HF in clusters of molecular hydrogen. I. Size evolution of quantum solvation by parahydrogen molecules

We present a theoretical study of the quantum solvation of the HF molecule by a small number of parahydrogen molecules, having n=1-13 solvent particles. The minimum-energy cluster structures determined for n=1-12 have all of the H2 molecules in the first solvent shell. The first solvent shell closes at n=12 and its geometry is icosahedral, with the HF molecule at the center. The quantum-mechanical ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. The zero-point energy of (p- H2) n HF clusters is unusually large, amounting to 86% of the potential well depth for n>7. The radial probability distribution functions (PDFs) confirm that the first solvent shell is complete for n=12, and that the 13th p- H2 molecule begins to fill the second solvent shell. The p- H2 molecules execute large-amplitude motions and are highly mobile, making the solvent cage exceptionally fluxional. The anisotropy of the solvent, very pronounced for small clusters, decreases rapidly with increasing n, so that for n∼8-9 the solvent environment is practically isotropic. The analysis of the pair angular PDF reveals that for a given n, the parahydrogen solvent density around the HF is modulated in a pattern which clearly reflects the lowest-energy cluster configuration. The rigidity of the solvent clusters displays an interesting size dependence, increasing from n=6 to 9, becoming floppier for n=10, and increasing again up to n=12, as the solvent shell is filled. The rigidity of the solvent cage appears to reach its maximum for n=12, the point at which the first solvent shell is closed.