Many-Electron Pseudopotential Formalism for Atomic and Molecular Excited-State Calculations

Abstract

The pseudopotential approach of Phillips and Kleinman is extended beyond the one-electron approximation for the purpose of obtaining correlated low-energy continuum and excited bound states of atomic and molecular systems with a minimum of computational effort. Pseudopotential equations are derived by a variational method. These and other nonvariational pseudopotential methods are shown to be quite useful in conjunction with either adiabatic or close-coupling methods. Calculations are performed on the following two-electron systems: e-H ${}_{}{}^1{}_{}{}^{}S$-wave elastic scattering, e-${\mathrm{He}}^{+}$ ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ elastic scattering, and ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ Rydberg states of He. In general, good results are obtained. The calculated Rydberg-state quantum defects usually agree with the experimental values to three decimal places, and the calculated e-H ${}_{}{}^1{}_{}{}^{}S$ zero-energy scattering length of 5.90 ± 0.08, which is a strict upper bound to the true value, compares favorably with the value 5.965 ± 0.003 obtained by Schwartz in a very much more involved calculation. The possible extension of these methods to larger atomic systems and to molecules is discussed. A differential equation method for obtaining bound-state wave functions and energies based on asymptotic properties of Coulomb functions is outlined in the Appendix.