# Italy: Computational modeling for muon spectroscopy

Density Functional Theory (DFT) is a computational quantum mechanical modelling method employed to calculate the electronic structure and electron density of atoms, molecules, condensed phases and other systems in physics, chemistry and materials science. Walter Kohn was awarded the Nobel Prize for Chemistry in 1998 for his fundamental contribution to the development of this workhorse of modern atomistic computation. It utilises fundamental and established scientific laws to determine total energies and atomic structures, a vast amount of spectroscopic and thermodynamic quantities and it serves as the basic ingredient for the investigation of exited state properties. The increase in computer power over the last decades, together with improved approaches and corrections to the DFT method have provided very valuable insight into structures and properties of materials .

### DFT for muon spectroscopy

DFT calculations are very useful in muon spectroscopy because they help answer two key questions related to muon data analysis.

1. Where is the muon?

Muons usually localize in interstitial lattice positions, i.e. they sit in the empty spaces within the crystal structure of the atoms. Exactly which sites in the sample are occupied by muons is very hard to determine experimentally, so DFT methods can provide excellent assistance by determining the expected implantation sites and, from this, the magnetic fields that the muons experience.

2. Does the muon change the magnetic structure?

The muon will locally distort the lattice around its implantation site and it could potentially change the local electronic structure of a material as well. The second effect, very rare, would generate very inaccurate information on the material if it was ignored. The first, when known, can be easily taken into account by small corrections. DFT calculations can evaluate the interactions and the distortion of the lattice around the muon (by comparing with the pristine material), and it can predict the rare cases where the muon locally alters the material properties significantly.

Thus DFT could be extensively used alongside experimental results to assist in the muon data analysis providing the knowledge of both the muon location and its influence on the local electronic properties. Standard implentation of these computational methods could even replace some expensive and time-consuming experimental measurements altogether.

*Acknowledgements: Roberto De Renzi, UNIPR and Thomas Holm Rod, ESS*

*References*:

Pietro Bonfa and Roberto De Renzi, **Toward the Computational Prediction of Muon Sites and Interaction Parameters**, J. Physical Society of Japan *1 July 2016*

J S Möller, P Bonfà, D Ceresoli, F Bernardini, S J Blundell, T Lancaster, R De Renzi, N Marzari, I Watanabe, S Sulaiman and M I Mohamed-Ibrahim, **Playing quantum hide-and-seek with the muon: localizing muon stopping sites**

Physica Scripta *4 December 2013*

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Other articles: University of Parma, *Data Treatment*, muonSR, Atomistic Modelling for Data Treatment