Electron affinities with diffusion quantum Monte Carlo for C2 and BO molecules

To verify the performance of the fixed-node diffusion quantum Monte Carlo method in electron affinities calculations, the adiabatic electron affinities of C(2) and BO molecules calculated by the fixed-node Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals are presented in this work. The random walk based results, 3.264(43) and 2.507(32) eV for C(2) and BO, respectively, are compared with the available best experimental determined values, 3.269(6) and 2.508(8) eV for C(2) and BO, respectively, and the results of other theoretical calculations.     

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.     

A diffusion quantum Monte Carlo study on the lowest singlet and triplet electronic states of BN molecule

Ab initio calculation of both the lowest singlet and triplet electronic states of BN has been performed by the fixed-node Ornstein-Uhlenbeck diffusion quantum Monte Carlo method with the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculation gives equilibrium bond lengths and equilibrium harmonic frequencies of 1.3317(7) A and 1529(7) cm(-1), respectively, for the lowest triplet state and 1.2751(7) A and 1709(8) cm(-1), respectively, for the lowest singlet state. Also, the Monte Carlo calculation reports an energy separation of 178(83) cm(-1) between the two electronic states and recommends the ground state is the lowest triplet state.     

Accuracy of a random-walk-based approach in the determination of equilibrium bond lengths and harmonic frequencies for some doublet first-row diatomic radicals

The accuracy of equilibrium bond lengths and harmonic frequencies for 12 doublet first-row diatomic radicals is presented as predicted by the fixed-node diffusion quantum Monte Carlo method based on the Ornstein-Uhlenbeck random walk guided by the floating spherical Gaussian orbital and spherical Gaussian geminal-type trial wave function. Compared to the experimental determined values, the random-walk-based approach gives the absolute mean deviations of 0.0019 A and 18 cm-1 for the equilibrium bond length and harmonic frequency, respectively. We also compare the random-walk-based results with some coupled-cluster-based values.     

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.     

Depletion force between anisometric colloidal particles

A simple mathematical model for the depletion force between two arbitrarily shaped large convex colloidal particles immersed in a suspension of small spherical particles is proposed. Using differential geometry, the interaction potential is expressed in terms of the mean and Gaussian curvature of the particle surfaces. The accuracy of theoretical results is tested by Monte Carlo simulations for parallel and nonparallel circular cylinders. The agreement between theoretical results and simulated data is very good if the density of the depletion agent is not too high.     

Conformation of Chains in Cores of Block Copolymer Micelles with Solubilized Homopolymer: a Monte Carlo Study

A system of compatible self‐avoiding polymer chains solubilized in spherical cores of block copolymer micelles was studied by lattice Monte Carlo simulations. The core is modeled as a spherical cavity on a simple cubic lattice, filled in partially by tethered (core‐forming) chains and partially by free (solubilized) chains. Molecular parameters (e.g., the ratio of the contour length of the model chains to the core radius) correspond to those in real micellar systems. The density (the fraction of lattice sites occupied) is 0.6 which corresponds to swollen micellar cores in real micellar systems. Simulations yield a constant segment density profile in the core. Both the tethered and solubilized chains acquire an ellipsoidal shape. The ellipsoids equivalent to both types of chains are more spherical than those in a melt and strongly oriented. The chains in the core show a Gaussian‐like behavior. Minor deviations from Gaussian behavior for tethered chains are due to surface effects.     

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.     

Radial dose profiles for pencil electron beams

The relationship between the Boltzmann and Fermi-Eyges-Yang equations governing electron transport is examined. Radial dose profiles for a pencil beam obtained by numerical solution of the Boltzmann equation in the small angle approximation are compared with both the Gaussian approximation and with Monte Carlo simulations for a carbon medium. For energies ranging from 5 to 20 MeV and penetration depths up to 75% of the range the numerical results are within 10% of the Monte Carlo results for the radial distance encompassing 63% of the energy deposition.     

Two-body correlations among particles confined to a spherical surface: packing effects

The two-point correlation functions among particles confined to move within a spherical two-dimensional space are studied here using Monte Carlo simulations in the canonical ensemble and the corresponding liquid theory concepts. This work takes a simple model system with soft-sphere interactions among the particles lying on the spherical surface. We focus this study on the ordering induced by the particle packing and the restrictions imposed by the system topology. The corresponding grand canonical results are obtained from the canonical Monte Carlo data using the standard statistical mechanics formulas. These grand canonical ensemble results show that as the strength of the interactions increases, the system transits between liquidlike states and crystal-like states as the average number of particles on the spherical surface matches certain specific values. The crystal-like states correspond to sharp minima in the plot of the standard deviation in the number of particles on the spherical surface versus the average value of this number. We also test the validity of the integral equation approaches for this kind of closed but boundless systems: It is found that the Percus-Yevick approximation overestimates the correlations for this system in a liquid state, whereas the hypernetted-chain approximation underestimates these correlations.     

