Computer simulation of sedimentation of ionic systems using the Wolf method

We present computer simulation results for 1:1 and 2:1 electrolyte solutions in the presence of a gravitational field, using the Monte Carlo method in the NVT ensemble for the restrictive primitive model. Coulombic interactions were taken into account comparing the Ewald and Wolf methods. Three variations of Ewald summations were considered: the exact method for slab geometries (EW2D), and the three-dimensional (3D) versions with and without a dipolar correction (EW3DC and EW3D, respectively). The equivalent 3D Wolf protocols were applied under the same conditions (WF3DC and WF3D, respectively). The Wolf and Ewald methods agree accurately in the prediction of several thermodynamic and structural properties for these inhomogeneous systems: excess internal energies, isochoric heath capacities, and density and electrostatic potential profiles. The main advantage using the Wolf method is the significant saving in computing time, which is approximately six times faster than EW3D and EW3DC, and sixty times faster than EW2D.     

Efficient algorithm for "on-the-fly" error analysis of local or distributed serially correlated data

We describe the Dynamic Distributable Decorrelation Algorithm (DDDA) which efficiently calculates the true statistical error of an expectation value obtained from serially correlated data "on-the-fly," as the calculation progresses. DDDA is an improvement on the Flyvbjerg-Petersen renormalization group blocking method (Flyvberg and Peterson, J Chem Phys 1989, 91, 461). This "on-the-fly" determination of statistical quantities allows dynamic termination of Monte Carlo calculations once a specified level of convergence is attained. This is highly desirable when the required precision might take days or months to compute, but cannot be accurately estimated prior to the calculation. Furthermore, DDDA allows for a parallel implementation which requires very low communication, O(log(2)N), and can also evaluate the variance of a calculation efficiently "on-the-fly." Quantum Monte Carlo calculations are presented to illustrate "on-the-fly" variance calculations for serial and massively parallel Monte Carlo calculations.     

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.     

Improved diffusion Monte Carlo for bosonic systems using time-step extrapolation "on the fly"

A diffusion Monte Carlo algorithm employing "on the fly" extrapolation with respect to the time step is implemented and demonstrated simulating realistic systems. Significant advantages are obtained when using on the fly extrapolation, leading to reduced systematic and statistical errors. The sound theoretical basis of extrapolation on the fly is discussed and compared to justifications for the a posteriori extrapolation.     

Study of the ST2 model of water close to the liquid-liquid critical point

We perform successive umbrella sampling grand canonical Monte Carlo computer simulations of the original ST2 model of water in the vicinity of the proposed liquid-liquid critical point, at temperatures above and below the critical temperature. Our results support the previous work of Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti [J. Chem. Phys., 2009, 131, 104508], who provided evidence for the existence and location of the critical point for ST2 using the Ewald method to evaluate the long-range forces. Our results therefore demonstrate the robustness of the evidence for critical behavior with respect to the treatment of the electrostatic interactions. In addition, we verify that the liquid is equilibrated at all densities on the Monte Carlo time scale of our simulations, and also that there is no indication of crystal formation during our runs. These findings demonstrate that the processes of liquid-state relaxation and crystal nucleation are well separated in time. Therefore, the bimodal shape of the density of states, and hence the critical point itself, is a purely liquid-state phenomenon that is distinct from the crystal-liquid transition.     

电解质溶液自扩散系数的布朗动力学模拟

采用布朗动力学方法对电解质溶液进行了模拟,在传统布朗动力学的基础上综合考虑了流体力学的影响,并且引入SmartMonteCarlo方法的接受概率,避免了离子不现实的移动和位型重叠,这样不仅可以将模拟过程中的时间步长大幅度提高,而且还可使溶质在相空间的演化过程更接近实际.模拟过程以电解质溶液的原始模型为基础,将溶剂看作连续介质,溶质分子之间的相互作用采用软核加静电的势能函数模型,长程静电力采用Ewald加和的处理方法.模拟得到KCl和NaCl溶液的径向分布函数g+-(r),g++(r)和g--(r),并与文献中HNC计算以及模拟的结果进行比较,使用推广的Green-Kubo公式模拟计算溶液中各种离子的自扩散性质,计算结果与实验数据吻合良好.     

