Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Monte Carlo simulations on mesophase formation using dipolar Gay-Berne model

We report the results of a Monte Carlo simulation of polar particles interacting via the Gay-Berne potential combining dipole-dipole interactions. Simulations were carried out on a system of 256 particles with either a zero dipole moment or longitudinal dipole moment located at the centre of the molecule. The system was found to spontaneously form nematic, smectic and crystal phases from an isotropic phase with a random configuration as temperature was decreased, irrespective of values of the dipole moment. The results do not give any indication of a net polarization even in the system with a strong dipole moment (μ* = 2.00). The transition temperature from the isotropic to nematic phase is not sensitive to the value of the dipole moment within the limits of statistical error, while the transition from the nematic to smectic phase depends on the strength of dipole moment. At lower temperatures forming the smectic or the crystal phase, the translational order along the director increases with increasing dipole moment. The dipolar interactions contribute to the long range ordering.     

A nonempirical anisotropic atom-atom model potential for chlorobenzene crystals

A nearly nonempirical, transferable model potential is developed for the chlorobenzene molecules (C6ClnH6-n, n = 1 to 6) with anisotropy in the atom-atom form of both electrostatic and repulsion interactions. The potential is largely derived from the charge densities of the molecules, using a distributed multipole electrostatic model and a transferable dispersion model derived from the molecular polarizabilities. A nonempirical transferable repulsion model is obtained by analyzing the overlap of the charge densities in dimers as a function of orientation and separation and then calibrating this anisotropic atom-atom model against a limited number of intermolecular perturbation theory calculations of the short-range energies. The resulting model potential is a significant improvement over empirical model potentials in reproducing the twelve chlorobenzene crystal structures. Further validation calculations of the lattice energies and rigid-body k = 0 phonon frequencies provide satisfactory agreement with experiment, with the discrepancies being primarily due to approximations in the theoretical methods rather than the model intermolecular potential. The potential is able to give a good account of the three polymorphs of p-dichlorobenzene in a detailed crystal structure prediction study. Thus, by introducing repulsion anisotropy into a transferable potential scheme, it is possible to produce a set of potentials for the chlorobenzenes that can account for their crystal properties in an unprecedentedly realistic fashion.     

Surface tensions of linear and branched alkanes from Monte Carlo simulations using the anisotropic united atom model

The anisotropic united atoms (AUA4) model has been used for linear and branched alkanes to predict the surface tension as a function of temperature by Monte Carlo simulations. Simulations are carried out for n-alkanes ( n-C5, n-C6, n-C7, and n-C10) and for two branched C7 isomers (2,3-dimethylpentane and 2,4-dimethylpentane). Different operational expressions of the surface tension using both the thermodynamic and the mechanical definitions have been applied. The simulated surface tensions with the AUA4 model are found to be consistent within both definitions and in good agreement with experiments.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials

A coarse-grained residue-residue interaction potential derived from a statistical analysis of the Protein Data Bank is used to investigate the coil-to-helix transition for polyalanine. The interaction potentials depend on the radial distance between interaction sites, as well as the relative orientation of the sites. Two types of interaction sites are present in the model: a site representing the amino acid side chain, and a site representing a "virtual backbone," i.e., a site located in the peptide bond which accounts for backbone hydrogen bonding. Two chain lengths are studied and the results for the thermodynamics of the coil-to-helix transition are analyzed in terms of the Zimm-Bragg model. Results agree qualitatively and quantitatively with all-atom Monte Carlo simulations and other reduced-model Monte Carlo simulations.     

Donnan potential of dilute colloidal dispersions: Monte Carlo simulations

Donnan equilibrium between a salt-free colloidal dispersion and an electrolyte solution has been investigated by Monte Carlo simulations. The Donnan potential is directly calculated by considering two compartments separated by a semipermeable membrane. In order to understand the role played by colloid–ion interactions, the influences of colloidal characteristics, including particle size R, intrinsic particle charge Z, counterion valency z_c, and concentration c_p, on Donnan potential Ψ_D and effective charge Z_eff are examined. Our simulations show that the electroneutrality condition is not followed in both compartments and the Donnan potential arises due to the net charge density. The Donnan potential grows by increasing c_p and Z_eff and by decreasing dielectric constant ε_r, i.e., Ψ_DZ_effc_p/ε_r approximately. Note that the effective charge varies with R,Z,c_p,ε_r and z_c as well. When the salt concentration is increased, the net charge density is lowered and thus the Donnan potential decays accordingly. The validity of the classical theory based on the Nernst equation and the electroneutrality assumption is also examined. In general, the simulation results at high-salt condition can be well represented by such mean-field theory.     

