Showing papers on "Monte Carlo molecular modeling published in 2008"
TL;DR: This work demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem (number of input random variables) in the final estimates, indicating for which problems the sparse grid stochastic collocation method is more efficient than Monte Carlo.
Abstract: This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems as in the Monte Carlo method. If the number of random variables needed to describe the input data is moderately large, full tensor product spaces are computationally expensive to use due to the curse of dimensionality. In this case the sparse grid approach is still expected to be competitive with the classical Monte Carlo method. Therefore, it is of major practical relevance to understand in which situations the sparse grid stochastic collocation method is more efficient than Monte Carlo. This work provides error estimates for the fully discrete solution using $L^q$ norms and analyzes the computational efficiency of the proposed method. In particular, it demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem (number of input random variables) in the final estimates. The derived estimates are then used to compare the method with Monte Carlo, indicating for which problems the former is more efficient than the latter. Computational evidence complements the present theory and shows the effectiveness of the sparse grid stochastic collocation method compared to full tensor and Monte Carlo approaches.
1,257 citations
07 Dec 2008
TL;DR: This paper will briefly describe the nature and relevance of Monte Carlo simulation, the way to perform these simulations and analyze results, and the underlying mathematical techniques required for performing these simulations.
Abstract: This is an introductory tutorial on Monte Carlo simulation, a type of simulation that relies on repeated random sampling and statistical analysis to compute the results. In this paper, we will briefly describe the nature and relevance of Monte Carlo simulation, the way to perform these simulations and analyze results, and the underlying mathematical techniques required for performing these simulations. We will present a few examples from various areas where Monte Carlo simulation is used, and also touch on the current state of software in this area.
467 citations
TL;DR: The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented and a discussion of the estimation of errors in properties calculated by Monte Carlo is given.
Abstract: A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the estimation of errors in properties calculated by Monte Carlo is given.
401 citations
TL;DR: Why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they are used to decide when to stop the simulation are discussed.
Abstract: Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.
320 citations
TL;DR: It is shown how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.
Abstract: Many important physiological processes operate at time and space scales far beyond those accessible to atom-realistic simulations, and yet discrete stochastic rather than continuum methods may best represent finite numbers of molecules interacting in complex cellular spaces. We describe and validate new tools and algorithms developed for a new version of the MCell simulation program (MCell3), which supports generalized Monte Carlo modeling of diffusion and chemical reaction in solution, on surfaces representing membranes, and combinations thereof. A new syntax for describing the spatial directionality of surface reactions is introduced, along with optimizations and algorithms that can substantially reduce computational costs (e.g., event scheduling, variable time and space steps). Examples for simple reactions in simple spaces are validated by comparison to analytic solutions. Thus we show how spatially realistic Monte Carlo simulations of biological systems can be far more cost-effective than often is assumed, and provide a level of accuracy and insight beyond that of continuum methods.
318 citations
TL;DR: Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.
Abstract: A real-time path-integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system coupled to a phonon background until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.
312 citations
TL;DR: In this article, the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles was solved using the diagrammatic Monte Carlo approach.
Abstract: We use the diagrammatic Monte Carlo approach to solve the problem of a single spin-down fermion resonantly interacting with a Fermi gas of spin-up particles Our solution is important for understanding the phase diagram and properties of the crossover from the BCS regime to the Bose-Einstein condensate in the strongly imbalanced regime On the technical side, we develop a generic sign-problem-tolerant method for exact numerical solution of polaron-type models This is a characteristic example of how Monte Carlo methods can be used to simulate divergent sign-alternating diagrammatic series
241 citations
TL;DR: The authors conclude that the predominantly employed method of using pseudo Monte Carlo draws is unlikely to result in leading to truly Bayesian efficient SC designs, and the Gaussian quadrature method is the recommended approximation method for the calculation of Bayesian efficiency of SC designs.
Abstract: This paper compares different types of simulated draws over a range of number of draws in generating Bayesian efficient designs for stated choice (SC) studies. The paper examines how closely pseudo Monte Carlo, quasi Monte Carlo and Gaussian quadrature methods are able to replicate the true levels of Bayesian efficiency for SC designs of various dimensions. The authors conclude that the predominantly employed method of using pseudo Monte Carlo draws is unlikely to result in leading to truly Bayesian efficient SC designs. The quasi Monte Carlo methods analysed here (Halton, Sobol, and Modified Latin Hypercube Sampling) all clearly outperform the pseudo Monte Carlo draws. However, the Gaussian quadrature method examined in this paper, incremental Gaussian quadrature, outperforms all, and is therefore the recommended approximation method for the calculation of Bayesian efficiency of SC designs.
