Abstract: 

First, we discuss an improvement to the self-consistent phonons algorithm (SCP). The SCP method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be
used to estimate its various dynamic and static properties. We combine SCP with ab initio (AI) potential energy evaluation, in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. Next, we discuss studying small para-hydrogen and ortho-deuterium clusters with the diffusion Monte Carlo method. Motivated by fascinating structural properties, as well as emerging numerical challenges, para-Hydrogen clusters have been explored in numerous publications in the past. Despite the enormous computational resources used by a number of groups, involving various methods, no consensus on the clusters’ energetic and structural properties has been established. Most studies reported strong size dependencies, e.g., “magic number” clusters, while strongly disagreeing with each other quantitatively. Only a few studies claimed the lack of size sensitivity. That is, hardly more than a couple of reports could be considered numerically converged and/or physically meaningful. Unlike most of the previous studies, we focus on small size range of Lennard-Jones N=34−39 clusters, for which using Diffusion Monte Carlo (DMC) we attempt to capture the true behavior of the systems accurately. Not only do we demonstrate that the para-hydrogen clusters for the chosen sizes have the ground state wavefunctions strongly delocalized over thousands of structurally identical isomers, but we also vary the quantum delocalization parameter Λ in the effective range between the hydrogen (Λ ∼ 0.28) and deuterium (Λ ∼ 0.20) regimes. We show that for the o-D2 clusters the ground state wavefunctions are strongly localized, yet they are still disordered. In this regime, the system dynamics associated with the DMC method becomes non-ergodic, e.g., the random walkers get trapped in the potential energy minima, where they have been initialized. (It is ergodic for hydrogen clusters.) Consequently we suggest that the structural change induced by decreasing the quantum parameter Λ from p-H2 to o-D2 has the character of a ”liquid-glass” transition.