Monte Carlo NPT系综法模拟考察几种水模型

应用NPT系综法模拟考察了五种水的势能模型 .模拟中采用周期边界条件、Metropolis抽样方法 ,并用Ewald方法对水分子间电荷作用进行长程校正 .模拟计算了内能 ,密度 ,压力及恒压热容等性质 .同时 ,还对这五种模型模拟得到的径向分布函数作了分析 .结果与文献及实验测定相比符合较好     

A Parallelised High Performance Monte Carlo Simulation Approach for Complex Polymerisation Kinetics

A novel, parallelised approach to Monte Carlo simulations for the computation of full molecular weight distributions (MWDs) arising from complex polymerisation reactions is presented. The parallel Monte Carlo method constitutes perhaps the most comprehensive route to the simulation of full MWDs of multiple chain length polymer entities and can also provide detailed microstructural information. New fundamental insights have been developed with regard to the Monte Carlo process in at least three key areas: (i) an insufficient system size is demonstrated to create inaccuracies via poor representation of the most improbable events and least numerous species; (ii) advanced algorithmic principles and compiler technology known to computer science have been used to provide speed improvements and (iii) the parallelisability of the algorithm has been explored and excellent scalability demonstrated. At present, the parallel Monte Carlo method presented herein compares very favourably in speed with the latest developments in the h‐p Galerkin method‐based PREDICI software package while providing significantly more detailed microstructural information. It seems viable to fuse parallel Monte Carlo methods with those based on the h‐p Galerkin methods to achieve an optimum of information depths for the modelling of complex macromolecular kinetics and the resulting microstructural information.

     

硝酸钾电解质溶液水化结构的分子动力学模拟

Molecular dynamics simulations were carried out to study the structure of ion clusters and hydration properties of KNO3 solution. The water molecule was treated as a simple-point-charge (SPC) model, and a four-site model for the nitrate ion was adopted. Both the Coulomb and Lennard-Jones interactions between all the charged sites were considered, and the long-range Coulomb electrostatic interaction was treated using Ewald summation techniques. The configuration of ionic pairs, the radial distribution function of the solution, and the effect of solution concentration on ionic hydration were studied in detail. It was found that there are ionic association phenomena in KNO3 solution and that the dimeric, triplet, solvent-separated ion pairs, and other complex clusters can be observed at high ionic concentration condition. As the concentration of solution decreases, the ionic hydration number increases, 5-7 for cation K+ and 3.5-4.7 for anion NO3-, which is in good agreement with former Monte Carlo and time-of-flight neutron diffraction results.     

Assessing group-based cutoffs and the Ewald method for electrostatic interactions in clusters and in saturated,superheated, and supersaturated vapor phases of dipolar molecules

Monte Carlo simulations in the canonical, isobaric-isothermal, grand canonical, and Gibbs ensembles were used to assess whether the computationally expensive Ewald summation method for the computation of the first-order electrostatic energy can be replaced with a simpler truncation approach for accurate simulations of the saturated, superheated, and supersaturated vapor phases of dipolar and hydrogen-bonding molecules. Rotationally averaged hydrogen fluoride dimer and trimer energies, thermophysical properties and aggregation in the superheated vapor phase of hydrogen fluoride, nucleation free energy barriers for water, and the vapor–liquid coexistence properties of hydrogen fluoride and water were investigated over a wide range of state points. We find that for densities not too close to the critical density, results obtained from simulations using a spherical potential truncation based on neutral groups (molecules or fragments) for the Coulomb interactions are statistically identical to those obtained using the Ewald summation method. Use of the simpler spherical truncation results in a significant reduction of the computational effort for simulations employing molecular mechanics force fields and also allows for straightforward implementation of many-body expansion methods to compute the potential energy from electronic structure calculations of subsystems of the entire vapor-phase system.     

