Resonant transition rates for charge transfer between diatomic molecular ions and simple metals

We provide a parameter-free perturbation treatment of the resonant electronic coupling between a simple diatomic molecule (${\mathrm{H}}_2$) and a jelliumlike metal surface [Al(110)]. Assuming the unperturbed molecular and metallic states to be orthogonal (which is a good approximation), the matrix element simplifies to the form 〈${\psi }_f$‖H‖${\psi }_i$〉, where ${\psi }_f$ is the neutral free-molecule final state, ${\psi }_i$ the product of the unperturbed metallic and molecular-ion wave functions, and H the Coulomb interaction of the metal electron with the nuclei and 1σ electron in ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$. Using scaled linear-combination-of-atomic-orbitals ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$, scaled Heitler-London ${\mathrm{H}}_2$, and jellium wave functions, this matrix element, including its spin dependence, is evaluated. With use of the golden-rule expression, the transition rates for charge transfer to the ${\mathrm{H}}_2$ X ${\mathrm{}}^1$ ${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ and b ${}^3$ ${\Sigma }_u^{+}$ states are calculated. The dependence of these transition rates on molecule-axis orientation, distance from the surface, resonance energy, and internuclear separation, is investigated.