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The physical processes at the interface of a low-temperature plasma and asolid are extremely complex. They involve a huge number of elementary processesin the plasma, in the solid as well as charge, momentum and energy transferacross the interface. In the majority of plasma simulations these surfaceprocesses are either neglected or treated via phenomenological parameters.However, those parameters are known only in some cases, so such an approach isvery inaccurate and does not have predictive capability. Therefore,improvements are highly needed. In this paper we briefly summarize relevanttheoretical methods from solid state and surface physics that are able tocontribute to an improved simulation of plasma-surface interaction in the nearfuture. Full \textit{ab initio} quantum simulations are feasible only forextremely short times and/or small system sizes. A substantial simplificationis achieved when electronic quantum effects are not treated explicitly. Thenone arrives at semi-classical molecular dynamics (MD) simulations for the heavyparticles that have become the main workhorse in surface science simulations.Using microscopically founded potentials and force fields as an input, these MDsimulations approach the quality of \textit{ab initio} simulations, in manycases. However, despite their simplified nature, these simulations require atime step that is of the order or below one femtosecond making it prohibitiveto reach experimentally relevant scales of minutes. To bridge this gap inlength and time scales without compromising the first principles character ofthe simulations, many physical and computational strategies have been putforward in surface science. This paper presents a brief overview on differentmethods and their underlying physical ideas, and we compare their strengths andweaknesses.

Extending \textit{ab initio} plasma-surface simulations to experimentally relevant scales