Role of Excited States in Resonant Charge Transfer during Li$^+$ Backscattering from MoS$_2$: A Multi-Orbital Theoretical Study

Abstract

We present a theoretical investigation of resonant charge transfer in low-energy Li$^+$ ions backscattered from a MoS$_2$ surface, focusing on the influence of excited projectile states. Using a time-dependent Anderson model in the infinite-$U$ limit, we evaluate the individual contributions from the Li $2s$, $2p_x$, $2p_y$, and $2p_z$ orbitals to the final charge state distribution. The Hamiltonian parameters are computed using an expanded Huzinaga basis set that explicitly incorporates lithium's $2p$ orbitals. Each orbital channel is treated separately, and electronic correlation effects are introduced approximately through a probabilistic exclusion principle applied to the final charge state. Theoretical calculations demonstrate that including $2p$ channels enhances the agreement with previously reported experimental neutral fractions, where the single-channel descriptions show noticeable discrepancies. Among excited states, the $2p_z$ orbital oriented perpendicular to the surface contributes most significantly due to its spatial extension toward the substrate. Examination of temporal evolution reveals that independent channel occupations exceed unity at small projectile$-$surface separations, highlighting the necessity of dynamical correlation treatments. These findings establish that excited states make non-negligible contributions to charge exchange processes for alkali ions interacting with transition metal dichalcogenide surfaces and should be incorporated for accurate quantitative modeling.