Diffusion Monte Carlo Simulations Research Articles

Deep-inelastic response of liquid helium

We calculate the deep-inelastic response of superfluid ${}^{4}\mathrm{He}$ and normal ${}^{3}\mathrm{He}.$ Following the Monte Carlo scheme of Carraro and Koonin, we represent the final-state effects by sampling the one-dimensional scattering wave function of the recoiling atom in a static background. We perform diffusion Monte Carlo simulations, using optimized trial functions and adopting the fixed node approximation for ${}^{3}\mathrm{He}.$ For ${}^{4}\mathrm{He}$ the agreement with recent high-precision measurements is excellent, whereas in the case of ${}^{3}\mathrm{He}$ a small but not negligible discrepancy with available experimental information exists. Possible biases in the calculation are discussed, but the question remains open. This is not the first instance where some inconsistency is found between theoretical calculations and the analysis of neutron-scattering data for ${}^{3}\mathrm{He}.$ We have also considered two very different fermion wave functions, yielding either a discontinuous or a continuous momentum distribution. They give hardly distinguishable results for the response, ruling out the possibility of detecting the discontinuity by deep-inelastic neutron scattering at the present level of experimental accuracy.

Response to “Comment on ‘Normal, single-file, and dual-mode diffusion of binary adsorbate mixtures in AlPO4-5’ ” [J. Chem. Phys. 109, 5691 (1998)

We present results from molecular dynamics simulations of single CF4 molecules diffusing in AlPO4-5 pores. The single particle diffusivities measured in these simulations are substantially smaller than the diffusivities that can be extrapolated from available experimental data. We also re-examine our previous smart Monte Carlo simulations of the dual-mode diffusion of Ne and CF4 in AlPO4-5. These results provide conclusive evidence that the presence of CF4 greatly reduces the diffusivity of Ne.

Quantum Monte Carlo simulations of Arn–CO2 clusters

Potential-energy functions for CO2–Arn clusters are constructed using the pairwise-additive approximation from the Ar–Ar potential of Aziz [J. Chem. Phys. 99, 4518 (1993)] and three different CO2–Ar potentials which have been reported recently. These are used to find minimum-energy structures and to carry out rigid-body diffusion Monte Carlo simulations of the ground vibrational state for CO2–Arn clusters with n up to 30, as well as the first excited state for n=1. From these results, the CO2 ν3 redshift is estimated. For all values of n, the Ar atoms tend to surround the CO2 molecule. A complete first solvation shell is first found for n=14, and the largest complete first solvation shell is found for n=17. Although the most recent semiempirical CO2–Ar potential function of Hutson et al. [J. Chem. Phys. 105, 9130 (1996)] gives more accurate predictions of spectroscopic properties for n=1 than the best available ab initio potential function [Marshall et al., J. Chem. Phys. 104, 6569 (1996)], both potential functions give quite similar predictions for structures and approximate CO2 ν3 redshifts for larger values of n.

Variational theory of bulk4Hewith shadow wave functions: Ground state and the phonon-maxon-roton spectrum

We apply an efficient optimization scheme to shadow wave functions (SWF's) for the ground state of liquid and solid ${}^{4}\mathrm{He}$. Results improve on previous variational energies in both phases. In the liquid, the gain over a wave function with only pair and triplet correlations increases with density, providing a quantitative estimate of the increasing effect of higher-order correlations. The discrepancy with the exact ground-state energy is nearly constant over a wide range of densities, yielding excellent estimates for the equilibrium, freezing, and melting densities. The optimal SWF's can be represented with high precision by density-independent sets of variational parameters for the liquid and the solid phases. An extensive study of ground-state properties demonstrates the uniformly good quality of the variational description afforded by the optimized SWF's. Based on such an accurate representation of the ground state, and including the correct long-range correlations due to the zero-point motion of phonons, we compute the excitation spectrum and the strength of the single quasiparticle excitation peak. While the use of optimized SWF's confirms the accuracy of previous studies in the maxon-roton region, the proper treatment of long-range correlations allows us to extend to the phonon region the agreement between theory and experiment. We simulate relatively large systems in order to explore the long-wavelength regime in detail. Even down to wave vectors where the excitation energy exhibits a highly linear dispersion, which would suggest a harmonic phonon mode, the kinetic and potential energies of the excitation are far from verifying equipartition. This result is supported by additional diffusion Monte Carlo simulations within the fixed node approximation. We locate the onset of the harmonic regime for the long-wavelength excitations at an extremely small value of the wave vector, $k\ensuremath{\lesssim}0.05 {\mathrm{\AA{}}}^{\ensuremath{-}1}$.

