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.

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.

Assessment of the Effects of Anisotropic Interactions among Hydrogen Molecules and Their Isotopologues: A Diffusion Monte Carlo Investigation of Gas Phase and Adsorbed Clusters.

Despite the fact that the para-hydrogen molecule (p-H2) and its isotopomers (o-D2 and p-T2) are commonly modeled as spherical objects due to the large separation between rotational states, there may be situations (e.g. adsorption in pores and on surfaces) in which such an approximation neglects important degrees of freedom (i.e. the rotational ones) and introduces uncontrolled biases in the predicted properties. To better understand when approximating such molecules as spheres introduces shortcomings in their representation, we employed diffusion Monte Carlo to simulate small/medium-sized molecular aggregates, either isolated in space or experiencing external model potentials, to compute energetic quantities and distribution functions. These were chosen to mimic situations possibly occurring in real systems, in which orientational isotropy is broken. The comparison between isolated clusters with molecules described as rigid rotors with a 4D potential or as spheres interacting via Adiabatic Hindered Rotor models shows that neither energetic nor structural quantities are affected by reducing the systems dimensionality. The orientational degrees of freedom of the rotors remains largely uncoupled from translational ones whatever the molecular mass. The same happens for rotors interacting with a frozen hydrogen molecule in the vicinity of a repulsive surface. Deviating from such behavior are molecular aggregates interacting with potentials mimicking the presence of ionic adsorption sites inside porous materials. Such difference is ascribable to the markedly anisotropic and longer ranged nature of those interactions, both features being relevant in defining the adsorption energy of the molecular species.

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 (Eads) 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 Eads, however, surprisingly indicates that the average kinetic energy (Ekin) and rotation energy (Erotkin) 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 Ekin and Erotkin 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.

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.

Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li(+)(CH3NO2)n (n = 1-20).

Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li(+)(CH3NO2)n (n = 1-20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first "magic number" is identified using the adiabatic solvent dissociation energy, and it marks the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.

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.

Ring polymer dynamics for rigid tops with an improved integrator.

When working in curved spaces, such as those created with the introduction of holonomic constraints, or those generated from the parameters of Lie groups, the presence of a non-uniform metric significantly alters the Ring Polymer Molecular Dynamics from its Cartesian space counterpart. The presence of a nonuniform metric causes difficulties manifested in significant long-time energy drift for the common integrators, which should be absent in a good algorithm. Using a new integrator developed with the aid of the variational principle, we implement a version of Ring Polymer Molecular Dynamics adapted to curved spaces [S. Wolf and E. Curotto, J. Chem. Phys. 137, 014109 (2012)], specifically testing a symmetric ellipsoid of inertia mapped by stereographic projection coordinates. We find that the algorithm conserves the energy without long-term energy drift and converges quadratically in the time step. To test this implementation of Ring Polymer Molecular Dynamics, we compute the position-position autocorrelation function for a rigid ammonia molecule in an external field, for several values of the Trotter number.

Infinite swapping in curved spaces.

We develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys. 135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.

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.

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

We identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusion Monte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)(n)]. We show that the set (DDW)(n) provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)(n) can be solved deterministically. We use the potential energy set (DDW)(n) to explore and identify methods that can enhance the diffusion Monte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ≫ 100 using just 1 × 10(6) moves in classical simulations (DDW)(n). Finally, we prove that smart darting, when incorporated into the regular or the guided diffusion Monte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusion Monte Carlo algorithm.

Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems.

Variational Monte Carlo, diffusion Monte Carlo, and stereographic projection path integral simulations are performed on eight selected species from the (NH(3))(n), (ND(3))(n), (NH(2)D)(n), and (NH(3))(n-1)(ND(3)) clusters. Each monomer is treated as a rigid body with the rotation spaces mapped by the stereographic projection coordinates. We compare the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH(3))(2-5) clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond.

The thermodynamic and ground state properties of the TIP4P water octamer.

