Quantum Melting and Isotope Effects from Diffusion Monte Carlo Studies of p-H2 Clusters

The Loss of Size Sensitivity in para-Hydrogen Clusters Due to the Strong Quantum Delocalization

para-Hydrogen (pH₂)_N clusters have been the focus of numerous computational studies. Originally motivated by the possibility of observing superfluidity, these studies also revealed rich and complex structural properties of (pH₂)_N. However, their structural analysis was typically limited to attempts to identify "magic number clusters" by computing their ground state energies E_N and the chemical potential μ_N = E_N-E_N-1 as a function of N. This was followed by structural analysis based on an ill-defined radial density profile. Surprisingly, however, there were remarkable discrepancies between the results reported in the literature for cluster sizes beyond approximately N = 25, and this ambiguity remained unsettled until now. In the present paper, we apply the diffusion Monte Carlo method to resolve inconsistencies in cluster sizes within the range (N = 24-28). Here, we try to avoid speculations based on the highly demanding energy calculations whose numerical accuracy harbors ambiguity. Instead, we focus on the direct and unambiguous structural analysis of the ground state wavefunctions, which supports the conclusion that the clusters are structurally the same in the size range considered. That is, there are no magic number clusters at least in the range N = 24-28, contrary to what some of the previous publications have suggested. This lack of size sensitivity of para-hydrogen clusters is a direct consequence of the strong quantum delocalization in these systems.

Magic numbers, quantum delocalization, and orientational disordering in anionic hydrogen and deuterium clusters

The Diffusion Monte Carlo (DMC) method was applied to anionic hydrogen clusters H^-(H₂)_n (n = 1-16, 32) and their deuterated analogs using a polarizable all-atom potential energy surface (PES) developed by Calvo and Yurtsever. For the hydrogen clusters, the binding energy ΔE_n appears to be a smooth function of the cluster size n, thus contradicting the previous claim that n = 12 is a "magic number" cluster. The structures of the low energy minima of the PES for these clusters belong to the icosahedral motif with the H₂ molecules aligned toward the central H^- ion. However, their ground state wavefunctions are highly delocalized and resemble neither the structures of the global nor local minima. Moreover, the strong nuclear quantum effects result in a nearly complete orientational disordering of the H₂ molecules. For the deuterium clusters, the ground state wavefunctions are localized and the D₂ molecules are aligned toward the central D^- ion. However, their structures are still characterized as disordered and, as such, do not display size sensitivity. In addition, DMC simulations were performed on the mixed H^-(H₂)_n(D₂)_p clusters with (n, p) = (6, 6) and (16, 16). Again, in contradiction to the previous claim, we found that the "more quantum" H₂ molecules prefer to reside farther from the central H^- ion than the D₂ molecules.

Isotopic Effects on Intermolecular and Intramolecular Structure and Dynamics in Hydrogen, Deuterium, and Tritium Liquids: Normal Liquid and Weakly and Strongly Cooled Liquids

Differences in properties such as phase-transition temperature and transport coefficients among liquids of different isotopic compositions, hydrogen, deuterium, and tritium, should originate from their differently pronounced nuclear quantum effects (NQEs) rather than from any subtle difference in the electronic interaction potentials. Accurate and efficient determination of structural and dynamical isotopic effects in the quantum liquids still remains as one of the challenging problems in condensed-phase physics. With a recently developed nonempirical real-time molecular dynamics method which describes nonspherical molecules with the NQEs, we computationally realized and investigated dynamical and quantum isotopic effects of not only traditionally studied isotopes, hydrogen, and deuterium but also a lesser known radioisotope, tritium, in broad thermodynamic conditions from normal liquid to weakly and strongly cooled liquids, which have been hindered by rapid crystallization in spite of numerous experimental attempts at supercooling. Reproducing the previously reported experimental isotope dependence on the bond length and vibrational frequencies of hydrogen, deuterium, and tritium liquids, we further demonstrate that distinctive isotope effects appear in their intermolecular and intramolecular structure and dynamics not only at lower temperature but also at higher temperature, which none has so far been able to obtain quantitative results for realistic systems. Rationalization of their physical origins and the obtained physical insights will help future experimental searching and monitoring intermolecular and intramolecular dynamics and structures of these isotopes not only in normal liquid but also in supercooled liquid.