Efficiency of nested Markov chain Monte Carlo for polarizable potentials and perturbed Hamiltonians

Nested Markov chain Monte Carlo is a rigorous way to enhance sampling of a given energy landscape using an auxiliary, approximate potential energy surface. Its practical efficiency mainly depends on how cheap and how different are the auxiliary potential with respect to the reference system. In this article, a combined efficiency index is proposed and assessed for two important families of energy surfaces. As illustrated for water clusters, many‐body polarizable potentials can be approximated by simplifying the polarization contribution and keeping only the two‐body terms. In small systems, neglecting polarization entirely is also acceptable. When the reference potential energy is obtained from diagonalization of a quantum mechanical Hamiltonian, a first‐order perturbation scheme can be used to estimate the energy difference occuring on a Monte Carlo move. Our results indicate that this perturbation approximation performs well provided that the number of steps between successive diagonalization is adjusted beforehand. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2342–2346, 2010     

Monte Carlo simulation of miscibility of polymer blends with repulsive interactions: effect of chain structure

The effects of the chain structure and the intramolecular interaction energy of an A/B copolymer on the miscibility of the binary blends of the copolymer and homopolymer C have been studied by means of a Monte Carlo simulation. In the system, the interactions between segments A, B and C are more repulsive than those between themselves. In order to study the effect of the chain structure of the A/B copolymer on the miscibility, the alternating, random and block copolymers were introduced in the simulations, respectively. The simulation results show that the miscibility of the binary blends strongly depends on the intramolecular interaction energy () between segments A and B within the A/B copolymers. The higher the repulsive interaction energy, the more miscible the A/B copolymer and homopolymer C are. For the diblock copolymer/homopolymer blends, they tend to form micro phase domains. However, the phase domains become so small that the blend can be considered as a homogeneous phase for the alternating copolymer/homopolymer blends. Furthermore, the investigation of the average end-to-end distance () in different systems indicates that the copolymer chains tend to coil with the decrease of whereas the of the homopolymer chains depends on the chain structure of the copolymers. As for the system containing the alternating or the random copolymers, the homopolymer chains also tend to coil with the decrease of . However, for the systems including the block copolymers, there is a slight difference in the of the homopolymer chains with the variation of .     

Monte Carlo simulation of the structure of mono- and bidisperse polyethylene nanocomposites

The structure of bidisperse polyethylene(PE) nanocomposite mixtures of 50:50(by mole) of long and short chains of C160H322/C80H162 and C160H322/C40H82 filled with spherical nanoparticles were investigated by a coarse-grained, on lattice Monte Carlo method using rotational isomeric state theory for short-range and Lennard-Jones for long-range energetic interactions. Simulations were performed to evaluate the effect of wall-to-wall distance between fillers(D), polymer-filler interaction(w) and polydispersity(number of short chains in the mixture) on the behavior of the long PE chains. The results indicate that long chain conformation statistics remain Gaussian regardless of the effects of confinement, interaction strength and polydispersity. The various long PE subchain structures(bridges, dangling ends, trains, and loops) are influenced strongly by confinement whereas monomer-filler interaction and polydispersity did not have any impact. In addition, the average number of subchain segments per filler in bidisperse PE nanocomposites decreased by about 50% compared to the nanocomposite system with monodisperse PE chains. The presence of short PE chains in the polymer matrix leads to a reduction of the repeat unit density of long PE chains at the interface suggesting that the interface is preferentially populated by short chains.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

Monte Carlo simulation of polymer analogous reaction in confined conditions: effects of ordering

The influence of energetic parameters of the interchain homo- and heterocontacts on a local ordering of Bernoullian copolymers has been studied using Monte Carlo simulations and probabilistic analysis. The results of both methods are in a good agreement. Then simple Monte Carlo procedure was employed to study the ordering in products of a polymeranalogous reaction with accelerating effect of neighboring groups. When the reaction with intra- and interchain acceleration and local ordering proceed simultaneously in confined conditions, the ordering might affect the process so that the formation of certain nano-structures (in particular, not trivial strip-like ones) is possible.     

Monte Carlo simulation on layered polymeric films

Thin films of polymer blends composed of alternating copolymer, diblock copolymer and/or homopolymer are studied using Monte Carlo simulation. A multilayer morphology is observed in the film, that is, the blended polymers assemble into individual domains arranged from interior to the surfaces of the film. The coexisting components residing throughout the neighboring domains in the film make no distinguishable interface between any neighboring domains. By this means, it forms a vertical composition gradient in the polymeric film. Being different from layer-by-layer deposition of polyelectrolyte or hydrogen bonding approach etc., the layered structure in this study is formed by polymer blending in one step. Alternating copolymers are found to be essential components to form vertical composition gradient （layered structure） in thin films.     

Monte Carlo Study of Heteroarm Star Copolymers in Good and Selective Solvents

Lattice Monte Carlo simulations of conformations of hereroarm star copolymers A_nB_n in selective solvents were performed using a special variant of the Siepman and Frenkel algorithm. The effects of solvent quality, the number and lengths of blocks on the collapse of the insoluble block A, segregation of the two types of blocks and the behavior of the soluble blocks B were studied mainly for “hairy” stars containing high numbers of long arms. The simulation shows that insoluble blocks collapse in strongly selective solvents and the gravity centers of soluble and insoluble blocks separate which suggests the possibility of the formation of non‐spherical structures.

