Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

O—酰基—α—酮肟光分解反应的Monte Carlo处理

本文首次对光化学反应体系用Monte Carlo方法进行模拟处理。通过5个O-酰基-α-酮肟光分解反应的Monte Carlo模拟,可避免解析解中由于对吸收光强须采用一级近似求解动力学微分方程组,而造成拟合反应在后期产生与实验结果的偏差。     

Quantum Monte Carlo calculations of the potential energy curve of the helium dimer

We report results of two quantum Monte Carlo methods -- variational Monte Carlo and diffusion Monte Carlo -- on the potential energy curve of the helium dimer. In contrast to previous quantum Monte Carlo calculations on this system, we have employed trial wave functions of the Slater-Jastrow form and used the fixed node approximation for the fermion nodal surface. We find both methods to be in excellent agreement with the best theoretical results at short range. In addition, the diffusion Monte Carlo results give very good agreement across the whole potential energy curve, while the Slater-Jastrow wave function fails to bind the dimer at all.     

Monte Carlo simulation of liquid Br2: Test of an effective hamiltoniain

Monte Carlo simulations for the structure of a fluid of molecules interacting with a pair potential having one Lennard- Jones center plus a quadrupole interaction is reported. The numerical experiments are compared with an approximation method previously suggested and with experimental results for the liquid Br₂ structure. This effective pair potential turns out to be unable to reproduce the Br₂ structure while the approximation method is only useful for quadrupole moments less than 1.2 × 10^?40 C m².     

Quantum Monte Carlo for 3d transition-metal atoms

The domain Green's function Monte Carlo method has been used to calculate the ground-state energy of the atoms Sc through Zn. The fixed node approximation with single-configuration explicitly correlated wave functions is used. A comparison with variational Monte Carlo energies is carried out. The quality of the ground-state energies reported here is similar to that achieved for few-electron atoms using similar techniques.     

Chlorine‐Enhanced Surface Mobility of Au(100)

Motivated by experimental studies of two‐dimensional Ostwald ripening on Au(100) electrodes in chlorine‐containing electrolytes, we have studied diffusion processes using density functional theory. We find that chlorine has a propensity to temporary form AuCl complexes, which diffuse significantly faster than gold adatoms. With and without chlorine, the lowest activation energy is found for the exchange mechanism. Chlorine furthermore reduces the activation energy for the detachment from kink sites. Kinetic Monte Carlo simulations were performed on the basis of extensive density functional theory calculations. The island‐decay rate obtained from these Monte Carlo simulations, as well as the decay rate obtained from the theoretical activation energies and frequency factors when inserted into analytical solutions for Ostwald ripening, are in agreement with experimental island‐decay rates in chlorine‐containing electrolytes.     

Quantum-instanton evaluation of the kinetic isotope effects

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H2 --> H2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than approximately 10%.     

Order parameters and molecular shapes of phosphonic acid dialkyl esters in a uniaxial hydrophobic environment. A theoretical study

The conformational behaviour of phosphonic acid dialkyl ester (PAE) molecules in a uniaxial hydrophobic environment was studied using the Monte Carlo method with the well-known Metropolis algorithm. The influence of the surrounding molecules on ordering processes of the intrinsic PAE molecules was taken into account by a molecular field. The intramolecular energy was calculated using 6–12 atom-atom and torsion potential functions. Conformations were analysed using torsion angle distributions, segment and bond order parameters. The order parameters of the C-H bonds are compared with experimental results of²H NMR. Further a general method of determining the effective shape of a molecule is presented. The shape is defined by probability distribution for finding atomic coordinates within volume elements during a Monte Carlo run. Thus the asymmetry of a molecule can be visualized. PAE molecules studied show a positive asymmetry in all cases.     

Cooperative motion in amorphous polymers; application to the study of free-radical migration in solids

A Monte Carlo method has been used for studying the effect of the motion of some submolecular structures on the migration of radical centres and on the free-radical decay and its dependence on density. Motions of crank, crankshaft, kink, and double kink type are considered. A cooperative type of motions is also taken into account. The results show that cooperative motions support diffusion of radical centres and thus also the free-radical decay but, at higher densities, the cooperation of motions is restricted. The density of the system, where the decay of radicals is followed, affects the rate of the decay, its increase causes radical decay retardation. This is in line with the high pressure effect, which also retards the radical decay rate.     

