(HCl)2 and (HF)2 in small helium clusters: Quantum solvation of hydrogen-bonded dimers

We present a rigorous theoretical study of the solvation of (HCl)2 and (HF)2 by small (He4) n clusters, with n=1-14 and 30. Pairwise-additive potential-energy surfaces of Hen (HX)2 (X=Cl and F) clusters are constructed from highly accurate four-dimensional (rigid monomer) HX-HX and two-dimensional (rigid monomer) He-HX potentials and a one-dimensional He-He potential. The minimum-energy geometries of these clusters, for n=1-6 in the case of (HCl)2 and n=1-5 for (HF)2, correspond to the He atoms in a ring perpendicular to and bisecting the HX-HX axis. The quantum-mechanical ground-state energies and vibrationally averaged structures of Hen (HCl)2 (n=1-14 and 30) and Hen (HF)2 (n=1-10) clusters are calculated exactly using the diffusion Monte Carlo (DMC) method. In addition, the interchange-tunneling splittings of Hen (HCl)2 clusters with n=1-14 are determined using the fixed-node DMC approach, which was employed by us previously to calculate the tunneling splittings for Hen (HF)2 clusters, n=1-10 [A. Sarsa, Phys. Rev. Lett. 88, 123401 (2002)]. The vibrationally averaged structures of Hen (HX)2 clusters with n=1-6 for (HCl)2 and n=1-5 for (HF)2 have the helium density localized in an effectively one-dimensional ring, or doughnut, perpendicular to and at the midpoint of the HX-HX axis. The rigidity of the solvent ring varies with n and reaches its maximum for the cluster size at which the ring is filled, n=6 and n=5 for (HCl)2 and (HF)2, respectively. Once the equatorial ring is full, the helium density spreads along the HX-HX axis, eventually solvating the entire HX dimer. The interchange-tunneling splitting of Hen (HCl)2 clusters hardly varies at all over the cluster size range considered, n=1-14, and is virtually identical to that of the free HCl dimer. This absence of the solvent effect is in sharp contrast with our earlier results for Hen (HF)2 clusters, which show a ∼30% reduction of the tunneling splitting for n=4. A tentative explanation for this difference is proposed. The implications of our results for the interchange-tunneling dynamics of (HCl)2 in helium nanodroplets are discussed.