Pair approximation for polarization interaction: efficient method for Monte Carlo simulations of polarizable fluids

A new method is presented for the Monte Carlo simulations of polarizable models with induced dipole moments. This method updates induced dipole moments on all molecules when a single molecule is moved, without evaluating all pair interactions. Thus, depending on the number of molecules, it is 10–20 times faster than Monte Carlo simulations with full iteration. The efficiency makes it a powerful tool for the study of phase equilibria of polarizable models in grand canonical and Gibbs ensembles.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

Monte Carlo calculations of atoms and molecules

The variational and Green's function Monte Carlo (GFMC) methods can treat many interesting atomic and molecular problems. These methods can give chemical accuracy for up to 10 or so electrons. The various implementations of the GFMC method, including the domain Green's function method and the short-time approximation, are discussed. Results are presented for several representative atoms and molecules.     

Hydrophobic/hydrophilic solvation: inferences from Monte Carlo simulations and experiments

In this study Monte Carlo simulations are used to determine the solvation properties of model hydrophobic (xenon and hard sphere) and hydrophilic (dimethyl ether) solutes in SPC/E water. Various contributions to the experimental solvation entropy, including the solvent reorganization entropy, have been determined. The main conclusion drawn, which is in accord with solubility data, is that poor solubility correlates with poor solute-water interaction. At room temperature, energy dominates the aqueous solubility of both hydrophobic and hydrophilic solutes, rather than entropy. However, at higher temperatures the solubility can pass through a minimum, and then entropy becomes dominant. Another interesting finding is the presence of larger than expected cavities in water. Two different simulation results support this finding. This unexpected hollow structure in water explains why a hard sphere solute is more soluble in water than in a comparable hard sphere or Lennard-Jones solvent. Hydrogen bonding causes water to aggregate into clusters that produce a few large cavities rather than many smaller cavities. The propensity for clustering also explains why water gives the illusion of being a low density liquid. Sufficient theoretical apparatus is developed to connect theoretical solvation properties to those measured by simulation and experiment. Finally, based on gas solubility, an intuitive hydrophobic/hydrophilic scale is developed.     

Discotic molecules in cylindrical nanopores: A Monte Carlo study

We report Monte Carlo simulations of a model discotic molecule embedded in cylindrical pores. We consider a planar anchoring of the molecules on the surface for two different cylinder radii: R ^* = 5 and R ^* = 10 , in units of the molecular diameter. For both radii, we note that the system is progressively structured in concentric shells when decreasing the temperature. With the small radius, we observe continuous transitions from an isotropic to a nematic phase and then to a crystal one. The radius of the pores is sufficiently small to force the crystal to grow along their main axis. However some orientational discrepancies are observed: some samples present a zigzag configuration. With the big radius, the situation is more complex and it is likely that different scenarios are available. The crystals can be built along the main axis of the cylinders, as for the small radius, but also in any other direction. Thus we observe samples with different orientational domains. In the case of crystals oriented along the nanopore axis, we note that only the first 5 shells close to the wall are sensitive to it.     

On the theory of the interatomic interaction potentials at high projectile velocities

The interatomic interaction potential dependence on the projectile velocity v is discussed on the basis of the theory proposed by the author in previous papers. It is shown that experimental results on the energy stopping power dependence for I ionschanneled in the (III) channel of gold crystal, reported by Appleton et al., confirm the theoretical predictions.     

A self-consistent method for the generation of configuration interaction coefficients using variational Monte Carlo

We have developed a new method for calculating configuration interaction coefficients for trial wavefunctions used in quantum Monte Carlo calculations of molecular structure. These numerical calculations can be carried out with optimized Jastrow functions included in the wavefunction. These calculations produce coefficients different from those obtained through methods using analytical integration without the Jastrow functions and lead to more accurate trial wavefunctions. We tested the method on the beryllium atom and found that the VMC energy obtained with improved coefficients (—14.6615 hartrees) was 0.9 millihartrees lower than the energy obtained using coefficients from analytical calculations (—14.6606 hartrees). This energy difference corresponds to about 1% of the correlation energy.     

