Diffusion Monte Carlo Simulations Research Articles

Evolution of Structure in CH5+ and Its Deuterated Analogues

Diffusion Monte Carlo simulations are used to investigate the effects of deuteration on the fluxionality of CH(5)(+) or CD(5)(+), using an ab initio potential surface, developed by Jin, Braams, and Bowman [J. Phys. Chem. 2006, 110, 1569]. We find that partial deuteration quenches the fluxional behavior. The spectral consequences are also investigated. We find that, while CH(5)(+) and CD(5)(+) are nearly spherical tops, partial deuteration breaks the rotational symmetry and the mixed isotopologues are generally better characterized as symmetric tops. In addition, we investigate the effects of deuteration on the low-resolution vibrational spectrum and anticipate that signatures of this delocalization will be observable in the vibrational spectrum.

Kinetics of the Nucleation and Growth of Helium Bubbles in bcc Iron

AbstractMicrostructural defects are introduced in materials upon irradiation with energetic particles. These defects can cause degradation of mechanical properties and contribute to material failure. Transmuted helium in irradiated stainless steels exerts deleterious effects on material properties. We have performed kinetic Monte Carlo (kMC) simulations of point defect diffusion and clustering in bcc alpha iron. The model includes helium and vacancy diffusion and spontaneous clustering and dissociation of the point defects from the clusters. We employ the kMC simulations to investigate the time evolution of the point defect configuration leading to defect clustering and bubble formation. The concentration of embryonic point defect clusters is determined as a function of the simulation time.

Diffusion Monte Carlo approaches for investigating the structure and vibrational spectra of fluxional systems

Recent advances in diffusion Monte Carlo (DMC) are reviewed within the context of the vibrational motions of systems that undergo large amplitude motions. Specifically, the authors describe the DMC approach for obtaining the ground state wave function and zero-point energy (ZPE) of the system of interest, as well as extensions to the method for evaluating probability amplitudes, rotational constants, vibrationally excited states and methods for obtaining vibrational spectra. The discussion is framed in terms of the properties of several systems of current experimental and theoretical interest, specifically complexes of neon atoms with OH or SH, , , and . The results of the DMC simulations provide the information necessary to characterize the extent of delocalization of the probability amplitudes, even in the ground vibrational states. Methods for evaluating expectation values and vibrationally excited states are explored, and, when possible, the results are compared with those from other approaches. Finally, the methods for evaluating intensities are described and existing and future challenges for the approach are reviewed. Contents PAGE 1. Introduction 78 2. Systems 79 2.1. Nen · XH complexes 79 2.2. and 80 2.3. 83 3. Ground state wave functions and energies 84 3.1. Theory 84 3.2. Results 86 4. Obtaining properties from DMC 89 4.1. Averaging by Pair Counting (AVPC) 89 4.2. Adiabatic DMC 89 4.3. Descendent weighting 91 4.4. Example 1 – Bond lengths in 91 4.5. Example 2 – Bond length distributions for and 91 4.6. Example 3 – Rotational constants 93 5. Excited states 96 5.1. Example 4 – The stretch fundamental in Ar3 99 5.2. Example 5 – The fundamentals in Ne2XH 100 5.3. Example 6 – Fundamental vibrations in and 102 6. Using DMC to interpret spectra 103 7. Summary and future prospects 104 Acknowledgements 105 References 105

Multireference configuration interaction calculations for complexes of positronium and B, C, N, and O atoms

Positronium (Ps) binding energies for complexes of Ps and atoms with open shell electrons, PsX (X=B, C, N, and O), are calculated using the multireference singly and doubly excited configuration interaction (MRSDCI) method. The effectiveness of this method for the complexes is verified. The MRSDCI calculations are carried out with a frozen-core approximation so as to incorporate only the most important valence correlation effects. Many-body correlation effects and contributions from higher angular momentum orbitals are estimated by extrapolation techniques. The resulting Ps binding energies agree well with the results of diffusion Monte Carlo simulations by Bressanini et al. (Phys Rev A 57:1678,1998) and by Jiang and Schrader (J Chem Phys 109:9430,1998). For PsO the Ps binding energy obtained by Jiang and Schrader is about 1.8 times larger than that of Bressanini et al.; the present calculated value is close to that of Jiang and Schrader.