Monte Carlo Analysis of Obstructed Diffusion in Three Dimensions: Application to Molecular Diffusion in Organelles

Molecular transport in the aqueous lumen of organelles involves diffusion in a confined compartment with complex geometry. Monte Carlo simulations of particle diffusion in three dimensions were carried out to evaluate the influence of organelle structure on diffusive transport and to relate experimental photobleaching data to intrinsic diffusion coefficients. Two organelle structures were modeled: a mitochondria-like long closed cylinder containing fixed luminal obstructions of variable number and size, and an endoplasmic reticulum-like network of interconnected cylinders of variable diameter and density. Trajectories were computed in each simulation for >105 particles, generally for >105 time steps. Computed time-dependent concentration profiles agreed quantitatively with analytical solutions of the diffusion equation for simple geometries. For mitochondria-like cylinders, significant slowing of diffusion required large or wide single obstacles, or multiple obstacles. In simulated spot photobleaching experiments, a ∼25% decrease in apparent diffusive transport rate (defined by the time to 75% fluorescence recovery) was found for a single thin transverse obstacle occluding 93% of lumen area, a single 53%-occluding obstacle of width 16 lattice points (8% of cylinder length), 10 equally spaced 53% obstacles alternately occluding opposite halves of the cylinder lumen, or particle binding to walls (with mean residence time=10 time steps). Recovery curve shape with obstacles showed long tails indicating anomalous diffusion. Simulations also demonstrated the utility of measurement of fluorescence depletion at a spot distant from the bleach zone. For a reticulum-like network, particle diffusive transport was mildly reduced from that in unobstructed three-dimensional space. In simulated photobleaching experiments, apparent diffusive transport was decreased by 39–60% in reticular structures in which 90–97% of space was occluded. These computations provide an approach to analyzing photobleaching data in terms of microscopic diffusive properties and support the paradigm that organellar barriers must be quite severe to seriously impede solute diffusion.

Monte Carlo simulation of diffusion and reaction in water radiolysis--a study of reactant 'jump through' and jump distances.

In Monte Carlo simulations of water radiolysis, the diffusion of reactants can be approximated by "jumping" all species randomly, to represent the passage of a short period of time, and then checking their separations. If, at the end of a jump, two reactant species are within a distance equal to the reaction radius for the pair, they are allowed to react in the model. In principle, the possibility exists that two reactants could "jump through" one another and end up with a separation larger than the reaction radius with no reaction being scored. Ignoring this possibility would thus reduce the rate of reaction below that intended by such a model. By making the jump times and jump distances shorter, any error introduced by 'jump through' is made smaller. This paper reports numerical results of a systematic study of 'jump through' in Monte Carlo simulations of water radiolysis. With a nominal jump time of 3 ps, it is found that more than 40% of the reactions of the hydrated electron with itself and of the H atom with itself occur when reactions during 'jump through' are allowed. For all other reactions, for which the effect is smaller, the contributions of 'jump through' lie in the range 1%-16% of the total. Corrections to computed rate constants for two reactions are evaluated for jump times between 0.1 and 30 ps. It is concluded that jump-through corrections are desirable in such models for jump times that exceed about 1 ps or even less. In a separate study, we find that giving all species of a given type the same size jump in a random direction yields results that are indistinguishable from those when the jump sizes are selected from a Gaussian distribution. In this comparison, the constant jump size is taken to be the root-mean-square jump size from the Gaussian distribution.

Extracting adsorbate diffusion dynamics from an STM experiment: a Monte Carlo study of flicker noise

The flicker noise produced by adatoms diffusing underneath a static STM tip has been simulated via a Monte Carlo simulation of surface diffusion. The need to approximate details of the tunnelling process inherent in the use of the autocorrelation function has been avoided by returning to the method of analysis originally proposed by Binnig et al. [Surf. Sci. 169 (1986) L295]. This method of analysis, however, is shown to be valid only at low coverages. A new method of analysis is proposed which allows diffusion activation energies to be extracted from such an experiment at a wide range of coverages, since the error in the analysis scales with the coverage, rather than the coverage squared. The inherent problems associated with adatom-adatom and adatom-tip interactions have also been investigated. In addition, it is shown that an analysis of the hopping probability gives, as expected, direct access to the diffusion constant of the surface diffusion process. An experimental method of measuring this quantity is proposed.

