Knowledge Bank

The electronic structure and bond distances for the three polyhedral alkanes, tetrahedrane ($C4H4$), cubane ($C8H8$), and dodecahedrane ($C20H20$) have been studied with Hartree-Fock-Roothaan molecular orbital wavefunctions. Contracted Gaussian (9s5p/4s), [4s3p/2s] basis sets of atomic orbitals were used. These are somewhat superior to double-zeta or split-valence basis sets, but lack polarization functions. Full use was made of the symmetry of the molecules. Both the CC and CH bond distances were optimized. As expected, $C4H4$ has the shortest CC bond distances, and $C8H8$ has the longest. The CH bond distances varied also, but to a somewhat smaller extent. All (vertical) valence ionization potentials were computed, both from the neutral molecule orbital energies (Koopmans’ Theorem) and from calculations of all of the positive-ion energies ($\Delta$SCF method). Relaxation energies of 0.1 eV were typical. The majority of the ion states are spatially degenerate, and the resulting Jahn-Teller splittings should have a large effect on the photoelectron spectra.