Valence States of Carbon in π-Electron Systems. I. Alternant-Hydrocarbon Ground States

When the molecular wavefunction is described in part by molecular‐orbital theory, new terms (Coulomb self‐repulsion integrals) enter the valence‐state energy over and above the classic valence‐bond valence state of Van Vleck. Atomic orbitals for π‐electron theory are obtained by minimizing the energy of carbon in a valence state appropriate for alternant‐hydrocarbon ground states. The 2pπ orbital so obtained with a non‐integral‐n ``double'' basis, with a simple valence‐bond σ wavefunction and a simple molecular‐orbital π wavefunction, gives a one‐center Coulomb repulsion integral ${\text{〈2pπ 2pπ | 1/r}}_{12}\text{| 2pπ2pπ〉=12.38\hspace{0.17em}}\mathrm{eV}$ , compared to the semiempirical value of ∼11 eV.