Submersion of sodium clusters in helium nanodroplets and critical assessment of He-He pseudopotentials

The submersion of neutral sodium clusters Nan (n = 10, 20, 30) in HeN (N ≲ 90 000) is investigated by zero-point averaged dynamics (ZPAD) simulations, the quantum nature of helium atoms being taken into account through the use of He-He pseudopotentials. Nan clusters are described by tight-binding models; their initial structures are taken from the Quantum Cluster Database, locally optimized, and compared with structures predicted by popular density functionals in order to confirm their suitability. Helium nanodroplets (HNDs) are formed by successive coalescences of smaller droplets, a process that may excite a HND vibrational mode with no influence on the propensity of Nan for submersion in helium. Interestingly, Na20 is found to possibly rearrange at the HND surface at the early times of Na20He79989 dynamics, a behavior absent from other calculations. Three He-He pseudopotentials were mainly tested. Simulations based on the two shallowest pseudopotentials yield swift submersion of Nan (t < 100 ps) at all n investigated here, in disagreement with experiments that predict that submersion should be a slow process occurring when n ≳ 21. The submersion dynamics of Nan is slower with the third and deepest pseudopotential, but calculations up to 250 ps did not enable us to identify a critical size nc ≈ 20 for submersion. We believe that ZPAD can help model the submersion of alkali clusters in HNDs of experimental size in a reasonable amount of time, provided that some effort is made to build He-He pseudopotentials more specific to submersion and large HNDs.