Optimization of 89Zr production using Monte Carlo simulations

Zirconium-89 (⁸⁹Zr) can be produced in a cyclotron by focusing the proton beam on an yttrium-89 (⁸⁹Y) foil target. Optimal combination of beam energy and target assembly configuration enables maximum production of ⁸⁹Zr while minimizing the formation of contaminant nuclides such as ⁸⁸Zr and ⁸⁸Y to allow efficient and effective radiopharmaceutical labeling. Accurate modeling of the proton beam and the target is therefore an essential step to assure the best beam and target specification. We used the radiation transport code MCNPX to simulate the transport of protons through the irradiation assembly and the nuclear reaction code TALYS to obtain the production cross sections of various nuclides from proton-⁸⁹Y reactions. Results from simulating the irradiation of 14 mm diameter targets with aluminum (Al) degrader at 19.8 mA for 1 h suggested that the 0.15 mm thick one would produce 227 MBq while the 0.3 mm thick one would produce 413 MBq of ⁸⁹Zr with less than 1 % uncertainty. These results show excellent agreement with experimental work in literature. This work provides the basis for further experimental and theoretical assessments of the use of ⁸⁹Zr as radiopharmaceutical labels.     

Stochastic potential switching algorithm for Monte Carlo simulations of complex systems

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20,000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude.     

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.     

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.     

Monte Carlo simulations of pure liquid substituted benzenes with OPLS potential functions

Intermolecular potential functions have been developed for use in computer simulations of substituted benzenes. Previously reported optimized potentials for liquid simulations (OPLS) for benzene and organic functional groups were merged and tested in Monte Carlo statistical mechanics simulations for the pure liquids of toluene, m-cresol, anisole, aniline, and benzonitrile at 25°C at 1 atm. The merged potential functions yielded acceptable thermodynamic results for the liquids except in the case of aniline, for which the error in the heat of vaporization was 12%. This was remedied by enhancing the polarity of the model to be more consistent with the observed dipole moment of aniline. Overall, the average errors in computed heats of vaporization and densities were then 2 and 1%, respectively. The structures of the liquids were characterized through energy and radial distribution functions. For m-cresol and aniline, the molecules participate in averages of 1.6 and 1.4 hydrogen bonds, respectively. Condensed phase effects on the torsional energies for anisole, m-cresol, and aniline were found to be small; m-cresol has a slightly enhanced tendency to be nonplanar in the liquid than in the gas phase, while anisole shows the opposite pattern. © 1993 John Wiley & Sons, Inc.     

Monte Carlo simulations of fluids whose particles interact with a logarithmic potential

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of sigma, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, phi(r)= -epsilon ln(fr), where epsilon sets the energy scale and fr=1-(sigma/r)m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as approximately -ln(r/sigma-1) in the r-->sigma limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r-->sigma limit at reduced temperatures greater than approximately 5. The mean square force F2 and infinite frequency shear Ginfinity and bulk Kinfinity moduli are only finite for T*=kBT/epsilon<1. The logarithmic fluid's physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition.     

自优化扩散量子Monte Carlo差值法

提出了自优化扩散量子MonteCarlo差值法,这是一个集优化、扩散和相关取样三项技术于一身的MonteCarlo新算法.这个算法能够在扩散过程中直接计算两个体系之间的能量差,且使计算结果的统计误差达到10^-5hartree数量级,获得相关能达80%以上.应用该方法研究分子势能面,使用"刚性移动"模型,利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性,因而能得到准确的能量差值和分子势能面.另外,我们还首创了"平衡后留样"技术,可节省50%以上的计算量.该算法还可应用于分子光谱、化学反应能量变化值等领域的研究.     

表面扩散的Monte Carlo初探

利用ＭｏｎｔｅＣａｒｌｏ方法模拟了理想表面和分形表面上的扩散过程；通过模拟可以发现，表面扩散系数不仅与表面浓度有关，而且还与扩散的时间、表面的几何形貌等有关。在表面覆盖度比较高时，表面扩散系数有一极大值。与理想表面相比，分形表面会使扩散系数减小。     

Rejection-free Monte Carlo scheme for anisotropic particles

We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed.     

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.     

Monte Carlo simulations of the hydration of substituted benzenes with OPLS potential functions

Intermolecular potential functions have been developed for use in computer simulations of substituted benzenes. Previously reported optimized potentials for liquid simulations (OPLS) for benzene and organic functional groups were merged and tested by computing free energies of hydration for toluene, p-xylene, phenol, anisole, benzonitrile, p-cresol, hydroquinone, and p-dicyanobenzene. The calculations featured Monte Carlo simulations at 25°C and 1 atm with statistical perturbation theory. The average difference between the computed results and experimental data for the absolute free energies of hydration is 0.5 kcal/mol. The AM1-SM2 method is also found to perform well in predicting the free energies of hydration for the substituted benzenes. In addition, the Monte Carlo simulations provided details on the hydration of the substituted benzenes, in particular for the solute–water hydrogen bonding. © 1993 John Wiley & Sons, Inc.     

Some formal aspects of using the atom-atom potential model in energy calculations

Institute of Hetero-organic Compounds, Russian Academy of Sciences, Moscow. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 2, pp. 96–102, March-April, 1992.