Parallel Markov chain Monte Carlo simulations

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.     

Visualizing molecular wavefunctions using Monte Carlo methods

Using explicitly correlated wavefunctions and variational Monte Carlo we calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree–Fock wavefunction and then comparing these values with our explicitly correlated values. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Efficient implementation of the Hellmann-Feynman theorem in a diffusion Monte Carlo calculation

Kinetic and potential energies of systems of (4)He atoms in the solid phase are computed at T = 0. Results at two densities of the liquid phase are presented as well. Calculations are performed by the multiweight extension to the diffusion Monte Carlo method that allows the application of the Hellmann-Feynman theorem in a robust and efficient way. This is a general method that can be applied in other situations of interest as well.     

Parallel and distributed computing in problems of supercomputer simulation of molecular liquids by the Monte Carlo method

An effective strategy of molecular Monte Carlo simulation is proposed. The strategy is based on a combination of two key approaches to parallel computing. The advantage of spatial (domain) decomposition is the high scalability of computing algorithms by splitting “big tasks” into several simultaneously solvable subtasks. However, the domain size in this method can be reduced to a certain limit only. Particle decomposition (division of program loops into portions) is, by contrast, very efficient in the study of small and medium size objects, but is poorly scalable and quickly exhausts the computer system memory with increasing size of the model. The combination of the approaches helps neutralize their limitations and create efficient supercomputing programs for the study of molecular models consisting of hundreds of millions of atoms.     

A gradient-directed Monte Carlo approach to molecular design

The recently developed linear combination of atomic potentials (LCAP) approach [M. Wang et al., J. Am. Chem. Soc. 128, 3228 (2006)] allows continuous optimization in a discrete chemical space, and thus is useful in the design of molecules for targeted properties. To address further challenges arising from the rugged, continuous property surfaces in the LCAP approach, we develop a gradient-directed Monte Carlo (GDMC) strategy as an augmentation to the original LCAP optimization method. The GDMC method retains the power of exploring molecular space by utilizing local gradient information computed from the LCAP approach to jump between discrete molecular structures. It also allows random MC moves to overcome barriers between local optima on property surfaces. The combined GDMC-LCAP approach is demonstrated here for optimizing nonlinear optical properties in a class of donor-acceptor substituted benzene and porphyrin frameworks. Specifically, one molecule with four nitrogen atoms in the porphyrin ring was found to have a larger first hyperpolarizability than structures with the conventional porphyrin motif.     

Efficient implementation of periodic boundary conditions in Monte Carlo simulation

Determination of the shortest distances between particles is one of the most time-consuming parts of molecular simulation by the Monte Carlo method. In this work, we demonstrate that the use of signed-integer storage of coordinates in a scaled box allows one to skip multiple conditional statements in realization of periodic boundary conditions in cubic and rectangular boxes, which, in turn, increases the performance. Performance of the improved procedure was tested in NVT Monte Carlo simulations for liquid krypton and water. © 2018 Wiley Periodicals, Inc.     

Hybrid Monte Carlo implementation of the Fourier path integral algorithm

This paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPI-HMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum Lennard-Jones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems.     

A simple Monte Carlo program for simulation of X-ray transport

A Monte Carlo-based program for treatment of photon transport, restricted to photon energies used in medical diagnostics, is developed. Only the photoabsorption and Compton scattering of photons are taken into account, a justifiable assumption for the energies involved. We can simply separate contributions of reflection events with one, two, three, or more successive collisions of X-rays with electrons of the target. This gives us insights and information about photon transport which otherwise would be inaccessible.     

Vectorization of the general Monte Carlo classical trajectory program VENUS

The general chemical dynamics computer program VENUS is used to perform classical trajectory simulations for large polyatomic systems, with many atoms and complicated potential energy functions. To simulate an ensemble of many trajectories requires a large amount of CPU time. Since each trajectory is independent, it is possible to parallel process a large set of trajectories instead of processing the trajectories by the conventional sequential approach. This enhances the vectorizability of the VENUS program, since the integration of Hamilton's equations of motion and the gradient evaluation, which comprise 97.8% of the CPU, can each be parallel processed. In this article, the vectorization and ensuing optimization of VENUS on the CRAY-YMP and IBM-3090 are presented in terms of both global strategies and technical details. A switching algorithm is designed to enhance the vector performance and to minimize the memory storage. A performance of 140 MFLOPS and a vector/scalar execution rate ratio of 10.6 are observed when this new version of VENUS is used to study the association of CH₃ with the H(Ar)₁₂ cluster on the CRAY-YMP.     

Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with the system size as a low power. A QMC approach with auxiliary fields, in principle, allows an exact solution of the Schrodinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few millihartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled cluster with single and double excitations and with noniterative triples [CCSD(T)]. For stretched bonds in H(2)O, our method exhibits a better overall accuracy and a more uniform behavior than CCSD(T).     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Parallelization strategies for molecular simulation using the Monte Carlo algorithm

We describe the development of Metropolis Monte Carlo algorithms for a general network of multiple instruction multiple data (MIMD) parallel processors. The implementation of farm, event, and systolic parallel algorithms on transputer-based computers is detailed and their relative performance discussed. Although the emphasis is on methodology, the application of such parallel algorithms will be important for addressing computational problems such as the determination of free energy differences in complex biologically important molecular systems. © 1993 John Wiley & Sons, Inc.     

Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations

An efficient Monte Carlo (MC) algorithm including concerted rotations is directly compared to molecular dynamics (MD) in all-atom statistical mechanics folding simulations of small polypeptides. The previously reported algorithm "concerted rotations with flexible bond angles" (CRA) has been shown to successfully locate the native state of small polypeptides. In this study, the folding of three small polypeptides (trpzip2/H1/Trp-cage) is investigated using MC and MD, for a combined sampling time of approximately 10(11) MC configurations and 8 micros, respectively. Both methods successfully locate the experimentally determined native states of the three systems, but they do so at different speed, with 2-2.5 times faster folding of the MC runs. The comparison reveals that thermodynamic and dynamic properties can reliably be obtained by both and that results from folding simulations do not depend on the algorithm used. Similar to previous comparisons of MC and MD, it is found that one MD integration step of 2 fs corresponds to one MC scan, revealing the good sampling of MC. The simplicity and efficiency of the MC method will enable its future use in folding studies involving larger systems and the combination with replica exchange algorithms.     

Monte Carlo calculations of the mean squared force in molecular liquids

The mean squared intermolecular force (F²₁) on a molecule in a diatomic liquid has been evaluated by a Monte Carlo calculation at reduced density p^* = 0.8 and reduced temperature 7^* = 0.72. The isotropic intermolecular potential is of Lennard-Jones form; anisotropic multipolar and overlap potentials of various strengths are used. For the largest strengths studied, the anisotropic contribution to (F²₁) is about 50–60% of the isotropic one.     

Size and persistence length of molecular bottle-brushes by Monte Carlo simulations

Single-chain simulations of densely branched comb polymers, or "molecular bottle-brushes" with side-chains attached to every (or every second) backbone monomer, were carried out by off-lattice Monte Carlo technique. A coarse-grained model, described by hard spheres connected by harmonic springs, was employed. Backbone lengths of up to 100 units were considered, and compared with the corresponding linear chains. The backbone molecular size was investigated as a function of its length at fixed arm size, and as a function of the arm size at fixed backbone length. The apparent swelling exponents obtained by a power-law fit were found to be larger than those for the corresponding linear polymers, indicative of stiffening of the comb backbone. The probability distribution function for the backbone end-to-end distance was also investigated for different backbone lengths and arm sizes. Analysis of this function yielded the critical exponents, which revealed an increase in the swelling exponent consistent with values found from the molecular size. The apparent persistence length of the backbone was also determined, and was found to increase with increasing branching density. Finally, the static structure factors of the whole bottle-brushes and of their backbones are discussed, which provides another consistent estimate of the swelling exponents.     

TRAVIS - a free analyzer and visualizer for Monte Carlo and molecular dynamics trajectories

We present TRAVIS ("TRajectory Analyzer and VISualizer"), a free program package for analyzing and visualizing Monte Carlo and molecular dynamics trajectories. The aim of TRAVIS is to collect as many analyses as possible in one program, creating a powerful tool and making it unnecessary to use many different programs for evaluating simulations. This should greatly rationalize and simplify the workflow of analyzing trajectories. TRAVIS is written in C++, open-source freeware and licensed under the terms of the GNU General Public License (GPLv3). It is easy to install (platform independent, no external libraries) and easy to use. In this article, we present some of the algorithms that are implemented in TRAVIS - many of them widely known for a long time, but some of them also to appear in literature for the first time. All shown analyses only require a standard MD trajectory as input data.     

CrystalGrower: a generic computer program for Monte Carlo modelling of crystal growth

A Monte Carlo crystal growth simulation tool, CrystalGrower, is described which is able to simultaneously model both the crystal habit and nanoscopic surface topography of any crystal structure under conditions of variable supersaturation or at equilibrium. This tool has been developed in order to permit the rapid simulation of crystal surface maps generated by scanning probe microscopies in combination with overall crystal habit. As the simulation is based upon a coarse graining at the nanoscopic level features such as crystal rounding at low supersaturation or undersaturation conditions are also faithfully reproduced. CrystalGrower permits the incorporation of screw dislocations with arbitrary Burgers vectors and also the investigation of internal point defects in crystals. The effect of growth modifiers can be addressed by selective poisoning of specific growth sites. The tool is designed for those interested in understanding and controlling the outcome of crystal growth through a deeper comprehension of the key controlling experimental parameters.

Generic in silico methodology – CrystalGrower – for simulating crystal habit and nanoscopic surface topology to determine crystallisation free energies.     

Cassandra: An open source Monte Carlo package for molecular simulation

Cassandra is an open source atomistic Monte Carlo software package that is effective in simulating the thermodynamic properties of fluids and solids. The different features and algorithms used in Cassandra are described, along with implementation details and theoretical underpinnings to various methods used. Benchmark and example calculations are shown, and information on how users can obtain the package and contribute to it are provided. © 2017 Wiley Periodicals, Inc.