Computational Prediction of Muon Stopping Sites: a Novel Take on the Unperturbed Electrostatic Potential Method

Abstract

Finding the stopping site of the muon in a muon-spin relaxation experiment is one of the main problems of muon spectroscopy, and computational techniques that make use of quantum chemistry simulations can be of great help when looking for this stopping site. The most thorough approach would require the use of simulations - such as Density Functional Theory (DFT)- to test and optimise multiple possible sites, accounting for the effect that the added muon has on its surroundings. However, this can be computationally expensive and sometimes unnecessary. Hence, in this work we present a software implementation of the Unperturbed Electrostatic Method (UEP), which is an approach used for finding the muon stopping site in crystalline materials that calculates the minima of the electrostatic potential in the crystalline material, and estimates the stopping site of the muon relying on the approximation that the muon presence does not significantly affect its surroundings. One of the main assumptions of the UEP is that the muon stopping site will be one of the electrostatic potential minima in the crystalline material. In this regard, we also propose some symmetry-based considerations about the properties of the electrostatic potential of the crystalline material. In particular, which sites are more likely to be its minima and why the unperturbed approximation may be sufficiently robust for them. We introduce the Python software package pymuon-suite and the various utilities it provides to facilitate these calculations, and finally, we demonstrate the effectiveness of the method with some chosen example systems.