Three-center atomic expansion method for ion-atom collisions

The three-center atomic expansion method for ion-atom collisions first described by Anderson et al. (1974) is reexamined and applied to a broader energy range to study the role of united-atom orbitals in a close collision. In this method the electronic wave function is expanded in terms of traveling atomic orbitals around the two moving centers as well as united-atom orbitals around the center of charge. For the symmetric resonant ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collision, it is found that electron-capture probabilities at small impact parameters are changed substantially with the addition of united-atom orbitals at the third center for low-velocity collisions ($v\le 0.5$), whereas there is almost no such change at higher velocities ($v\sim 1$). This illustrates the velocity range in which the relaxation of electronic orbitals occurs toward the united-atom orbitals in a close collision and implies the velocity range where an adiabatic molecular-orbital expansion becomes inappropriate.