Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

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.

Quest for Inexpensive Hydrogen Isotopic Fractionation: Do We Need 2D Quantum Confining in Porous Materials or Are Rough Surfaces Enough? The Case of Ammonia Nanoclusters

We study the adsorption energetics and quantum properties of the molecular hydrogen isotopes H₂, D₂, and T₂ onto the surface of rigid ammonia nanoclusters with quantum simulations and accurate model potential energy surfaces (PES). A highly efficient diffusion Monte Carlo (DMC) algorithm for rigid rotors allowed us to accurately define zero-point adsorption energies for the three isotopes, as well as the degree of translational and rotational delocalization that each affords on the surface. From the data emerges that the quantum adsorption energy (E_ads) of T₂ can be up to twice the one of H₂ at 0 K, suggesting the possibility of exploiting some form of solid ammonia to selectivity separate hydrogen isotopes at low temperatures (≃20 K). This is discussed by focusing on the structural motif that may be more effective for the task. The analysis of the contributions to E_ads, however, surprisingly indicates that the average kinetic energy (E^kin) and rotation energy (E_rot^kin) of T₂ can also be, respectively, 2 times and 20 times higher than those of H₂; this finding markedly deviates from what is predicted for hydrogen molecules inside carbon nanotubes (CNT) or metallic-organic frameworks (MOF), where E^kin and E_rot^kin is higher for H₂ due to the unavoidable effects of confinement and hindrance to its rotational motion. The rationale for these differences is provided by the geometrical distributions for the rigid rotors, which reveal an increasingly stronger coupling between rotational and translational degrees of freedom upon increasing the isotopic mass. This effect has never been observed before on adsorbing surfaces (e.g., graphite) and is induced by a strongly anisotropic and anharmonic bowl-like potential experienced by the rotors.

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.

Improving the detection sensitivity of chromatography by stochastic resonance

This review aims to provide readers with an overview of various methodologies and approaches used to improve sensitivity through stochastic resonance (SR) methods, with special emphasis on applications to improve the detectability of analytes in chromatographic signals.

Exploring the importance of quantum effects in nucleation: the archetypical Ne(n) case

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne(8) as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability P(s)(b) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%-20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates k(diss) are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomer dissociation energy due to zero point energy effects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for k(diss) seem to follow a common "corresponding states" behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.

Higher order diffusion Monte Carlo propagators for linear rotors as diffusion on a sphere: development and application to O2@He(n)

Exploiting the theoretical treatment of particles diffusing on corrugated surfaces and the isomorphism between the "particle on a sphere" and a linear molecule rotation, a new diffusion kernel is introduced to increase the order of diffusion Monte Carlo (DMC) simulations involving linear rotors. Tests carried out on model systems indicate the superior performances of the new rotational diffusion kernel with respect to the simpler alternatives previously employed. In particular, it is evidenced a second order convergence toward exact results with respect to the time step of dynamical correlation functions, a fact that guarantees an identical order for the diffusion part of the DMC projector. The algorithmic advantages afforded by the latter are discussed, especially with respect to the "a posteriori" and "on the fly" extrapolation schemes. As a first application to the new algorithm, the structure and energetics of O(2)@He(n) (n = 1-40) clusters have been studied. This was done to investigate the possible cause of the quenching of the reaction between O(2) and Mg witnessed upon increasing the size of superfluid He droplets used as a solvent. With the simulations on O(2) indicating a strong localization in the cluster core, the behaviour as a function of n is ascribed to the extremely fluxional comportment of Mg@He(n), which dwells far from the droplet center, albeit being solvated, when n is large.

Snowballs, quantum solvation and coordination: lead ions inside small helium droplets

Ab initio calculations are used to construct an analytical many-body potential for Pb(2+)He(n) and Pb(+)He(n) clusters which accounts for non pairwise additive interactions. The potential surface reproduces the global minima for cluster sizes ranging from n = 1 to n = 16 obtained from explicit ab initio calculations and found in a previous search for ultrahigh coordination numbers. Ground state energies and structures obtained by accurate diffusion quantum Monte Carlo calculations are used to investigate if quantum effects qualitatively affect the formation of coordination shells. For Pb(2+) doped clusters a first solvation shell is closed at n = 12 and gradually softened by additional helium atoms which start to form a distinct second shell only at n = 16. Spin-orbit coupling profoundly influences the structure of Pb(+)He(n) clusters and causes a gradual structural evolution without pronounced solvation shells.

Improved diffusion Monte Carlo for bosonic systems using time-step extrapolation “on the fly”

A diffusion Monte Carlo algorithm employing "on the fly" extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.