Several stochastic simulations of the TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)] water octamer are performed. Use is made of the stereographic projection path integral and the Green's function stereographic projection diffusion Monte Carlo techniques, recently developed in one of our groups. The importance sampling for the diffusion Monte Carlo algorithm is obtained by optimizing a simple wave function using variational Monte Carlo enhanced with parallel tempering to overcome quasiergodicity problems. The quantum heat capacity of the TIP4P octamer contains a pronounced melting peak at 160 K, about 50 K lower than the classical melting peak. The zero point energy of the TIP4P water octamer is 0.0348+/-0.0002 hartree. By characterizing several large samples of configurations visited by both guided and unguided diffusion walks, we determine that both the TIP4P and the SPC [H. J. C. Berendsen, J. P. Postma, W. F. von Gunsteren, and J. Hermans, (Intermolecular Forces, Reidel, 1981). p. 331] octamer have a ground state wave functions predominantly contained within the D(2d) basin of attraction. This result contrasts with the structure of the global minimum for the TIP4P potential, which is an S(4) cube. Comparisons of the thermodynamic and ground-state properties are made with the SPC octamer as well.

Thermodynamic properties of ammonia clusters (NH3)n n = 2-11: comparing classical and quantum simulation results for hydrogen bonded species.

Classical and quantum simulations of ammonia clusters in the dimer through the hendecamer range are performed using the stereographic projection path integral. Employing the most recent polarizable potential to describe intermolecular interactions, energetic and structural data obtained with our simulations provide support for a more fluxional or flexible nature at low temperature of the ammonia dimer, pentamer, and hexamer than in the other investigated species. The octamer and the hendecamer display a relatively strong melting peak in the classical heat capacity and a less intense but significant melting peak in the quantum heat capacity. The latter are shifted to lower temperature (roughly 15 and 40 K lower, respectively) by the quantum effects. The features present in both classical and quantum constant volume heat capacity are interpreted as an indication of melting even in the octamer case, where a large energy gap is present between its global minimum and second most stable species. We develop a first order finite difference algorithm to integrate the geodesic equations in the inertia ellipsoid generated by n rigid nonlinear bodies mapped with stereographic projections. We use the technique to optimize configurations and to explore the potential surface of the hendecamer.

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

A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic projection coordinates used to map its orientation. Methods are developed to compute the classical and quantum Jacobian terms so that the proper infinitely stiff spring constant limit is recovered in the classical limit, and so that the nonconstant nature of the Riemann Cartan curvature scalar is properly accounted in the quantum simulations. The theory is used to investigate the effects of the geometric coupling between the bending and the rotating degrees of freedom for the water monomer in an external field in the 250 to 500 K range. We detect no evidence of geometric coupling between the bending degree of freedom and the orientations.

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates.

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.

Stereographic projection path integral simulations of (HCl)n clusters (n=2-5): evidence of quantum induced melting in small hydrogen bonded networks.

We investigate the quantum thermodynamic properties of small (HCl)(n) clusters using stereographic projection path integral simulations. The HCl stretches are rigid, the orientations are mapped with stereographic projection coordinates, and we make use of the reweighted random series techniques to obtain cubic convergence with respect to the number of path coefficients. Path integral simulations are converged at and above 10 K for the pentamer and above 15 K for the dimer and the trimer. None of the systems display a melting feature in the classical limit. We find an evidence of quantum induced melting between 15 and 45 K.

Structure and energetics of ammonia clusters (NH3)n (n = 3-20) investigated using a rigid-polarizable model derived from ab initio calculations.

An analytical model has been developed to describe the interaction between rigid ammonia molecules including the explicit description of induction. The parameters of the model potential were chosen by fitting high quality ab initio data obtained using second-order Møller-Plesset (MP2) perturbation theory and extended basis sets. The description of polarization effects is introduced by using a noniterative form of the "charge on spring model", the latter accounting for more than 95% of the dipole induction energy and of the increased molecular dipole. Putative global minima for (NH3)n (n = 3-20) have been optimized using this new model, the structure and energetics of the clusters with n = 3-5 being found in good agreement with previous ab initio results including electronic correlation. Results for larger species have been compared with previous structural studies where only nonpolarizable models were employed. Our model predicts larger binding energies for any cluster size than previous analytical surfaces, the results often suggesting a reorganization of the relative energy ranking and a different structure for the global minimum.