Quantum Monte Carlo Simulation of Overpressurized LiquidHe4

A diffusion Monte Carlo simulation of superfluid 4He at zero temperature and pressures up to 275 bar is presented. Increasing the pressure beyond freezing (approximately 25 bar), the liquid enters the overpressurized phase in a metastable state. In this regime, we report results of the equation of state and the pressure dependence of the static structure factor, the condensate fraction, and the excited-state energy corresponding to the roton. Along this large pressure range, both the condensate fraction and the roton energy decrease but do not become zero. The roton energies obtained are compared with recent experimental data in the overpressurized regime.

Nondispersive Two-Electron Wave Packets in a Helium Atom

We demonstrate the existence of stable nondispersing two-electron wave packets in the helium atom in combined magnetic and circularly polarized microwave fields. These packets follow circular orbits and we show that they can also exist in quantum dots. Classically the two electrons follow trajectories which resemble orbits discovered by Langmuir and which were used in attempts at a Bohr-like quantization of the helium atom. Eigenvalues of a generalized Hessian matrix are computed to investigate the classical stability of these states. Diffusion Monte Carlo simulations demonstrate the quantum stability of these two-electron wave packets in the helium atom and quantum-dot helium with an impurity center.

A Monte Carlo simulation of nutrient diffusion and reaction in immobilized cell systems

In this study a Monte Carlo simulation was used to investigate the effect of cell reactivities and particle diffusivities in the cells and matrix on the diffusion and reaction rate constants in gel-immobilized cell systems with different spatial cell configurations. A variety of conditions were examined ranging from instantaneous to very slow reactions with reaction probabilities equal to or less than one, and diffusivity ratios bigger or smaller than one in a spherical domain. In the case of high reactivity (diffusion-limited), the simulation results indicated a decrease in the reaction rate constants when heterogeneity in the cell distribution was increased. In the case of low reactivity (reaction-limited), however, cell distribution did not significantly affect the reaction rate constants as both homogeneous and heterogeneous cell distributions resulted in similar rate constants. The simulation results also indicated an inverse dependence of the reaction rate constants on the diffusivity ratio in reaction-limited cases.

Predicting atomic dopant solvation in helium clusters: The MgHen case

We present a quantum Monte Carlo study of the solvation and spectroscopic properties of the Mg-doped helium clusters MgHen with n=2–50. Three high-level [MP4, CCSD(T), and CCSDT] MgHe interaction potentials have been used to study the sensitivity of the dopant location on the shape of the pair interaction. Despite the similar MgHe well depth, the pair distribution functions obtained in the diffusion Monte Carlo simulations markedly differ for the three pair potentials, therefore indicating different solubility properties for Mg in Hen. Moreover, we found interesting size effects for the behavior of the Mg impurity. As a sensitive probe of the solvation properties, the Mg excitation spectra have been simulated for various cluster sizes and compared with the available experimental results. The interaction between the excited P1 Mg atom and the He moiety has been approximated using the diatomics-in-molecules method and the two excited Π1 and Σ1 MgHe potentials. The shape of the simulated MgHe50 spectra shows a substantial dependency on the location of the Mg impurity, and hence on the MgHe pair interaction employed. To unravel the dependency of the solvation behavior on the shape of the computed potentials, exact density-functional theory has been adapted to the case of doped Hen and various energy distributions have been computed. The results indicate the shape of the repulsive part of the MgHe potential as an important cause of the different behaviors.

Vacancy-assisted arsenic diffusion and time-dependent clustering effects in silicon

We present results of kinetic lattice Monte Carlo (KLMC) simulations of substitutional arsenic diffusion in silicon mediated by lattice vacancies. Large systems are considered, with 1000 dopant atoms and long-range ab initio interactions, to the 18th nearest lattice neighbor, and the diffusivity of each defect species over time is calculated. The concentration of vacancies is greater than equilibrium concentrations in order to simulate conditions shortly after ion implantation. A previously unreported time dependence in the applicability of the pair diffusion model, even at low temperatures, is demonstrated. Additionally, long-range interactions are shown to be of critical importance in KLMC simulations; when shorter interaction ranges are considered, only clusters composed entirely of vacancies form. An increase in arsenic diffusivity for arsenic concentrations up to ${10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ is observed, along with a decrease in arsenic diffusivity for higher arsenic concentrations, due to the formation of arsenic-dominated clusters. Finally, the effect of vacancy concentration on diffusivity and clustering is studied, and increasing vacancy concentration is found to lead to a greater number of clusters, more defects per cluster, and a greater vacancy fraction within the clusters.

