HF in clusters of molecular hydrogen: II. Quantum solvation by H2 isotopomers, cluster rigidity, and comparison with CO-doped parahydrogen clusters

We present a comprehensive theoretical study of the quantum solvation of the HF molecule by small clusters of the H2 isotopomers, p-H2, HD, and o-D2, with up to 13 hydrogen solvent molecules. This complements our earlier work on the HF-doped parahydrogen clusters [H. Jiang and Z. Bacic, J. Chem. Phys. 122, 244306 (2005)]. The ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. Detailed information is obtained regarding the size and isotopomer dependences of the energetics, vibrationally averaged structures, and their rigidity. The rigidity of these clusters is investigated further by analyzing the distributions of their principal moments of inertia from the diffusion Monte Carlo simulations. The clusters are found to be rather rigid, especially when compared with the pure parahydrogen clusters of the same size. Extensive comparison is made with the quantum Monte Carlo results for the CO-doped parahydrogen clusters and significant differences are observed in the size evolution of certain properties, notably the chemical potential.     

Path integral ground state study of finite-size systems: application to small (parahydrogen)N (N=2-20) clusters

We use the path integral ground state method to study the energetic and structural properties of small para-H2 clusters of sizes ranging from 2 to 20 molecules. A fourth order formula is used to approximate the short imaginary-time propagator and two interaction potentials are considered. Our results are compared to those of exact basis set calculations and other quantum Monte Carlo methods when available. We find that for all cluster sizes considered, our results show a lower ground state energy than literature values obtained by diffusion Monte Carlo and variational Monte Carlo. For the dimer and trimer, ground state energies are in good agreement with exact results obtained using the discrete variable representation. Structural properties are found to be insensitive to the choice of interaction potential. We explore the use of Pekeris coordinates to analyze the importance of linear arrangement in trimers and for trimers within clusters of larger size.     

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.     

Spatial delocalization in para-H2 clusters

We applied the quantum path integral Monte Carlo method for the study of (para-H)N (N = 5-33) clusters at T = 2 K, exploring static and dynamic order, which originates from the effects of zero-point energy, kinetic energy, and thermal fluctuations in quantum clusters. Information on dynamic structure was inferred from the asymptotic tails of the cage correlation function calculated from the centroid Monte Carlo trajectory. The centroid cage correlation function decays to zero for large clusters (N = 15-33), manifesting the interchange of molecules between different solvation shells, with statistically diminishing back interchange. Further evidence for the floppiness of para-hydrogen clusters emerges from the Monte Carlo evolution of the centroid of a tagged molecule, which exhibits significant changes in the list of its first and second solvation shells due to the interchange of molecules between these shells.     

Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: algorithm and benchmark calculations

A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Electron-ion recombination in dense gaseous and liquid argon: effects due to argon cation clusters allow to explain the experimental data

The role of cation clusters in the bulk electron-ion recombination in dense gaseous and liquid argon is investigated. The size and structure of cation clusters in those systems are determined by a Monte Carlo simulation. Then, the rate constants of electron-ion recombination are calculated by another simulation method that takes into account the presence of cation clusters in the considered systems. A good agreement with experiment for both dense gaseous and liquid argon is obtained.     

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.     

The nature of base stacking: a Monte Carlo study

To elucidate the physical origin of the preference of nucleic acid bases for stacking over hydrogen bonding in water, Monte Carlo simulations were performed starting from Watson?CCrick structures of the adenine?Cthymine, adenine?Curacil and guanine?Ccytosine base pairs, as well as from the Hoogsteen adenine?Cthymine base pair, in clusters comprising 400 and 800 water molecules. The simulations employed a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. All simulations reached stacked structures, confirming that such structures are preferred over the hydrogen-bonded Watson?CCrick and Hoogsteen base pairs. The Monte Carlo simulations show the complete transition from hydrogen-bonded base pairs to stacked structures in the Monte Carlo framework. Analysis of the average energies shows that the preference of stacked over hydrogen-bonded structures is due to the increased water?Cbase interaction in these structures. This is corroborated by the increased number of water?Cbase hydrogen bonds in the stacked structures.     

