Submersion of sodium impurities in finite cryogenic droplets: A path-integral molecular dynamics study forHe4and para-H2

Abstract

The size-dependent submersion of sodium clusters into helium and para-hydrogen droplets has been computationally investigated using continuum models and path-integral molecular dynamics (PIMD) simulations. All-atom explicit potential energy surfaces combining a semiempirical many-body model for the alkali-metal subpart and a pairwise additive repulsion-dispersion contribution for the solvent-alkali-metal interactions parametrized on quantum chemical calculations were employed for the simulations. Direct evidence for the submersion process was found by placing a sufficiently large sodium cluster, $\mathrm{Na}_{55}$, initially at the surface of a $^{4}\mathrm{He}_{300}$ droplet, whereas $\mathrm{Na}_{13}$ spontaneously migrates to the surface when initially placed at the center of this droplet. Under the normal fluid conditions probed by our approach, submersion in larger helium droplets appears thermally activated but the potential of mean force harvested from out-of-equilibrium PIMD trajectories confirms that the submersion transition occurs near the size of 20 atoms, in agreement with earlier investigations. In the case of para-hydrogen media, temperature and the crystalline nature of the cryogenic host were both found to play significant roles: while a single sodium atom migrates to the surface of liquid $p\ensuremath{-}{\mathrm{H}}_{2}$ clusters, it remains stuck inside at 2 K. Similarly, a $\mathrm{Na}_{13}$ cluster remains at the surface in a cold $p\ensuremath{-}{\mathrm{H}}_{2}$ cluster but becomes readily submerged at 16 K. Our results also indicate that submersion is disfavored in smaller droplets of the cryogenic medium.