Approximate Electronic Energy Surfaces from Cuspless Wave Functions

The eigenfunctions of a molecular Hamiltonian in which all Coulomb potentials have been replaced by Hooke's law potentials are easily determined. Their electronic parts are essentially single-particle single-center harmonic oscillator, or Gaussian wave functions originating at the center of nuclear charge. An investigation is made to determine the feasibility of using these cuspless base functions in variational calculations of relative molecular electronic energies. It is found that: A. Addition of Coulombic or delta-function singularities to the Hooke's law potentials leads to the formation of rigid molecular systems. B. The Coulomb potentials in 21–26 electron triatomics can be treated as a perturbation upon quadratic potentials. In agreement with experiment it is noted that: C. Approximately homonuclear (i.e., nonhydride) 8-, 20-, and 40-electron polyatomics are configurationally unstable. D. The molecules CO2+, CO2, N2O, NCO—, BO2—, N3—, and NO2+ should all be linear. E. The molecules NO2—, O3, FNO, F2O, and a number of excited states of the molecules (D) should all be nonlinear. F. The stable form of nitrous oxide should be N–N–O rather than N–O–N. A number of general features of the treatment are discussed and several of its limitations are pointed out. A tabulation of coefficients required in Clebsch-Gordan expansions of products of Hermite polynomials is given.