A rare event sampling method for diffusion Monte Carlo using smart darting

Electrolyte clusters as hydrogen sponges: diffusion Monte Carlo simulations

We carry out Diffusion Monte Carlo simulations of up to five hydrogen molecules aggregated with two Stockmayer clusters that solvate a single lithium ion. The first one contains six point dipole solvent particles with parameters tuned to emulate nitromethane. The second cluster is a relative large system investigated recently [G. DiEmma, S. Kalette, and E. Curotto, Chem. Phys. Lett. 2019, 725, 80-86]. In both cases we find that the aggregated hydrogen molecules perturb significantly the ground state of the host cluster and form a distorted tetrahedral cage around the Li⁺ ion. The fifth hydrogen molecule is absorbed by the larger Stockmayer cluster while remaining in the proximity of the solvated charge.

Neural mode jump Monte Carlo

Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method that increases convergence in systems composed of many metastable states. This method aims to connect metastable regions directly using generative neural networks in order to propose new configurations in the Markov chain and optimizes the acceptance probability of large jumps between modes in the configuration space. We provide a comprehensive theory as well as a training scheme for the network and demonstrate the method on example systems.

Diffusion Monte Carlo simulations of gas phase and adsorbed D2-(H2)n clusters

We have computed ground state energies and analyzed radial distributions for several gas phase and adsorbed D₂(H₂)_n and HD(H₂)_n clusters. An external model potential designed to mimic ionic adsorption sites inside porous materials is used [M. Mella and E. Curotto, J. Phys. Chem. A 121, 5005 (2017)]. The isotopic substitution lowers the ground state energies by the expected amount based on the mass differences when these are compared with the energies of the pure clusters in the gas phase. A similar impact is found for adsorbed aggregates. The dissociation energy of D₂ from the adsorbed clusters is always much higher than that of H₂ from both pure and doped aggregates. Radial distributions of D₂ and H₂ are compared for both the gas phase and adsorbed species. For the gas phase clusters, two types of hydrogen-hydrogen interactions are considered: one based on the assumption that rotations and translations are adiabatically decoupled and the other based on nonisotropic four-dimensional potential. In the gas phase clusters of sufficiently large size, we find the heavier isotopomer more likely to be near the center of mass. However, there is a considerable overlap among the radial distributions of the two species. For the adsorbed clusters, we invariably find the heavy isotope located closer to the attractive interaction source than H₂, and at the periphery of the aggregate, H₂ molecules being substantially excluded from the interaction with the source. This finding rationalizes the dissociation energy results. For D₂-(H₂)_n clusters with n≥12, such preference leads to the desorption of D₂ from the aggregate, a phenomenon driven by the minimization of the total energy that can be obtained by reducing the confinement of (H₂)₁₂. The same happens for (H₂)₁₃, indicating that such an effect may be quite general and impact on the absorption of quantum species inside porous materials.

Smart darting diffusion Monte Carlo: Applications to lithium ion-Stockmayer clusters

In a recent investigation [K. Roberts et al., J. Chem. Phys. 136, 074104 (2012)], we have shown that, for a sufficiently complex potential, the Diffusion Monte Carlo (DMC) random walk can become quasiergodic, and we have introduced smart darting-like moves to improve the sampling. In this article, we systematically characterize the bias that smart darting moves introduce in the estimate of the ground state energy of a bosonic system. We then test a simple approach to eliminate completely such bias from the results. The approach is applied for the determination of the ground state of lithium ion-n-dipoles clusters in the n = 8-20 range. For these, the smart darting diffusion Monte Carlo simulations find the same ground state energy and mixed-distribution as the traditional approach for n < 14. In larger systems we find that while the ground state energies agree quantitatively with or without smart darting moves, the mixed-distributions can be significantly different. Some evidence is offered to conclude that introducing smart darting-like moves in traditional DMC simulations may produce a more reliable ground state mixed-distribution.

On the convergence of diffusion Monte Carlo in non-Euclidean spaces. I. Free diffusion

We develop a set of diffusion Monte Carlo algorithms for general compactly supported Riemannian manifolds that converge weakly to second order with respect to the time step. The approaches are designed to work for cases that include non-orthogonal coordinate systems, nonuniform metric tensors, manifold boundaries, and multiply connected spaces. The methods do not require specially designed coordinate charts and can in principle work with atlases of charts. Several numerical tests for free diffusion in compactly supported Riemannian manifolds are carried out for spaces relevant to the chemical physics community. These include the circle, the 2-sphere, and the ellipsoid of inertia mapped with traditional angles. In all cases, we observe second order convergence, and in the case of the sphere, we gain insight into the function of the advection term that is generated by the curved nature of the space.