Abstract
The rapid developments of computational quantum chemistry methods and supercomputing facilities motivate the renewed interest in the analysis of the muon/electron interactions in $\mu$SR experiments with \emph{ab initio} approaches. Modern simulation methods seem to be able to provide the answers to the frequently asked questions of many $\mu$SR experiments: where is the muon? Is it a passive probe? What are the interaction parameters governing the muon-sample interaction? In this review we describe some of the approaches used to provide quantitative estimations of the aforementioned quantities and we provide the reader with a short discussion on the current developments in this field.
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