Predicting atomic dopant solvation in helium clusters: the MgHe$_n$ case

We present a quantum Monte Carlo study of the solvation and spectroscopic properties of the Mg doped helium clusters MgHe$_n$ with $n=2-50$. Three high level (MP4, CCSD(T) and CCSDT) MgHe interaction potentials have been used to study the sensitivity of the dopant location on the shape of the pair interaction. Despite the similar MgHe well depth, the pair distribution functions obtained in the diffusion Monte Carlo simulations markedly differ for the three pair potentials, therefore indicating different solubility properties for Mg in He$_n$. Moreover, we found interesting size effects for the behavior of the Mg impurity. As a sensitive probe of the solvation properties, the Mg excitation spectra have been simulated for various cluster sizes and compared with the available experimental results. The interaction between the excited $^1$P Mg atom and the He moiety has been approximated using the Diatomics-in-Molecules method and the two excited $^1\Pi$ and $^1\Sigma$ MgHe potentials. The shape of the simulated MgHe$_{50}$ spectra show a substantial dependency on the location of the Mg impurity, and hence on the MgHe pair interaction employed. To unravel the dependency of the solvation behavior on the shape of the computed potentials, exact Density Functional Theory has been adapted to the case of doped He$_n$ and various energy distributions have been computed. The results indicate the shape of the repulsive part of the MgHe potential as an important cause of the different behaviours.