196 citations
TL;DR: In this paper, a continuous-time Monte Carlo method for quantum impurity models is presented, which combines a weak-coupling expansion with an auxiliary-field decomposition.
Abstract: We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean-field theory (DMFT) calculations.
192 citations
TL;DR: In this article, a modified version of the standard SMC technique is proposed for smoothing in general state space models, which relies on forgetting properties of the filtering dynamics and the quality of the estimates produced.
Abstract: This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces degeneracy of the approximation in the path space. However, when performing maximum likelihood estimation via the EM algorithm, all functionals involved are of additive form for a large subclass of models. To cope with the problem in this case, a modification of the standard method (based on a technique proposed by Kitagawa and Sato) is suggested. Our algorithm relies on forgetting properties of the filtering dynamics and the quality of the estimates produced is investigated, both theoretically and via simulations.
183 citations
TL;DR: In this paper, first-principles calculations and Monte Carlo simulation were used to predict ferromagnetic coupling in C doped CdS, resulting from carbon substitution of sulfur.
Abstract: Carbon doping of CdS is studied using first-principles calculations and Monte Carlo simulation. Our calculations predict ferromagnetism in C doped CdS, resulting from carbon substitution of sulfur. A single carbon substitution of sulfur favors a spin-polarized state with a magnetic moment of $1.22{\ensuremath{\mu}}_{B}$. Ferromagnetic coupling is generally observed between these magnetic moments. A transition temperature of $270\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is predicted through Monte Carlo simulation. The ferromagnetism of C doped CdS can be explained by the hole-mediated double exchange mechanism.
TL;DR: In this paper, a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy, which are self-consistently expressed in terms of renormalized particle propagators, is presented.
Abstract: We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy, which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single spin-down fermion resonantly interacting with the Fermi gas of spin-up particles. Though the original series based on bare propagators are sign alternating and divergent, one can still determine the answer behind them by using two strategies (separately or together): (i) using proper series resummation techniques and (ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e., making the entire scheme self-consistent. Our solution is important for understanding the phase diagram and properties of the Bardeen-Cooper-Schrieffer--Bose-Einstein Condensation crossover in the strongly imbalanced regime. On the technical side, we develop a generic sign-problem tolerant method for exact numerical solution of polaron-type models and, possibly, of the interacting many-body Hamiltonians.
TL;DR: An efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo is introduced, supporting the stability of the liquid phase at approximately 300 GPa and approximately 400 K.
Abstract: We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: (i) the forces are computed with finite and small variance, which allows the simulation of a large number of atoms, (ii) the statistical noise corresponding to the forces is used to drive the dynamics at finite temperature by means of an appropriate Langevin dynamics. A first application to the high-density phase of hydrogen is given, supporting the stability of the liquid phase at $\ensuremath{\simeq}300\text{ }\text{ }\mathrm{GPa}$ and $\ensuremath{\simeq}400\text{ }\text{ }\mathrm{K}$.
TL;DR: The adaptive kinetic Monte Carlo method uses minimum-mode following saddle point searches and harmonic transition state theory to model rare-event, state-to-state dynamics in chemical and material systems, focusing on low energy processes and asserting a minimum probability of finding any saddle.
Abstract: The adaptive kinetic Monte Carlo method uses minimum-mode following saddle point searches and harmonic transition state theory to model rare-event, state-to-state dynamics in chemical and material systems. The dynamical events can be complex, involve many atoms, and are not constrained to a grid—relaxing many of the limitations of regular kinetic Monte Carlo. By focusing on low energy processes and asserting a minimum probability of finding any saddle, a confidence level is used to describe the completeness of the calculated event table for each state visited. This confidence level provides a dynamic criterion to decide when sufficient saddle point searches have been completed. The method has been made efficient enough to work with forces and energies from density functional theory calculations. Finding saddle points in parallel reduces the simulation time when many computers are available. Even more important is the recycling of calculated reaction mechanisms from previous states along the dynamics. For systems with localized reactions, the work required to update the event table from state to state does not increase with system size. When the reaction barriers are high with respect to the thermal energy, first-principles simulations over long time scales are possible.
TL;DR: In this paper, the kinetic activation relaxation technique (k-ART) is proposed to identify and evaluate activation barriers using an off-lattice, self-learning, on-the-fly identification and evaluation.
Abstract: Many materials science phenomena, such as growth and self-organisation, are dominated by activated diffusion processes and occur on timescales that are well beyond the reach of standard-molecular dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental timescales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a more flexible approach -- the kinetic activation-relaxation technique (k-ART) -- which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. The validity and power of the method are demonstrated through the study of vacancy diffusion in crystalline silicon.
