Scattering of Electrons fromH2+: The Method of Polarized Single-Center Orbitals

A generalization of the method of polarized orbitals is introduced to calculate the scattering of electrons from diatomic molecules in the Born-Oppenheimer (fixed-nuclei) approximation. The molecule is described by a single-center expansion which in lowest order is spherically symmetric and therefore an atomic-like function. This function can be polarized in complete analogy with an atomic orbital. Furthermore, the first approximation beyond the spherically symmetric can be included to give a permanent distortion correction. In the $s$-wave results, the induced polarization effects are larger than the first-order correction. The $p$-wave phase shifts are in some cases much larger than the $s$ wave, and very complicated by virtue of the combined effects of exchange, polarization, and first permanent distortion. The method also yields, as a by-product of the polarizability of ${\mathrm{H}}_2^{+}$. The first part of the paper contains a general analysis of the partial-wave expansion from diatomic molecules in the Born-Oppenheimer approximation. The scattered amplitude is given in terms of phase shifts which are independent of the angles between the internuclear axis and the incident direction. The dependence on these angles is shown to be factorable and analytically expressible independent of the dynamical problem.