The calculation of electron transfer probabilities in slow ion-metal surface collisions

Abstract

We consider the interaction of an atomic ion colliding with a solid metal surface, resulting in electronic charge transfer and neutralization of the ion. The coupling of electronic and nuclear degrees of freedom in extended systems is described with a general methodology based on an eikonal representation of nuclear motions, and density matrices for the electronic degrees of freedom. We show how one can computationally deal with two very different time scales in the differential equation for the density operator by separating there the contributions of electronic relaxation and of driving forces. The boundary conditions of the solid perturbed by the ion are described by introducing electronically adiabatic and diabatic regimes. Electron transfer at short distances is calculated in a basis of localized surface states, and partitioning the density matrix into primary and secondary regions, to derive a reduced equation for its primary part. A substantial part of this article details the construction of generalized Wannier functions used in the calculation of electronic energy integrals. Results are presented for Hamiltonian matrix elements and for the time-evolution of atomic populations, in a model appropriate to the Na + + W(110) collisions with energies between 1.0 and 100.0 au. The calculated time-evolving populations provide a unique insight on the dynamics of electronic screening and transfer during collisions.