Spectral shift of sodium in a liquid-helium environment: A sequential Monte Carlo time-dependent density-functional-theory study

Abstract

The excitation lineshift and linewidth of the principal resonance line of Na embedded in liquid He have been obtained using combined Monte Carlo (MC) simulation and quantum mechanics (QM) calculations. The metropolis MC simulation used interatomic potentials obtained from high-level quantum mechanics results. Using the structures of the simulation statistically relevant configurations are sampled for subsequent QM calculations. The transition wavelengths for the $3s\ensuremath{\rightarrow}3p$ principal resonance line of atomic Na were obtained using time-dependent density-functional-theory calculations of the central alkali-metal atom surrounded by the first solvation shell composed of 42 He atoms. The widths are obtained by the statistical distribution of calculated transitions. Three different functionals were used. Statistically converged results using the $\mathrm{PBE}1\mathrm{PBE}∕6\text{\ensuremath{-}}311++\mathrm{G}(\mathrm{d},\mathrm{p})$ give a blueshift of 14.7 nm and a width at half maximum of 7.8 nm. Similar results are obtained using the Beeke-Lee-Yang-Parr three parameter exchange functional and the Becke three-parameter exchange with the Perdew nonlocal correlation functional models. These results seem to give a reasonable statistical representation of the structure of the He cavity enclosing the host Na atom and the consequent solvent effect on the $3s\ensuremath{\rightarrow}3p$ excitation.