Molecular-orbital description of the states of two-electron systems.

Abstract

The molecular-orbital (MO) method introduced previously by us [Phys. Rev. Lett. 57, 984 (1986)] to treat two-electron atoms is developed further. The states of systems consisting of two electrons and one positively charged particle are analyzed with use of the interelectronic distance as an adiabatic coordinate in analogy to the interprotonic distance in ${\mathrm{H}}_{2}^{+}$. The motion of two electrons then separates into rotational, vibrational, and internal motion, the latter being described by MO, exactly as in molecules. Indeed, adiabatic MO potential curves for atomic systems are obtained by scaling the corresponding curves for ${\mathrm{H}}_{2}^{+}$. Approximate quantum numbers for two-electron states, derived previously by empirical methods or from an ad hoc rovibrational model, arise naturally since the two-center Coulomb problem is exactly separable in MO coordinates and the corresponding nodal surfaces are conserved for all interelectronic separations. In addition, the gerade-ungerade symmetry of MO is exactly preserved and appears as a fundamental symmetry of two-electron states.