Modeling the concentration dependence of diffusion in zeolites. III. Testing mean field theory for benzene in Na–Y with simulation

We have performed kinetic Monte Carlo (KMC) simulations of benzene tracer diffusion in Na–Y for various loadings and temperatures to test the analytical diffusion theory presented in Paper I of this series. Our theory and simulations assume that benzene molecules jump among SII and W sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. Our diffusion theory is based on a mean field approximation (MFA) which yields Dθ=16kθaθ2, where aθ≅11 Å is the mean intercage jump length and 1/kθ is the mean supercage residence time. KMC simulations of D(θ), kθ, and aθ at 300 and 400 K show that our MFA is essentially exact for loadings that allow SII site vacancies, and that the concentration dependence is controlled by kθ. For higher loadings, the MFA error is independent of temperature, and increases roughly linearly with loading to a maximum value of ca. 25%, resulting from correlated motion. We present an analytical theory for such correlated motion at infinite vacancy dilution, which predicts the corresponding KMC simulated diffusivities to within statistical Monte Carlo error.

Monte Carlo Simulation of Diffusion and Adsorption Processes in Porous Media.

A Monte Carlo method is presented to simulate the diffusion process with adsorption in porous media. The result of Monte Carlo simulation is compared with that of the difference equation method. It is shown that the Monte Carlo method is more efficient than the difference equation method. The effect of configuration of the adsorption particles upon the total concentration of molecules is investigated by the use of the Monte Carlo method. It is found that the configuration of the adsorption particles has an important effect on the diffusion and adsorption processes. Also, the effect of the adsorption rate upon the total concentration is studied.

Lattice Monte Carlo simulations as link between ab-initio calculations and macroscopic behavior of dopants and defects in silicon

In this work, we show that lattice Monte Carlo simulations can be used to span the time and distance scales between underlying atomistic processes and macroscopic diffusion behavior. We use ab- initio calculations of binding energies versus configuration to calculate hopping rates of vacancies for use in lattice Monte Carlo (LMC) simulations of diffusion and aggregation in silicon. The LMC simulations consider the biased nature of vacancy hop frequencies in the neighborhood of dopants, with interactions up to sixth-nearest- neighbor distances included. We use these simulations to investigate the expected macroscopic diffusion behavior, as well as the process by which dopant/defect aggregation occurs. Specific phenomena investigated include collective behavior leading to greatly enhanced diffusivity at high doping levels, the time dependence of effective diffusivity due to the formation of dopant/vacancy clusters, and dopant fluxes in the presence of a vacancy gradient.

The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study

Monte Carlo simulations of transmitter diffusion and its interactions with postsynaptic receptors have been used to study properties of quantal responses at central synapses. Fast synaptic responses characteristic of those recorded at glycinergic junctions on the teleost Mauthner cell (time to peak approximately 0.3-0.4 ms and decay time constant approximately 3-6 ms) served as the initial reference, and smaller contacts with fewer postsynaptic receptors were also modeled. Consistent with experimental findings, diffusion, simulated using a random walk algorithm and assuming a diffusion coefficient of 0.5-1.0 x 10(-5) cm2 s(-1), was sufficiently fast to account for transmitter removal from the synaptic cleft. Transmitter-receptor interactions were modeled as a two-step binding process, with the double-bound state having opened and closed conformations. Addition of a third binding step only slightly decreased response amplitude but significantly slowed both its rising and decay phases. The model allowed us to assess the sources of response variability and the likelihood of postsynaptic saturation as functions of multiple kinetic and spatial parameters. The method of nonstationary fluctuation analysis, typically used to estimate the number of functional channels at a synapse and single channel current, proved unreliable, presumably because the receptors in the postsynaptic matrix are not uniformly exposed to the same profile of transmitter concentration. Thus, the time course of the probability of channel opening most likely varies among receptors. Finally, possible substrates for phenomena of synaptic plasticity, such as long-term potentiation, were explored, including the diameter of the contact zone, defined by the region of pre- and postsynaptic apposition, the number and distribution of the receptors, and the degree of vesicle filling. Surprisingly, response amplitude is quite sensitive to the size of the receptor-free annulus surrounding the receptor cluster, such that expansion of the contact zone could produce an appreciable increase in quantal size, normally attributed to either the presence of more receptors or the release of more transmitter molecules.

