One-Center Perturbation Approach to Molecular Electronic Energies. IV. Ten-Electron Molecules of Type MHk

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Abstract
Taking the spherically symmetric molecular puff as the zero‐order problem, we carry out a perturbation calculation of the energies of the HF, H2O, NH3, and CH4 molecules. The first‐order correction function is obtained through the diagonal Sternheimer approximation in which each orbital is perturbed independently by the one‐electron perturbing potential. For the energy increment between puff and molecule, the integral Hellmann–Feynman formula is employed. At several M–H distances energies are computed, and for H2O and NH3 the energy also is examined as a function of the H–M–H bond angle. Stretching and bending force constants in H2O, NH3, and CH4 are found to have the right order of magnitude, although computed equilibrium internuclear separations are not so good. An extremely flat potential curve near the minimum of the energy gives a poor equilibrium angular geometry in the case of H2O. The inversion barrier of NH3 is calculated to be 0.0135 a.u. compared with the experimental value of 0.0093 a.u. It is argued that the integral Hellmann–Feynman formula combined with the Sternheimer approximation form a consistent many‐electron perturbation method.