Computational prediction of muon stopping sites: A novel take on the unperturbed electrostatic potential method.

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 optimize 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 Potential (UEP) Method: an approach used for finding the muon stopping site in crystalline materials. The UEP method requires only one DFT calculation, necessary to compute the electronic density. This, in turn, is used to calculate the minima of the crystalline material's electrostatic potential and the estimates of the muon stopping site, relying on the approximation that the muon's presence does not significantly affect its surroundings. One of the main UEP's assumptions is that the muon stopping site will be one of the crystalline material's electrostatic potential minima. In this regard, we also propose some symmetry-based considerations about the properties of this crystalline material's electrostatic potential, 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.

Comparison between density functional theory and density functional tight binding approaches for finding the muon stopping site in organic molecular crystals.

Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.

Computational prediction of muon stopping sites using ab initio random structure searching (AIRSS).

The stopping site of the muon in a muon-spin relaxation experiment is in general unknown. There are some techniques that can be used to guess the muon stopping site, but they often rely on approximations and are not generally applicable to all cases. In this work, we propose a purely theoretical method to predict muon stopping sites in crystalline materials from first principles. The method is based on a combination of ab initio calculations, random structure searching, and machine learning, and it has successfully predicted the MuT and MuBC stopping sites of muonium in Si, diamond, and Ge, as well as the muonium stopping site in LiF, without any recourse to experimental results. The method makes use of Soprano, a Python library developed to aid ab initio computational crystallography, that was publicly released and contains all the software tools necessary to reproduce our analysis.