Scheme for adding electron-nucleus cusps to Gaussian orbitals

A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a general improvement in the efficiency of all-electron VMC and DMC calculations using Gaussian basis sets.     

Computer simulation of reverse micelles and water-in-oil microemulsions

The literature data are reviewed on molecular simulation of reverse micelles and water-in-oil microemulsions by the molecular dynamics and Monte Carlo methods. Different models of reverse micelles from a spherical cavity with an impenetrable wall to an atomistic ensemble of surfactant molecules are considered. The main structural and thermodynamic properties, as well as the dynamics of micelle components are considered. The results are compared with the data obtained using both a single model and models of different levels.     

A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules

This article describes an approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method based on the floating spherical Gaussians. In conjunction with a projected and renormalized Hellmann-Feynman gradient and an electronic energy at variational Monte Carlo and diffusion quantum Monte Carlo, respectively, the quasi-Newton algorithm implemented with the Broyden-Fletcher-Goldfarb-Shanno updated Hessian was used to find the optimized molecular geometry. We applied this approach to N2 and H2O molecules. The geometry and harmonic frequencies calculated were consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.     

A fast variational Gaussian wavepacket method: size-induced structural transitions in large neon clusters

The variational Gaussian wavepacket (VGW) approximation provides an alternative to path integral Monte Carlo for the computation of thermodynamic properties of many-body systems at thermal equilibrium. It provides a direct access to the thermal density matrix and is particularly efficient for Monte Carlo approaches, as for an N-body system it operates in a non-inflated 3N-dimensional configuration space. Here, we greatly accelerate the VGW method by retaining only the relevant short-range correlations in the (otherwise full) 3N × 3N Gaussian width matrix without sacrificing the accuracy of the fully coupled VGW method. This results in the reduction of the original O(N(3)) scaling to O(N(2)). The fast-VGW method is then applied to quantum Lennard-Jones clusters with sizes up to N = 6500 atoms. Following Doye and Calvo [JCP 116, 8307 (2002)] we study the competition between the icosahedral and decahedral structural motifs in Ne(N) clusters as a function of N.     

取样方差估计值的精度与样本数目之间的关系

通过数学推导建立了取样方差估计值的精度与样本数目之间的定量关系。实验也证明,取样方差估计值的标准偏差与样本数目的平方根之积可近似为一常数。应用蒙特卡罗技术模拟随机取样,对该关系式进行了验证,并探讨了取样方差估计值的分布规律,表明其规律对于组分含量服从正态分布,均匀随机分布及多项分布总体是相似的。     

Monte Carlo and event-driven dynamics of Brownian particles with orientational degrees of freedom

Recently, a simple scaling argument was introduced that allows us to map, with some precautions, Brownian and Monte Carlo dynamics for spherical particles. Here, we extend the scaling to study systems that have orientational degrees of freedom and carefully asses its validity over a wide region of temperature and density. Our work allows us to devise a Brownian Monte Carlo algorithm that produces, to a good approximation, physically meaningful trajectories with a minimum programming effort, although at the expense of some sampling efficiency.     

Estimation of protein folding rate from Monte Carlo simulations and entropy capacity

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 10(8) Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.     

Quantum statistical mechanics with Gaussians: equilibrium properties of van der Waals clusters

The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.     

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.     

Quantification of surface roughness effect on elastically backscattered electrons

Electron inelastic mean free path can be obtained from a measured elastic peak electron spectroscopy spectrum combined with a Monte Carlo simulation. It is thus necessary to know the influence of various experimental factors to the measured and calculated results. This work investigates the effect of the surface roughness or the surface topography on the intensity of the elastic peak. A Monte Carlo simulation, by taking into account of realistic surface roughness for both Gaussian and non‐Gaussian type rough surfaces experimentally prepared, has been employed to study the surface topography effect. The simulations of elastic peak electron spectroscopy were performed for both planar and rough Al and Cu surfaces and for varied primary energies ranging from 200 to 2000 eV. To quantify the surface roughness effect, the surface roughness parameter is introduced according to the ratio of elastic peak intensities between a rough surface and an ideal planar surface. Simulation results have shown that surface roughness parameter is important in a certain range of emission angle and particularly for large emission angles. For grazing emission, the elastic peak intensity can be largely enhanced by roughness even at nanometer scale. Copyright © 2014 John Wiley & Sons, Ltd.