A multi-dimensional microcanonical Monte Carlo study of S0 → T1 intersystem crossing of isocyanic acid

A general formula for the multi-dimensional Monte Carlo microcanonical nonadiabatic rate constant expressed in configuration space is applied to calculate the rate of intersystem crossing (ISC) between the ground (S₀) and first excited triplet (T₁) states for isocyanic acid. One-, two- and three-dimensional potential energy surfaces are constructed by coupled-cluster single-double CCSD calculations, which are used for Monte Carlo sampling. The calculated S₀→T₁ ISC rate is in good agreement with experimental findings, which gives us a reason to believe that the multi-dimensional Monte Carlo microcanonical nonadiabatic rate theory is a very effective method for calculating nonadiabatic transition rate of a polyatomic molecule.     

Interfacial colloidal sedimentation equilibrium. I. Intensity based confocal microscopy

This paper reports confocal microscopy measurements of inhomogeneous colloidal sedimentation equilibrium profiles near planar wall surfaces for conditions when colloid dimensions are comparable to the characteristic gravitational length scale. The intensity based confocal method developed in this work enables real-space measurements of one-dimensional density profiles of Brownian colloids without identifying many single colloid centers in large imaging volumes. Measured sedimentation equilibrium profiles for single-phase interfacial fluids and for coexisting inhomogeneous fluid and solid phases are in agreement with a perturbation theory and Monte Carlo simulations within the local density approximation. Monte Carlo simulated colloid scale density profiles display some minor differences with confocal images in terms of microstructural transitions involving the onset of interfacial crystallization and the precise elevation of the fluid-solid interface. These discrepancies are attributed to polydispersity unaccounted for in the analyses, sensitivity of the perturbation theory to the effective hard sphere size, and the influence of ensemble, system size, and box shape in Monte Carlo simulations involving anisotropic/inhomogeneous solids. Successful demonstration of intensity based confocal microscopy provides a basis for future measurements of three-dimensional colloidal interactions, dynamics, and structure near surfaces.     

Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition-state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low-order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat-capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial (-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.     

Computational methods in coupled electron-ion Monte Carlo simulations.

In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.     

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson-Boltzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.     

Perturbed-chain equation of state for the solid phase

A perturbed chain equation of state for the solid phase has been derived. Although the equation is general with respect to intermolecular potential, we incorporate the Lennard-Jones potential in this work in order to compare results from the model with available Monte Carlo simulation data. Two forms of the radial distribution function for the hard-sphere solid chain reference state are used in the model. First, a theoretically rigorous approach is taken by using a correlation of actual solid-phase Monte Carlo hard-sphere chain data for the radial distribution function. This results in good agreement with the Monte Carlo data only at high density. Second, a simple extended-density approximation was used for the radial distribution function. This second approach was found to work well across the entire density range including the vicinity of the solid-fluid equilibrium.     

A local density functional approximation for the ion distribution near a charged electrode in the restricted primitive model electrolyte

A local HNC/MSA approximation is developed and applied to the 1:1 restricted primitive model electrolyte. Improvement of ion density profiles in front of a charged electrode is achieved by employing ion—ion direct correlation functions from homogeneous systems of non-neutral composition as found locally in the inhomogeneous double layer. This approximation is related to the density functional approach for inhomogeneous fluids. The local HNC/MSA method predicts, at higher surface charges, layering of counterions and charge inversion as seen in Monte Carlo data, a strong increase of the surface potential with charging and a maximum in the double layer capacitance.     

On a class of extended mean spherical approximations

The extended mean spherical approximation of Martina B, and del Rio is solved variationally for the restricted primitive model of 1—1 and 2—2 electrolyte solutions. Thermodynamic properties are calculated and compared to Monte Carlo results for the same model. A modification of the extended mean spherical approximation is presented that is more internally self-consistent and is in better agreement with Monte Carlo data.     

Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.     

Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo

Improvements beyond the primitive approximation in the path integral Monte Carlo method are explored both in a model problem and in real systems. Two different strategies are studied: The Richardson extrapolation on top of the path integral Monte Carlo data and the Takahashi-Imada action. The Richardson extrapolation, mainly combined with the primitive action, always reduces the number-of-beads dependence, helps in determining the approach to the dominant power law behavior, and all without additional computational cost. The Takahashi-Imada action has been tested in two hard-core interacting quantum liquids at low temperature. The results obtained show that the fourth-order behavior near the asymptote is conserved, and that the use of this improved action reduces the computing time with respect to the primitive approximation.     

多维微正则蒙特卡罗方法计算异氰酸S0→T1系间窜跃速率

推导了通用的坐标空间多维蒙特卡罗微正则非绝热速率计算公式,并应用于计算异氰酸基5（S0）到第一激发三态（T1）的系间窜跃（ISC）速率．在CCSD水平上构建了一,二,三维势能面用于蒙特卡罗抽样．计算所得S0→T1 ISC速率与实验符合较好,因此可以预期多维蒙特卡罗微正则非绝热速率理论将成为计算多原子分子非绝热反应速率的有效手段之一．