Theory Monte Carlo

De Raedt H 1996 Quantum theory Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed K Binder and G Ciccotti (Bologna Italian Physical Society) pp 401-42... 

The fluctuations of isolated steps have been studied, both theoretically - using Langevin theory, Monte Carlo simulations of SOS models, as well as exact methods, and experimentally by scanning tunneling microscopy (caution is needed in the measurements to avoid artefacts of tip assisted motions of the steps O-... 

Over the last two decades, there has been increasing interest in probabilistic, or stochastic, robust control theory. Monte Carlo simulation methods have been used to synthesize and analyze controllers for uncertain systems [170,255], First- and second-order reliability methods were incorporated to compute the probable performance of linear-quadratic-regulator... 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

Aqueous Interfaces Force Fields A Brief Introduction Force Fields A General Discussion Free Energy Changes in Solution Free Energy Simulations Intermolecular Interactions by Perturbation Theory Monte Carlo Simulations for Complex Fluids Monte Carlo Simulations for Polymers OPLS Force Fields Supercritical Water and Aqueous Solutions Molecular Simulation. 

G2 Theory Monte Carlo Quantum Methods for Electronic Structure. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Bunker D L and Pattengill M 1968 Monte Carlo calculations. VI. A re-evaluation of the RRKM theory of unimolecular reaction rates J. Chem. Phys. 48 772-6... 

Ra]agopal G, Needs R J, James A, Kenney S D and Foulkes W M C 1995 Variational and diffusion quantum Monte Carlo calculations at nonzero wave vectors theory and application to diamond-structure germanium Phys. Rev. B 51 10 591-600... 

Yethira] A and Woodward C E 1995 Monte Carlo density functional theory of nonuniform polymer melts J Chem. Phys. 102 5499... 

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

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