A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water

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.

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.

On the convergence of diffusion Monte Carlo in non-Euclidean spaces. II. Diffusion with sources and sinks

We test the second order Milstein method adapted to simulate diffusion in general compact Riemann manifolds on a number of systems characterized by nonconfining potential energy surfaces of increasing complexity. For the 2-sphere and more complex spaces derived from it, we compare the Milstein method with a number of other first and second order approaches. In each case tested, we find evidence that demonstrate the versatility and relative ease of implementation of the Milstein method derived in Part I.

Quantum simulations of the hydrogen molecule on ammonia clusters

Mixed ammonia-hydrogen molecule clusters [H2-(NH3)n] have been studied with the aim of exploring the quantitative importance of the H2 quantum motion in defining their structure and energetics. Minimum energy structures have been obtained employing genetic algorithm-based optimization methods in conjunction with accurate pair potentials for NH3-NH3 and H2-NH3. These include both a full 5D potential and a spherically averaged reduced surface mimicking the presence of a para-H2. All the putative global minima for n ≥ 7 are characterized by H2 being adsorbed onto a rhomboidal ammonia tetramer motif formed by two double donor and two double acceptor ammonia molecules. In a few cases, the choice of specific rhombus seems to be directed by the vicinity of an ammonia ad-molecule. Diffusion Monte Carlo simulations on a subset of the species obtained highlighted important quantum effects in defining the H2 surface distribution, often resulting in populating rhomboidal sites different from the global minimum one, and showing a compelling correlation between local geometrical features and the relative stability of surface H2. Clathrate-like species have also been studied and suggested to be metastable over a broad range of conditions if formed.

Ring polymer dynamics in curved spaces

We formulate an extension of the ring polymer dynamics approach to curved spaces using stereographic projection coordinates. We test the theory by simulating the particle in a ring, T(1), mapped by a stereographic projection using three potentials. Two of these are quadratic, and one is a nonconfining sinusoidal model. We propose a new class of algorithms for the integration of the ring polymer Hamilton equations in curved spaces. These are designed to improve the energy conservation of symplectic integrators based on the split operator approach. For manifolds, the position-position autocorrelation function can be formulated in numerous ways. We find that the position-position autocorrelation function computed from configurations in the Euclidean space R(2) that contains T(1) as a submanifold has the best statistical properties. The agreement with exact results obtained with vector space methods is excellent for all three potentials, for all values of time in the interval simulated, and for a relatively broad range of temperatures.