Monte Carlo Simulation of Diffusion with Uniform Sinks and Sources for Vacancies

A new concept of generation and annihilation of vacancies at uniform sinks and sources for vacancies is incorporated into the standard Monte Carlo model for vacancy mediated diffusion. This model enables to treat the vacancy wind as well as the deformation of the specimen and the shift of the Kirkendall plane. The Monte Carlo model is used for the testing of the recent phenomenological theories of diffusion by Darken, Manning and Moleko. The agreement with the self-consistent Moleko theory is excellent. On the other hand the agreement with the classical Darken theory used very often for the explanation of the Kirkendall effect is rather poor.

Monte Carlo simulation of diffusion in a spatially nonhomogeneous medium: A biased random walk on an asymmetrical lattice

Monte Carlo (MC) simulation of diffusion processes has proved to be a powerful and valuable adjunct to deterministic solutions of the diffusion equation. In its simplest one-dimensional implementation, a particle is stepped to left or right, with equal probability, a distance 2 D Δ t where D is the diffusion coefficient and Δ t is the timestep. This gives accurate results if D is constant, but in the case where D is spatially dependent a systematic error occurs, as shown by comparing MC averages with deterministic solutions. Furthermore, this error does not reduce when the timestep Δ t is reduced. We show that the results can be reconciled by altering both the MC stepsize and stepping probability, and give simple formulas for the correction terms that are also applicable in higher dimensions. This supplements our previous work on corrections to the Gaussian-step MC method [J. Comput. Phys. 198 (2004) 65].

Modelling light transport in dry foams by a coarse-grained persistent random walk

A two-dimensional persistence random walk model with two states is considered. In the immobile state, the particle chooses a new direction according to some probability function, while in the mobile state it persists on its direction and performs a ballistic motion. Starting from a master equation, we are able to calculate the diffusion constant for this model. The model was developed to explain Monte Carlo simulations of photon diffusion in two-dimensional dry foams. While it gives the leading term in the diffusion constant D, it fails to reproduce the details in D which depend on the amount of disorder in foams. This might show that diffusing photons probe local structural correlations in foams.

Dielectric matrix and plasmon dispersion in strongly coupled electronic bilayer liquids

We develop a dielectric matrix and analyze plasmon dispersion in strongly coupled charged-particle bilayers in the T = 0 quantum domain. The formulation is based on the classical quasilocalized charge approximation (QLCA) and extends the QLCA formalism into the quantum domain. Its development, which parallels that of the two-dimensional companion paper [Phys. Rev. E 70, 026406 (2004)] by three of the authors, generalizes the single-layer scalar formalism therein to a bilayer matrix formalism. Using pair correlation function data generated from diffusion Monte Carlo simulations, we calculate the dispersion of the in-phase and out-of-phase plasmon modes over a wide range of high- r(s) values and layer separations. The out-of-phase spectrum exhibits an exchange-correlation induced long-wavelength energy gap in contrast to earlier predictions of acoustic dispersion softened by exchange and correlations. The energy gap is similar to what has been previously predicted for classical charged-particle bilayers and subsequently confirmed by recent molecular dynamics computer simulations.

Hybrid radiative-transfer–diffusion model for optical tomography

A hybrid radiative-transfer-diffusion model for optical tomography is proposed. The light propagation is modeled with the radiative-transfer equation in the vicinity of the laser sources, and the diffusion approximation is used elsewhere in the domain. The solution of the radiative-transfer equation is used to construct a Dirichlet boundary condition for the diffusion approximation on a fictitious interface within the object. This boundary condition constitutes an approximative distributed source model for the diffusion approximation in the remaining area. The results from the proposed approach are compared with finite-element solutions of the radiative-transfer equation and the diffusion approximation and Monte Carlo simulation. The results show that the method improves the accuracy of the forward model compared with the conventional diffusion model.

Interpolated potential energy surfaces: How accurate do the second derivatives have to be?