Modeling the concentration dependence of diffusion in zeolites. II. Kinetic Monte Carlo simulations of benzene in Na-Y

We have performed kinetic Monte Carlo simulations of benzene diffusion in Na-Y at finite loadings for various temperatures to test the analytical theory presented in Paper I, immediately preceding this paper. Our theory and simulations assume that benzene molecules jump among SII and W sites, located near Na+ ions in 6-rings and in 12-ring windows, respectively. The theory exploits the fact that supercages are identical on average, yielding Dθ=16kθaθ2=κaθ2/6〈τ1〉[1+Keq(1→2)], where kθ is the cage-to-cage rate coefficient, Keq(1→2) is the W→SII equilibrium coefficient, 〈τ1〉 is the mean W site residence time, and κ is the transmission coefficient for cage-to-cage motion. The simulations use fundamental rate coefficients calculated at infinite dilution for consistency with the theory in Paper I. Our theory for kθ, Keq(1→2) and 〈τ1〉 agrees quantitatively with simulation for various temperatures and loadings. The simulated transmission coefficient is nearly 12 for all but the highest loadings, qualitatively validating our mean field approximation. Comparison between our theory and experimental data shows excellent qualitative agreement with tracer zero-length column data, but also shows qualitative disagreement with both pulsed field gradient NMR and frequency response data.

Nonadiabatic wavefunctions as linear expansions of correlated exponentials. A quantum Monte Carlo application to H 2+ and Ps 2

We propose to expand the nonadiabatic solution of the Schrödinger equation as a linear combination of explicity correlated exponentials. A series of trial wavefunctions has been optimized minimizing the variance of the local energy for the H 2 + and dipositronium (Ps 2) molecules in their ground state, without resorting to the Born-Oppenheimer approximation: the calculations have been performed using the variational Monte Carlo method. In a diffusion Monte Carlo simulation a 6-term wavefunction allowed us to compute the exact energy of the Ps 2 system −0.51601 hartree with a variance of 0.00001 hartree.

Modeling orientational randomization in zeolites: A new probe of intracage mobility, diffusion and cation disorder

We have performed kinetic Monte Carlo simulations of benzene orientational randomization (BOR) and diffusion in Na-Y zeolite for various Na(II) occupancies and Na(II) spatial patterns. Full Na(II) occupancy gives BOR rates controlled by intracage motion, whereas half Na(II) occupancy gives BOR rates sensitive to both intracage and intercage motion, but insensitive to particular Na(II) spatial patterns. Alternatively, BOR with one quarter Na(II) occupancy demonstrates qualitative sensitivity to different Na(II) spatial patterns. Calculated diffusion coefficients vary weakly with decreasing Na(II) occupancy until ca. one Na(II) per supercage. Diffusion coefficients and mean square displacements reveal no information about intracage motion, and are insensitive to different spatial patterns of Na(II) cations. Our computational results thus suggest that measuring orientational randomization in zeolites can provide important information regarding intracage motion, diffusion and cation disorder.

Void closure by viscous flow during coalescence of hard latex particles

Steady state fluorescence (SSF) technique was used to study the void closure process during coalescence of hard latex particles. Latex films were prepared by annealing pyrene (Py)-labelled poly(methyl methacrylate) particles above the glass transition temperature. During the annealing processes, the optical clarity of the film increased considerably. Direct fluorescence emission from excited pyrene was monitored as a function of annealing temperature to detect these changes. Scanning electron microscopy in conjunction with Monte Carlo simulations of photon diffusion in latex film were used to interpret the fluorescence results. Void Closure temperature (Tc) and time (tc) were measured at the point at which the fluorescence emission intensity becomes maximum. This was associated with the longest optical path of a photon in latex film. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 651–659, 1997

