Coordination-driven magic numbers in protonated argon clusters

Abstract

The structural properties of rare-gas clusters can be primarily described by a simple sphere packing model or by pairwise interactions. Remarkably, adding a single proton yields a large set of magic numbers that has remained unexplained. In this Letter, we unravel their origin by combining quantum Monte Carlo techniques with many-body ab initio potentials that correctly capture the proton's coordination environment. Thanks to this approach, we find that argon atoms are mainly localized around the classical minimum, resulting in a particularly rigid behavior in stark contrast to lighter rare-gas clusters. Moreover, as cluster size increases, we identify a clear structural transition from many-body coordination-driven stability to a regime dominated by two-body interactions, reflecting a reshaping of the underlying potential energy landscape.

Figures (3)

• Figure 1: (Top panel) Experimentally observed ion abundances as a function of the number of argon atoms. Due to the top-down fragmentation process, these abundances reflect the relative stability of the clusters. (Bottom panel) Absolute value of theoretical evaporation energies of Ar$_n$H$^+$ clusters. The gray points show the potential energy differences $V_n-V_{n-1}$ computed using the classical optimization technique CSA. The black points show the ground state energy differences $E_n-E_{n-1}$, accounting for the zero-point energy in the vibrational motion of the nuclei, computed using DMC. The green points show the energy differences $\overline{E}_n-\overline{E}_{n-1}$, which also accounts for the thermal distribution, computed using PIMC. The dotted lines show the experimentally-observed magic numbers of Ar$_n$H$^+$ clusters. The clusters Ar$_n$H$^+$ in the blue region have a second shell consisting of pentagonal rings, while the clusters in the magenta region have an icosahedral second shell. This structural change correlates with a transition from many-body effects (blue region) to few-body effects (magenta). The classical structures are shown for $n=7$, 13, 19, 34 and 55; from left to right in the plot.
• Figure 2: Theoretical evaporation energies of Ar$_n$H$^+$ clusters. The black points show the ground state energy differences $E_n-E_{n-1}$, accounting for the zero-point energy in the vibrational motion of the nuclei, computed using DMC, including the 3B and 4B terms. The red points are for a DMC calculation including only pair-wise interaction potentials.
• Figure 3: Ar-H$^+$ distance distributions obtained from the classical configurations used to initiate the QM simulations (black) and by means of the PIMC calculation (red) for the Ar$_{19}$H$^+$ (top) and Ar$_{34}$H$^+$ (bottom) clusters. The insets show probability distributions for both clusters.