TL;DR: It is concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.
Abstract: The binding of a ligand to a receptor is often associated with the displacement of a number of bound water molecules. When the binding site is exposed to the bulk region, this process may be sampled adequately by standard unbiased molecular dynamics trajectories. However, when the binding site is deeply buried and the exchange of water molecules with the bulk region may be difficult to sample, the convergence and accuracy in free energy perturbation (FEP) calculations can be severely compromised. These problems are further compounded when a reduced system including only the region surrounding the binding site is simulated. To address these issues, we couple molecular dynamics (MD) with grand canonical Monte Carlo (GCMC) simulations to allow the number of water to fluctuate during an alchemical FEP calculation. The atoms in a spherical inner region around the binding pocket are treated explicitly while the influence of the outer region is approximated using the generalized solvent boundary potential (GSBP). At each step during thermodynamic integration, the number of water in the inner region is equilibrated with GCMC and energy data generated with MD is collected. Free energy calculations on camphor binding to a deeply buried pocket in cytochrome P450cam, which causes about seven water molecules to be expelled, are used to test the method. It concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.
TL;DR: A novel scheme for fully scalable White Monte Carlo is developed and is used as a forward solver in the evaluation of experimental time-resolved spectroscopy, exploring the low albedo regime of time-domain photon migration in a regime where the diffusion approximation of radiative transport theory breaks down.
Abstract: A novel scheme for fully scalable White Monte Carlo (WMC) has been developed and is used as a forward solver in the evaluation of experimental time-resolved spectroscopy. Previously reported scaling problems are avoided by storing detection events individually, turning spatial and temporal binning into post-simulation activities. The approach is suitable for modeling of both interstitial and noninvasive settings (i.e., infinite and semi-infinite geometries). Motivated by an interest in in vivo optical properties of human prostate tissue, we utilize WMC to explore the low albedo regime of time-domain photon migration--a regime where the diffusion approximation of radiative transport theory breaks down, leading to the risk of overestimating both reduced scattering (mu(s)') and absorption (mu(a)). Experimental work supports our findings and establishes the advantages of Monte Carlo-based evaluation.
TL;DR: A kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes, is presented.
Abstract: We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.
01 Jan 2008
TL;DR: In this article, the authors concentrate primarily on world-line methods with loop updates, for spins and also for spin-phonon systems, as well as on the auxiliary field quantum Monte Carlo (QMC) method.
Abstract: In this chapter we will concentrate primarily on world-line methods with loop updates, for spins and also for spin-phonon systems, as well as on the auxiliary field quantum Monte Carlo (QMC) method. Both approaches are based on a path integral formulation of the partition function which maps a d-dimensional quantum system onto a d+1 dimensional classical system. The additional dimension is nothing but the imaginary time. World-line based approaches for quantum spin systems offer a simple realization of the mapping from quantum to classical, and serve as a nice introduction to QMC methods for correlated systems. Auxiliary field QMC methods provide access to fermionic systems both at finite temperature and in the ground state. An important example is the Hirsch-Fye approach that allows for an efficient simulation of impurity models, such as the Kondo and Anderson models, and is widely used in the domain of dynamical mean field theories (DMFT).
TL;DR: Two methods are presented-one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia-Norman-Cannon algorithm.
TL;DR: The CFC move can be combined with other Monte Carlo moves to enable efficient simulation of dense strongly associating fluids that are to this point infeasible to model with standard methods.
Abstract: The continuous fractional component Monte Carlo (CFC MC) move (J Chem Theory Comput, 2007, 3, 1451) is extended to the Gibbs ensemble The algorithm is validated against conventional simulations for the Lennard Jones fluid and a flexible water model The method is also used to compute the vapor-liquid coexistence densities of a model for SO2 The CFC molecule exchange move relies on the gradual insertion and deletion of molecules in conjunction with a self-adapting bias potential As a result, the method does not require the formation of spontaneous voids in the dense fluid phase to be successful, leading to molecule exchange acceptance probabilities that are nearly independent of temperature For example, over 1% of the vapor-liquid molecule exchange moves are successful for water at 280 K, whereas advanced rotational and configurational bias methods have success rates of less than 003% The CFC move can be combined with other Monte Carlo moves to enable efficient simulation of dense strongly associating fluids that are to this point infeasible to model with standard methods © 2008 Wiley Periodicals, Inc J Comput Chem, 2008
TL;DR: In this paper, the Anderson impurity model is extended to the case of fermionic continua with finite bandwidths, and the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.
