Monte Carlo methods, molecular modeling

In recognition of the rapid expansion of computational chemistry in the 1980s, Andre Bandrauk and Andre Michel of the University of Sherbrooke organized the First Canadian Symposium on Computational Chemistry in May 1991 in Orford, Quebec. The conference included invited papers on dynamics, density functional methods, molecular modeling, Monte Carlo methods, and topics in quantum chemistry and statistical mechanics. About half of the invited speakers were from abroad (mostly from the United States). 

ON THE STRUCTURE OF MOLECULAR MODELING MONTE CARLO METHODS AND MULTISCALE MODELING... 

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. 

In this chapter we shall discuss some of the general principles involved in the two most common simulation techniques used in molecular modelling the molecular dynamics and the Monte Carlo methods. We shall also discuss several concepts that are common to both of these methods. A more detailed discussion of the two simulation methods can be found in Chapters 7 and 8. 

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Monte Carlo calculations have been carried out to simulate the spin transition behaviour in both mono- and dinuclear systems [197]. The stepwise transition in [Fe(2-pic)3]Cl2-EtOH as well as its modification by metal dilution and application of pressure have been similarly modelled by considering short- and long-range interactions [52, 198, 199]. An additional study of the effect of metal dilution was successfully simulated with the Monte Carlo treatment considering direct and indirect inter-molecular interactions [200]. A very recent report deals with the application of the Monte Carlo method to mimic short- and long-range interactions in cooperative photo-induced LS—>HS conversion phenomena in two- and three-dimensional systems [201],... 

Quantum mechanical methods follow a similar path, except that the starting point is the solution of the Schrodinger equation for the system under investigation. The most successful and widely used method is that of Density Functional Theory. Once again, a key point is the development of a realistic model that can serve as the input to the computer investigation. Energy minimization, molecular dynamics, and Monte Carlo methods can all be employed in this process. 

This Chapter has outlined several different approaches to the computational determination of solution properties. Two of these address solute-solvent interactions directly, either treating the effects of individual solvent molecules upon the solute explicitly or by means of a reaction field due to a continuum model of the solvent. The other procedures establish correlations between properties of interest and certain features of the solute and/or solvent molecules. There are empirical elements in all of these methods, even the seemingly more rigorous ones, such as the parameters in the molecular dynamics/Monte Carlo intermolecular potentials, Eqs. (16) and (17), or in the continuum model s Gcavitation and Gvdw, Eqs. (40) and (41), etc. 

Fu et al. [16] analyzed a set of 57 compounds previously used by Lombardo and other workers also. Their molecular geometries were optimized using the semiempirical self-consistent field molecular orbital calculation AMI method. Polar molecular surface areas and molecular volumes were calculated by the Monte Carlo method. The stepwise multiple regression analysis was used to obtain the correlation equations between the log BB values of the training set compounds and their structural parameters. The following model was generated after removing one outlier (Eq. 50) ... 

These two methods are different and are usually employed to calculate different properties. Molecular dynamics has a time-dependent component, and is better at calculating transport properties, such as viscosity, heat conductivity, and difftisivity. Monte Carlo methods do not contain information on kinetic energy. It is used more in the lattice model of polymers, protein stmcture conformation, and in the Gibbs ensemble for phase equilibrium. 

The Monte-Carlo method is utilized to investigate the conformational distribution in the central section of a PIB decamer at various temperatures. It is checked that a six-state RIS model based on the two matrices P and Pj constitutes a description of the conformational distribution in PIB. The Monte-Carlo results are in excellent agreement with the experimental data on the average dimensions of PIB chains, as well as with the molecular scattering functions of this polymer in solution and in bulk. 

Simulations. In addition to analytical approaches to describe ion—solid interactions two different types of computer simulations are used Monte Carlo (MC) and molecular dynamics (MD). The Monte Carlo method relies on a binary collision model and molecular dynamics solves the many-body problem of Newtonian mechanics for many interacting particles. As the name Monte Carlo suggests, the results require averaging over many simulated particle trajectories. A review of the computer simulation of ion—solid interactions has been provided (43). 

A conformational study of novel polyhydroxylated azepanes has been reported in which the 1H NMR spectroscopy and molecular modeling (molecular mechanics, molecular dynamics, and Monte Carlo methods) afforded insights into aspects of the conformational analysis <2004EJ04119>. 

The fits of Janev et al. [12] stem from a compilation of the results obtained with different theoretical approaches (i) semi-classical close-coupling methods with a development of the wave function on atomic orbitals (Fritsch and Lin [16]), molecular orbitals (Green et al [17]), or both (Kimura and Lin [18], (ii) pure classical model - i.e. the Classical Trajectory Monte Carlo method (Olson and Schultz [19]) - and (iii) perturbative quantum approach (Belkic et al. [20]). In order to get precise fits, theoretical results accuracy was estimated according to many criteria, most important being the domain of validity of each technique. 

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