Snapshots of star a in a very bad solvent (T = 3.00) for blocks A. There are two different views of the star with a total number of arms f = 16 and number of segments N = 300.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

端点附壁的高分子链形状的Monte Carlo模拟

分别基于简立方格点和四面体格点模型对一端吸附在无限大平面的高分子链（平面接枝高分子链）的形状进行了Ｍｏｎｔｅ Ｃａｒｌｏ模拟,结果表明,接枝高分子链的形状更偏离球形,〈Ｌ＾２１〉：〈Ｌ＾２２〉：〈Ｌ＾２３〉的极限值约为１：２．７５：１２．５,其中〈Ｌ＾２１〉,〈Ｌ＾２２〉和〈Ｌ＾２３〉分别为回转半径张量的本征值Ｌ＾２１,Ｌ＾２２和Ｌ＾２３（Ｌ＾２１〈Ｌ＾２２〈Ｌ＾２３）的统计平均;链长相同时,接枝     

A Monte Carlo simulation of a knotted linear chain system as an elementary network fragment

We present the results of the Monte Carlo simulations of the dynamics of the linear chain system. The chains were constructed on a simple cubic lattice. The simulations were carried out by means of the classical Metropolis sampling method with the excluded volume effect present. No other interactions were introduced into the system (athermal polymer case). The linear chains in the system were constructed in such a way that there were knots at certain positions. Also, some chains were threaded through the knots forming the topological constraints in the system. The system under consideration underwent a series of micromodifications during the simulation run. Then the trajectory was analysed and the dynamics of the system was described by means of the autocorrelation functions. The short-time dynamics enabled us to investigate whether or not the knotted constraints affect the local dynamics of the chains. Also the long-time dynamics of the system can be useful in the characterizations of the dynamical properties of the fragments of the networks.     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

Dynamic Monte Carlo simulation of chain growth polymerization and its concentration effect

Polymerization kinetics and chain configuration are two of lasting hotspots in Polymer Science. As these problems are concerned, computer experiment affords a very useful method besides theoretical and experi-mental investigations. The conventional Monte …     

Reverse Monte Carlo and Voronoi-Delaunay simulation and structure analysis for liquid metals

This paper discusses the applicability of the integrated reverse Monte Carlo and Voronoi-Delaunay approach to local structure analysis and medium-scale structure determination of liquid metals. The advantages of this approach are shown: generation of 3D structural models using experimental diffraction data and subsequent structure determination by atomic coordinate analysis.Original Russian Text Copyright © 2004 by A. S. Roik, V. P. Kazimirov, and V. E. SokolskiiTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 683–691, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

Positron backscattering from an Al target: analytical calculation and Monte Carlo simulation

Positron backscattering coefficients are analytically calculated and numerically simulated for an Al target in the positron energy range 0.50–4 keV and for incident angles between 0° and 80° . The differential elastic scattering cross section has been obtained using the Bentabet and Bouarissa approximation (Phys. Lett. 2006; A 355: 390). Both the analytical and simulated results show good agreement with the experiment and previous theoretical work. Copyright © 2007 John Wiley & Sons, Ltd.     

Monte Carlo simulation of diffusion effects on chain‐extension reactions

The diffusion effects on chain‐extension reactions using carboxyl‐terminated polyamide‐12 as a model reactant with bisoxazolines were investigated by the stochastic Monte Carlo method. Thus, complicated direct modeling and numerical calculations were avoided. The chain‐length dependence and detailed diffusive behavior were discussed in depth. The diffusion effects retarded the progress of chain‐extension reactions and led to lower coupling efficiency. The simulated results indicated that the diffusion effects could make the final molecular weight distributions wider. In the presence of diffusion and with the progress of the coupling efficiency, peaks in the evolution curves of the weight‐average molecular weight and valleys in the evolution curves of the polydispersity index were observed, respectively, when the coupling efficiency was low enough. These phenomena were different from those without diffusion effects and were analyzed in detail. The critical entanglement chain length had strong effects on the simulated results of the diffusion effects, especially when its value was near the average chain length. The results also showed that the effects of the reactant degradation made the molecular weight distribution of the reaction system wider and weakened the diffusion effects on the coupling reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2902–2911, 2006     

Monte Carlo simulation of the local ordering of water molecules. I. Binary spatial correlations

The pair distribution functions (DFs) of the oxygen and hydrogen atoms over space around one of the water molecules were calculated during Monte Carlo simulation (Metropolis procedure for the NVT ensemble at normal density and 300 K). An analysis of the isosurfaces of the DF_OO and DF_OH constructed around the selected water molecule for several fixed values of local density allowed us to obtain detailed information about the most probable localization of water molecules in the second and third coordination spheres.     

Wavelet-accelerated Monte Carlo sampling of polymer chains

We introduce a new method for coarse-graining polymer chains, based on the wavelet transform, a multiresolution data analysis technique. This method, which assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, reduces the complexity of the problem significantly by dividing the simulation into several stages, each with a small fraction of the number of beads in the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. We show that, with this wavelet-accelerated Monte Carlo method, coarse-grained Gaussian and self-avoiding random walks can reproduce results obtained from atomistic simulations to a high degree of accuracy in orders of magnitude less time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 897–910, 2005