Weinhold’s lower bounding formula for the overlap between the exact wavefunction and an approximate wavefunction is applied to the hydrogen atom. The lower bound is examined as a function of both the number of basis set terms used in the bounding inequality and the nonlinear variational parameter in this basis set. A method is then proposed and tested for approximating the integrals over H2 and H3 required by Weinhold’s technique as products of integrals involving only H. In the case studied, the resulting approximate overlap bounds converged to the true bound.
The perturbation energy series of Byers Brown and Power, applied to the case of one−electron diatomics, is analyzed for various internuclear separations to obtain the radius of convergence. The convergence of the series is limited by a branch point on the real axis for nonphysical values of the perturbation parameter.
Perturbation theory of the electron correlation cusp based on a partitioning of the electron-electron interaction into long-and short-range components Numerical results for various perturbation series for atomic interactions at short range are presented for the energy, dipole moment, and dipole polarizahility of one-electron diatomics. Although third-order energy results are accurate at short range, there is appreciable error in the other property values. The convergence of the series is considered in a companion paper.
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