spin densities to appear at these positions. On the whole, the inclusion of d‐orbitals does not greatly alter the interpretation of resonance energies and bond lengths given by the simple Hückel theory. Nor does it shed any light on the problem of the anamolous length of the central bond of naphthalene. The effect of d‐hybrids may prove to have an importance in the interpretation of some properties at least as great as that of other refinements of MO theories of aromatic hydrocarbons, such as configuration interaction.

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