Void closure by viscous flow during coalescence of hard latex particles

Steady state fluorescence (SSF) technique was used to study the void closure process during coalescence of hard latex particles. Latex films were prepared by annealing pyrene (Py)-labelled poly(methyl methacrylate) particles above the glass transition temperature. During the annealing processes, the optical clarity of the film increased considerably. Direct fluorescence emission from excited pyrene was monitored as a function of annealing temperature to detect these changes. Scanning electron microscopy in conjunction with Monte Carlo simulations of photon diffusion in latex film were used to interpret the fluorescence results. Void Closure temperature (Tc) and time (tc) were measured at the point at which the fluorescence emission intensity becomes maximum. This was associated with the longest optical path of a photon in latex film. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 651–659, 1997

Monte Carlo simulation of Boron diffusion during low energy implantation and high temperature annealing

ABSTRACTWe use a kinetic Monte Carlo model to simulate the implantation of low energy Boron in Silicon, from 0.5 to 1 keV, at high doses, 1015 ions/cm2. The damage produced by each ion is calculated using UT-Marlowe, based on a binary collision approximation. During implantation at room temperature,, silicon self-interstitials, vacancies and boron interstitials are allowed to migrate and interact. The diffusion kinetics of these defects and dopants has been obtained by ab initio calculations as well as Stillinger Weber molecular dynamics. Clustering of both self-interstitials, vacancies and boron atoms is included. We also model the diffusion of the implanted dopants after a high temperature annealing in order to understand the transient enhanced diffusion (TED) phenomenon. We observe two different stages of TED During the first stage vacancies are present in the lattice together with interstitials and the diffusion enhancement is small. The second stage starts after all the vacancies disappear and gives rise to most of the final TED.

The effect of potential obstacles on charge transfer in image sensors

Numerical methods are presented to investigate charge transfer in charge-coupled devices (CCDs) when potential barriers or wells occur. A Monte Carlo simulation of electron thermal diffusion and field-aided drift is used to determine the time scale for charge transfer. The Monte Carlo approach is useful for exploring new problems, but it requires considerable amounts of computer time. A quicker technique, that of the mean first passage time, is introduced. This method reduces the solution of the carrier continuity equation for charge transfer to the evaluation of a double integral that yields the characteristic time /spl tau/ for e/sup -t//spl tau//. This provides the leading or dominant time dependence of the carrier continuity equation's solution. Numerical examples are presented to show how /spl tau/ varies with the size and location of the potential obstacle. The mean first passage time approach permits rapid estimates of the effects of potential obstacles on charge transfer in CCD's. These estimates are in excellent agreement with the results of the Monte Carlo simulations.

Monte Carlo simulation of correlation effects in a random bcc alloy

Abstract Results of high-accuracy Monte Carlo simulations of vacancy and tracer diffusion in a random bcc alloy A-B are reported. The vacancy and tracer correlation factors are calculated using the Einstein equation and the mean square displacements in the absence of driving forces. Additionally, the vacancy correlation factor is calculated from the vacancy drift in the presence of a driving force. The results are compared with the predictions of Manning's random alloy model. Good agreement is observed only for the vacancy correlation factor f v, and the atomic correlation factors f A and f B in the impurity limits. In the range of concentrated alloys the Manning model markedly overestimates f A and f B even for relatively small exchange frequency ratios such as w A/w B = 5. The percolation behaviour of f v and f A when w A ≫ w B is analysed in detail. The percolation threshold and the critical exponents are reasonably consistent with other Monte Carlo simulations. By comparison with the Monte Carlo resul...

Momentum distribution of liquid helium

We have obtained the one--body density matrix and the momentum distribution $n(p)$ of liquid $^4$He at $T=3D0^o$K from Diffusion Monte Carlo (DMC) simulations, using trial functions optimized via the Euler Monte Carlo (EMC) method. We find a condensate fraction smaller than in previous calculations. Though we do not explicitly include long--range correlations in our calculations, we get a momentum distribution at long wavelength which is compatible with the presence of long--range correlations in the exact wave function. We have also studied $^3$He, using fixed--node DMC, with nodes and trial functions provided by the EMC. In particular, we analyze the momentum distribution $n(p)$ with respect to the discontinuity $Z$ as well as the singular behavior, at the Fermi surface. We also show that an approximate factorization of the one-body density matrix $\rho(r)\simeq \rho_0(r)\rho_B(r)$ holds, with $\rho_0(r)$ and $\rho_B(r)$ respectively the density matrix of the ideal Fermi gas and the density matrix of a Bose $^3$He.