Monte Carlo simulations of neon and argon using ab initio potentials

Gibbs ensemble Monte Carlo simulations of neon and argon have been performed with pair potentials taken from literature as well as with new ab initio potentials from just above the triple point to close to the critical point. The densities of the coexisting phases, their pair correlation functions, the vapour pressure and the enthalpy and entropy of vaporization have been calculated. The influence of the potential choice and of the addition of the Axilrod-Teller (AT) three-body potential on the above mentioned properties have been investigated. It turns out that an accurate ab initio two-body potential in connection with the AT potential yields very good results for thermodynamic properties of phase equilibria.     

Effect of exchange interaction in ferromagnetic superlattices:A Monte Carlo study

The Monte Carlo simulation is used to investigate the magnetic properties of ferromagnetic superlattices through the Ising model. The reduced critical temperatures of the ferromagnetic superlattices are studied each as a function of layer thickness for different values of exchange interaction. The exchange interaction in each layer within the interface and the crystal field in the unit cell are studied. The magnetic coercive fields and magnetization remnants are obtained for different values of exchange interaction, different values of temperature and crystal field with fixed values of physical parameters.     

Application of the Monte Carlo method to anharmonic force constant calculations: The anharmonic potential functions of some nonlinear symmetrical triatomic molecules

The nonuniqueness of the solution of the quartic anharmonic potential function for some symmetrical nonlinear triatomic molecules is demonstrated using the empirical potential function of Pliva and a Monte Carlo estimation technique. A modification of the method to allow for a varying harmonic force field is introduced. The results obtained indicate that the method might be used as a basis for selection of physically acceptable solutions, with a possible extension to the determination of harmonic potential constants for more complex molecules.     

The ultrasonic activation of non-polar collectors in the flotation of hydrophobic minerals

Based on the results of the authors' own investigations concerning the effect of ultrasound on the flotation of phosphorites and the emulsification of oils, the paper deals with the favourable effect of ultrasound on the activity of non-polar collectors, and their positive influence on the enrichment of hydrophobic minerals is explained.     

蒙特卡罗方法在径迹显微技术中的应用

径迹显微技术(PTA)是研究硼的晶界偏聚的行之有效的方法.本文运用蒙特卡罗方法建立了径迹固体探测器上蚀坑带宽度与晶界区域硼富集带实际宽度之间的对应关系.模拟计算结果表明,蚀坑带宽度受实际富集带宽度和晶界平面与磨面夹角2个因素影响.蚀坑带宽度随晶界硼富集带宽度的增加与晶界面与探测器平面夹角的减小而增加,利用本文程序计算结果,可根据蚀坑带宽度和晶界平面与磨面夹角更准确的获得实际富集带宽度.     

Long-range interactions in Monte Carlo simulation of confined water

We investigate methods for the treatment of long-range interactions in the context of grand canonical Monte Carlo (GCMC) simulations of water adsorption in slit-shaped activated carbon pores. Several approaches, ranging from the simple minimum image convention to the more complex two-dimensional Ewald summations, are implemented and compared with respect to accuracy and speed of computation. The performance of some of these methods in GCMC is found to be significantly different from that in molecular dynamics applications. Of all the methods studied, one proposed by Heyes and van Swol was the most promising, providing the best balance between accuracy and speed. In our application, it was shown to be about 2 times faster than the fastest of the two-dimensional Ewald methods. We expect this conclusion to apply in general to systems that are periodic in two dimensions and finite in the third.     

Investigation of the interatomic interaction and structure in liquid metals by the pseudopotential method

The calculation of the interatomic interaction by the pseudopotential method with different models for the form factors has been considered, and the effect of the kind of screening of the electron gas on the form of the potential has been investigated. The potentials of the pair interaction which were calculated have been used to solve the Bogolyubov-Born-Green and the Percus-Yevick integral equations for the radial distribution function. Questions about the applicability of this method for computing the structure and thermodynamic properties of liquid metals are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 44–49, November, 1979.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.