Local Monte Carlo for electrostatics in anisotropic and nonperiodic geometries

We present an implementation of a local Monte Carlo algorithm for simulating charged particles in anisotropic and nonperiodic geometries. Specifically, we consider a quasi-two-dimensional periodic slab geometry with an either infinite or finite third dimension. For the infinite case, we show that the method generates accurate electrostatics equivalent to standard two-dimensional Ewald formulas. We then implement constant charge or constant potential (Dirichlet) boundary conditions, which frequently occur in experimental studies of charged complex fluids or polyelectrolytes. As a demonstration of the versatility of the approach, we compute ion density profiles in front of oppositely charged surfaces (the electric double layer) and find excellent agreement with theory in known analytic limits.     

Monte carlo integration with oscillatory integrands: implications for feynman path integration in real time

A new method is described for the Monte Carlo evaluation of integrals of the form

exp[iS(x)] that occur in the Feynman path integral representation of the time evolution operator, exp(−iHt/h). The method is general, strictly Monte Carlo based (and thus applicable to high dimensionality), and has the desirable feature that the stationary phase (i.e. semiclassical) approximation to the integral is obtained in its worst limit. Application to a non-trivial test case (the Airy integral) illustrates these features.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.     

Computer simulation of charged hard spherocylinders

In this work we present a computer simulation study of charged hard spherocylinders of aspect ratio L/sigma=5, using NVT and NPT Monte Carlo methods. Coulombic interactions are handled using the Wolf method [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. Thermodynamic and structural properties are in excellent agreement with the results obtained with the standard Ewald summation method. A partial prediction of the corresponding phase diagram is obtained by studying two isotherms of this system. The stability of the liquid crystalline phases is examined and compared with the phase diagrams of neutral hard spherocylinders and dipolar hard spherocylinders.     

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.     

Super-Monte Carlo: A photon/electron dose calculation algorithm for radiotherapy

Super-Monte Carlo (SMC) is a method of dose calculation for radiotherapy which combines both analytical calculations and Monte Carlo electron transport. Analytical calculations are used where possible, such as the determination of photon interaction density, to decrease computation time. A Monte Carlo method is used for the electron transport in order to obtain high accuracy of results. To further speed computation, Monte Carlo is used once only, to form an electron track kernel (etk). The etk is a dataset containing the lengths and energy deposition of each step of a number of electron tracks. The etk is transported from each incident particle interaction site, from which the dose is calculated. Dose distributions calculated in heterogeneous media show SMC results similar to those of Monte Carlo. For the same statistical uncertainty, SMC takes an order of magnitude less computation time than a full Monte Carlo simulation. SMC has only been implemented for photons and electrons, however the same basic method could be used for the transport of other particles. Current development includes the optimisation of the etks and the code in order to decrease computation time, and also the inclusion of SMC onto a clinical planning system.     

Fast protein structure prediction using Monte Carlo simulations with modal moves

Using normal modes to generate torsion space moves in Monte Carlo simulations of peptides and proteins is not a new idea; nevertheless, despite its power it has not received widespread application. We show that such a "Modal Monte Carlo" approach is an efficient tool for ab initio predictions of small-protein structures. We apply this method to the Trp cage, a 20-residue polypeptide designed to fold rapidly into a structure that includes tertiary contacts, despite its short length. We achieve a high-quality ab initio structure prediction in about 2 orders of magnitude less computation time than state of the art molecular dynamics techniques.     

A version of diffusion Monte Carlo method based on random grids of coherent states. II. Six-dimensional simulation of electronic states of H2

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.     

Biomolecular free energy profiles by a shooting/umbrella sampling protocol, "BOLAS"

We develop an efficient technique for computing free energies corresponding to conformational transitions in complex systems by combining a Monte Carlo ensemble of trajectories generated by the shooting algorithm with umbrella sampling. Motivated by the transition path sampling method, our scheme "BOLAS" (named after a cowboy's lasso) preserves microscopic reversibility and leads to the correct equilibrium distribution. This makes possible computation of free energy profiles along complex reaction coordinates for biomolecular systems with a lower systematic error compared to traditional, force-biased umbrella sampling protocols. We demonstrate the validity of BOLAS for a bistable potential, and illustrate the method's scope with an application to the sugar repuckering transition in a solvated deoxyadenosine molecule.