A global potential energy surface for the water dimer is constructed using the modified Shepard interpolation scheme of Collins et al. According to this interpolation scheme, the energy at an arbitrary geometry is expressed as a weighted sum of Taylor series expansions from neighboring data points, where the energy and derivative data required are obtained from ab initio calculations. For some ab initio methods, errors are introduced into the second derivative matrix, either by numerical differencing of ab initio energies or numerical integration during the ab initio calculation. Therefore, we test the accuracy required of the second derivative data by truncation of the exact second derivatives to a series of approximate second derivatives, and assess the effect on the results of a quantum diffusion Monte Carlo (QDMC) simulation. Our results show that the calculated zero-point energy and wave function histograms converge to within the numerical uncertainty of the QDMC simulation by inclusion of either three significant figures or three decimal places in the second derivatives.

Statistical mechanical description and Monte Carlo simulation of diffusion in two-component lattice systems

Two different approaches based on linear response theory are considered in this paper. One of them results in quite general and exact expressions for kinetic diffusion coefficients in terms of mean square particle displacements that do not explicitly use any information concerning lattice gas dynamics or interparticle interactions. Relations between kinetic and chemical diffusion coefficients are considered as well. The other approach invokes the lattice gas master equation. It leads to a representation of the kinetic diffusion coefficient as a sum of static and memory-dependent terms. For the former, a closed form expression is derived in the case of thermally activated particle jumps in the model of traps. On this basis, the thermodynamic and memory aspects of multicomponent diffusion are considered. Monte Carlo (MC) simulation and calculation results are discussed. It is shown that memory effects are more pronounced as compared to one-component systems.

Characterizing non-Gaussian diffusion by using generalized diffusion tensors.

Diffusion tensor imaging (DTI) is known to have a limited capability of resolving multiple fiber orientations within one voxel. This is mainly because the probability density function (PDF) for random spin displacement is non-Gaussian in the confining environment of biological tissues and, thus, the modeling of self-diffusion by a second-order tensor breaks down. The statistical property of a non-Gaussian diffusion process is characterized via the higher-order tensor (HOT) coefficients by reconstructing the PDF of the random spin displacement. Those HOT coefficients can be determined by combining a series of complex diffusion-weighted measurements. The signal equation for an MR diffusion experiment was investigated theoretically by generalizing Fick's law to a higher-order partial differential equation (PDE) obtained via Kramers-Moyal expansion. A relationship has been derived between the HOT coefficients of the PDE and the higher-order cumulants of the random spin displacement. Monte-Carlo simulations of diffusion in a restricted environment with different geometrical shapes were performed, and the strengths and weaknesses of both HOT and established diffusion analysis techniques were investigated. The generalized diffusion tensor formalism is capable of accurately resolving the underlying spin displacement for complex geometrical structures, of which neither conventional DTI nor diffusion-weighted imaging at high angular resolution (HARD) is capable. The HOT method helps illuminate some of the restrictions that are characteristic of these other methods. Furthermore, a direct relationship between HOT and q-space is also established.

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former.

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.

Monte Carlo simulation of diffusion in a spatially nonhomogeneous medium: correction to the Gaussian steplength

Monte Carlo (MC) simulation of diffusion processes has proved to be a powerful and valuable adjunct to deterministic solutions of the diffusion equation. For the case of a constant diffusion coefficient it is well established that a MC method using a steplength chosen from the appropriate Gaussian distribution gives accurate results. However, in the case where the diffusion coefficient is spatially dependent, straightforward modification of this method, involving replacing the constant diffusion coefficient by the spatially dependent one in the steplength formula, leads to a systematic error, as shown by comparing MC averages with deterministic solutions. Furthermore, reducing the timestep, and hence the average steplength, does not reduce this error. In this paper, we trace the source of the error and provide a simple and readily calculated correction to the Gaussian steplength that reconciles the MC and deterministic approaches.

Atomistic simulations of the effect of Coulombic interactions on carrier fluctuations in doped silicon

Carrier distributions associated with point charges in silicon are calculated via the quantum perturbation method and used to determine Coulombic interactions between charged defects in the presence of carrier screening. The resulting interactions are used in kinetic lattice Monte Carlo simulations of defect-mediated diffusion to study dopant redistribution and associated variations in carrier concentration. Over a broad range of doping concentrations, Coulombic repulsion between like dopants leads to ordering, resulting in a more uniform electrical potential distribution (and therefore reduced threshold voltage variations) compared with random doping, the standard condition assumed in previous doping fluctuation analyses.