Melting of palladium clusters – density of states determination by Monte Carlo simulation

The density of states (DOS) has been calculated for the metal clusters Pd₁₃, Pd₅₅ and Pd₁₄₇ using the recently proposed reference system equilibration (RSE) method. The interaction within the clusters was described by a many-body alloy potential. Using this DOS, the caloric curve of Pd₁₃ has been calculated and excellent agreement with canonical Monte Carlo simulations is obtained. For Pd₅₅ and Pd₁₄₇, the solid and one molten isomers have been isolated in order to calculate the DOS for the isomers separately. The melting of the clusters occurs when the DOS for the solid and the molten isomers are equal. Comparison with previous microcanonical Monte Carlo simulations shows that the number of statistically equivalent molten isomers are 1.1×10¹⁸ for Pd₅₅ and 4.1×10⁴¹ for Pd₁₄₇.     

Electronically excited rubidium atom in helium clusters and films. II. Second excited state and absorption spectrum

Following our work on the study of helium droplets and film doped with one electronically excited rubidium atom Rb(?) ((2)P) [M. Leino, A. Viel, and R. E. Zillich, J. Chem. Phys. 129, 184308 (2008)], we focus in this paper on the second excited state. We present theoretical studies of such droplets and films using quantum Monte Carlo approaches. Diffusion and path integral Monte Carlo algorithms combined with a diatomics-in-molecule scheme to model the nonpair additive potential energy surface are used to investigate the energetics and the structure of Rb(?)He(n) clusters. Helium films as a model for the limit of large clusters are also considered. As in our work on the first electronic excited state, our present calculations find stable Rb(?)He(n) clusters. The structures obtained are however different with a He-Rb(?)-He exciplex core to which more helium atoms are weakly attached, preferentially on one end of the core exciplex. The electronic absorption spectrum is also presented for increasing cluster sizes as well as for the film.     

Interdimensional degeneracies in van der Waals clusters and quantum Monte Carlo computation of rovibrational states

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest interdimensional degeneracy in N-1 and N+1 spatial dimensions. We derive this property by mapping the Schrodinger eigenvalue problem onto an eigenvalue equation in which D appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

Temperature measurement from scattering spectra of clusters: theoretical treatment

Scattering spectra from X-ray, electron or neutron diffraction experiments are sufficient to describe the phase behaviour of noble gas clusters and to determine their temperature. Using classical Monte Carlo simulations combined with optimized data analysis and Path Integral Monte Carlo calculations as “idealized experiments” we obtain scattering spectra of Ar- and Ne-clusters. Starting from the classical and quantum mechanical hypervirial theorems we devise a method to estimate the temperature and the caloric curves (which describe the phase behaviour of the noble gas clusters) directly from these scattering spectra using an interatomic potential function as input. As applications we studied for Ar-clusters the effect of different model potentials on the temperature estimate thus contributing to the intricate question of what experimentally is the temperature of an isolated cluster. For Ne-clusters we investigate the differences between classical and quantum mechanical treatment.     

Bosonic helium clusters doped by alkali metal cations: interaction forces and analysis of their most stable structures

Ab initio potentials are computed for alkali metal cationic partners interacting with ⁴He and an overall many-body potential is constructed for each of the ionic dopants in helium clusters. The structures are then obtained via a genetic algorithm approach and results compared with Basin-Hopping Monte Carlo simulations. The classical arrangements are analyzed and quantum effects discussed in comparison with what has been found with Diffusion Monte Carlo calculations. Further corrections to the classical picture by including three-body forces and radial delocalization of the helium adatoms are also considered and their effects analyzed. This work is dedicated to the late Nando Bernardi, an eclectic and gifted scientist and a dear friend whose early departure has left a sad void in our community.     