Abstract: We discuss the transient effects in the Anderson impurity model that occur when two fermionic continua with finite bandwidths are instantaneously coupled to a central level. We present results for the analytically solvable noninteracting resonant-level system first and then consistently extend them to the interacting case using the conventional perturbation theory and recently developed nonequilibrium Monte Carlo simulation schemes. The main goal is to gain an understanding of the full time-dependent nonlinear current-voltage characteristics and the population probability of the central level. We find that, contrary to the steady state, the transient dynamics of the system depends sensitively on the bandwidth of the electrode material.
Proceedings Article•
08 Dec 2008TL;DR: A simple new Monte Carlo algorithm for evaluating probabilities of observations in complex latent variable models, such as Deep Belief Networks, which is much cheaper than gold-standard annealing-based methods and only slightly more expensive than the cheapest Monte Carlo methods.
Abstract: We present a simple new Monte Carlo algorithm for evaluating probabilities of observations in complex latent variable models, such as Deep Belief Networks. While the method is based on Markov chains, estimates based on short runs are formally unbiased. In expectation, the log probability of a test set will be underestimated, and this could form the basis of a probabilistic bound. The method is much cheaper than gold-standard annealing-based methods and only slightly more expensive than the cheapest Monte Carlo methods. We give examples of the new method substantially improving simple variational bounds at modest extra cost.
TL;DR: Monte Carlo simulations in the constant pressure ensemble are performed and several important properties of the pressure effect are reproduced in a unified way with a microscopic mechanism for the first time.
Abstract: Pressure-induced phase transitions of spin-crossover materials are studied in a microscopic model taking into account the elastic interaction among distortions of lattice due to the difference of the molecular sizes between the high-spin state and the low-spin state. We perform Monte Carlo simulations in the constant pressure ensemble and reproduce several important properties of the pressure effect in a unified way with a microscopic mechanism for the first time. The simulation newly reveals how the temperature dependence of the ordering process changes with the pressure.
TL;DR: In this article, the authors compare the results obtained by the Monte Carlo method for the two examples compared to the corresponding results when applying the Guide to the Expression of Uncertainty in Measurement (GUM).
Abstract: The Guide to the Expression of Uncertainty in Measurement (GUM) is the de facto standard for the evaluation of measurement uncertainty in metrology. Recently, evaluation of measurement uncertainty has been proposed on the basis of probability density functions (PDFs) using a Monte Carlo method. The relation between this PDF approach and the standard method described in the GUM is outlined. The Monte Carlo method required for the numerical calculation of the PDF approach is described and illustrated by its application to two examples. The results obtained by the Monte Carlo method for the two examples are compared to the corresponding results when applying the GUM.
20 Oct 2008
TL;DR: A novel tracking algorithm based on the Wang-Landau Monte Carlo sampling method which efficiently deals with the abrupt motions and efficiently samples the object's states even in a whole state space without loss of time is proposed.
Abstract: We propose a novel tracking algorithm based on the Wang-Landau Monte Carlo sampling method which efficiently deals with the abrupt motions. Abrupt motions could cause conventional tracking methods to fail since they violate the motion smoothness constraint. To address this problem, we introduce the Wang-Landau algorithm that has been recently proposed in statistical physics, and integrate this algorithm into the Markov Chain Monte Carlo based tracking method. Our tracking method alleviates the motion smoothness constraint utilizing both the likelihood term and the density of states term, which is estimated by the Wang-Landau algorithm. The likelihood term helps to improve the accuracy in tracking smooth motions, while the density of states term captures abrupt motions robustly. Experimental results reveal that our approach efficiently samples the object's states even in a whole state space without loss of time. Therefore, it tracks the object of which motion is drastically changing, accurately and robustly.
TL;DR: This paper presents a new approach to propagating the density matrix based on a time stepping procedure arising from a Trotter factorization and combining the forward and backward incremental propagators.
Abstract: This paper presents a new approach to propagating the density matrix based on a time stepping procedure arising from a Trotter factorization and combining the forward and backward incremental propagators. The sums over intermediate states of the discrete quantum subsystem are implemented by a Monte Carlo surface hopping-like procedure, while the integrals over the continuous variables are performed using a linearization in the difference between the forward and backward paths of these variables leading to classical-like equations of motion with forces determined by the quantum subsystem states. The approach is tested on several models and numerical convergence is explored.
TL;DR: In this paper, two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques.
TL;DR: In this article, the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases have been carried out using a Monte Carlo simulation technique.
Abstract: An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.