Structures of a trivalent actinium cation in helium clusters (Ac ⋅He ) have been studied by quantum path integral molecular dynamics simulations with different cluster sizes, n=18-200. The nuclear quantum effect of helium atoms plays an important role in the vibrational amplitude of the Ac -He complex at low temperatures (1-3 K) at which the complex is stable. We found that the coordination number of helium atoms comprising the first solvation shell can be as high as eighteen. In this case, the helium atoms are arranged in D symmetry. The Ac -He complex becomes more rigid as the cluster increases in size, which implies that it becomes more stable. The simulation results are based on an accurate description of the Ac -He interaction using relativistic ab initio calculations.

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