Solidification of Small p-H2 Clusters at Zero Temperature

Ground state chemical potential of parahydrogen clusters of size N = 21-40

We report the ground state chemical potential of parahydrogen clusters between N = 21-40 calculated using the Langevin equation Path Integral Ground State method. There has been much debate in the past whether the chemical potential size evolution in this region is jagged (indicating magic number cluster sizes) or if it is smooth (indicating some quantum melting below 1 K). We compare to previous diffusion Monte Carlo and Path Integral Ground State (PIGS) results, including very recent Variational Path Integral Molecular Dynamics (VPIMD) calculations [S. Miura, J. Chem. Phys. 148, 102333 (2018)]. We find that the ground state chemical potential is not a smooth curve and that magic number clusters are present, consistent with VPIMD and PIGS Monte Carlo results.

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.

Assessing the Performance of the Diffusion Monte Carlo Method As Applied to the Water Monomer, Dimer, and Hexamer

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 10(3)). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 10(5) walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

Population size bias in diffusion Monte Carlo

The size of the population of random walkers required to obtain converged estimates in diffusion Monte Carlo (DMC) increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by DMC and path integral ground state (PIGS) techniques. We contend that the bias associated with a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.