Colloidal aggregation induced by long range attractions

The structure of colloidal clusters formed by long-range attractive interactions under diluted conditions is studied by means of Monte Carlo simulations. For a not-too-long attraction range, clusters show self-similar internal structure with lower density than that typical for diffusive aggregation. For long-range interactions, low kappa, nonfractal clusters are formed (dense at short scales but open at long ones). The dependence on the volume fraction shows that more-compact clusters are grown the higher the colloidal density for diffusive aggregation and attraction-driven aggregation in the fractal regime. The whole trend is explained in terms of the interpenetration among aggregates. In attraction-driven aggregations, the interpenetration of clusters competes with aggregation in the tips of the clusters, causing low-density clusters.     

Rigid quantum Monte Carlo simulations of condensed molecular matter: water clusters in the n=2-->8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.     

Quantum monte carlo vibrational dynamics in a property-based interaction potential scheme for weakly bound clusters

The typical shallowness of the potential surfaces of weakly bound clusters implies sizable ground-state vibrational excursions in the weak modes, a feature often complicated by considerable anharmonicity. The difficulties of vibrational analysis are exacerbated as the number of weak modes increases with the number of molecules in a cluster. Quantum Monte Carlo (QMC) approaches offer a general suitability to the problem of vibrational dynamics of weakly bound clusters in that they can fully account for anharmonicity and large amplitude motions. We report on the effectiveness and convergence behavior of diffusion quantum Monte Carlo for both energies and the key spectroscopic values of vibrationally averaged rotational constants. QMC involves recurring evaluations of the interaction potential, and we show how property-based, two-and three-body potentials (e.g., those involving intrinsic molecular tensor properties) may be carefully linked to the QMC propagation steps. © 1997 by John Wiley & Sons, Inc.     

MOCASSIN: Metropolis and kinetic Monte Carlo for solid electrolytes

The combination of density functional theory and Monte Carlo simulations is a powerful approach for the atomistic modeling of defect transport in solid electrolytes. The present contribution introduces the MOCASSIN software (Monte Carlo for Solid State Ionics) for kinetic and Metropolis Monte Carlo simulations of crystalline materials. MOCASSIN combines model building, visualization, and simulation, aiming to provide accessible MC for end users. Developed for the investigation of solid electrolytes, MOCASSIN is ideal for screening common variation parameters, such as temperature and doping fraction. The input effort is minimized using space groups for processing symmetry. The graphical interface for model building allows complex model input, including multiple mobile species, multiple migration paths, small polaron hopping, vehicle movements, multiple complex migration mechanisms, and custom interaction clusters. The software is provided free of charge for noncommercial usage.     

Investigation of the formation process of MCs+-molecular ions during sputtering

In secondary ion mass spectrometry, the detection of MCs+ clusters (with M an element of the specimen) under a Cs bombardment is frequently used for the quantification of major elements. Despite some very good results obtained by this method, some problems still remain. In order to gain some more insight into these problems, the formation mechanism of the MCs+ clusters is investigated using a Monte Carlo model. It is shown that the majority of the constituent particles of the formed clusters are initially first or second neighbor atoms at the surface and that the velocity distribution of the MCs+ clusters becomes broader and peaked at higher velocities with increasing surface binding energy of the M atom. In addition, it is demonstrated that the interaction potential between the M and Cs+ particle has no influence on the velocity distribution of the MCs+ clusters. On the other hand, the cluster formation probability, defined as the probability that a sputtered M and Cs+ particle will form a MCs+ cluster, is extremely sensitive to this interaction potential. It is also shown that the cluster formation probability decreases with increasing surface binding energy. Finally, a good correspondence is obtained between the calculated and experimental velocity distributions of MCs+ clusters sputtered from different monoatomic materials. As a consequence, the Monte Carlo model and the discussed results can be validated.