Time-Dependent Density Functional Theory for Atomic Collisions: A Progress Report

In this paper, the current status of time-dependent density functional theory (TDDFT)-based calculations for ion-atom collision problems is reviewed. Most if not all reported calculations rely on the semiclassical approximation of heavy particle collision physics and the time-dependent Kohn-Sham (TDKS) scheme for computing the electronic density of the system. According to the foundational Runge-Gross theorem, all information available about the electronic many-body system is encoded in the density; however, in practice it is often not known how to extract it without resorting to modelling and approximations. This is in addition to a necessarily approximate implementation of the TDKS scheme due to the lack of precise knowledge about the potential that drives the equations. Notwithstanding these limitations, an impressive body of work has been accumulated over the past few decades. A sample of the results obtained for various collision systems is discussed here, in addition to the formal underpinnings and theoretical and practical challenges of the application of TDDFT to atomic collision problems, which are expounded in mostly nontechnical terms. Open problems and potential future directions are outlined as well.