Al. Statistical-mechanical computations of the second virial coefficient and pair-correlation-coefficients of liquid N2, O2, [Pg.565]

The interfacial pair correlation functions are difficult to compute using statistical mechanical theories, and what is usually done is to assume that they are equal to the bulk correlation function times the singlet densities (the Kirkwood superposition approximation). This can be then used to determine the singlet densities (the density and the orientational profile). Molecular dynamics computer simulations can in [Pg.132]

There is no general-purpose or user-friendly software available for statistical mechanical computations, in comparison with the availability of useful and convenient tools to do single molecule quantum mechanical computations. There are many properties that can be computed, but users usually have to write their own computer programs to do each computation, so that it is a small research project instead of a convenient tool for product engineers. Westmoreland and Panagiotopoulos (2004) said that the availability [Pg.123]

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57 [Pg.2288]

The linkage of microscopic and macroscopic properties is not without challenges, both theoretical and experimental. Statistical mechanics and thermodynamics provide the connection between molecular properties and the behavior of macroscopic matter. Coupled with statistical mechanics, computer simulation of the structure, properties, and dynamics of mesoscale models is now feasible and can handle the increase in length and time scales. [Pg.689]

The theories described in 1 were all considered in general terms either for very simple models of molecules and intermolecular forces or without introducing more realistic descriptions at the molecular level. In this section we describe for equilibrium behavior results obtained by statistical mechanical evaluations and computer simulation for various models of molecular structure and pair interactions.. For background the nature and usefulness of information [Pg.70]

Statistical mechanics is the mathematical means to extrapolate thermodynamic properties of bulk materials from a molecular description of the material [14]. Statistical mechanics computations are often performed at the end of ab initio calculations for gas-phase properties. For condensed-phase properties, often molecular dynamics calculations are necessary in order to do a computational experiment. Thermodynamics is one of the best-developed physical theories and it gives a good theoretical starting point for the analysis of molecular systems. [Pg.321]

The study of the adsorption of rare gases onto well-characterized surfaces is a clear historical example of how the combination of experimental techniques, statistical-mechanics methods, and computer simulations is the appropriate way to understand and interpret the behavior of real systems. [Pg.500]

Assume now that we are in the position to be able to calculate reliable pair potentials. The next task is to employ some statistical thermodynamic model which would permit us to pass from the pair complexes solvent-solute and solvent-solvent to a real liquid, A theoretical analysis of this problem is beyond the scope of this book, so that we restrict ourselves to stating that, in the conjucticn with ab initio calculations, the most sophisticated approach appears to be the statistical mechanics computer simulation of the finite system of N molecules in the volume V at the temperature T. The essence of the [Pg.189]

Nowadays, the basic framework of our understanding of elementary processes is the transition state or activated complex theory. Formulations of this theory may be found in refs. 1—13. Recent achievements have been the Rice—Ramsperger—Kassel—Marcus (RRKM) theory of unimol-ecular reactions (see, for example, ref. 14 and Chap. 4 of this volume) and the so-called thermochemical kinetics developed by Benson and co-workers [15] for estimating thermodynamic and kinetic parameters of gas phase reactions. Computers are used in the theory of elementary processes for quantum mechanical and statistical mechanical computations. However, this theme will not be discussed further here. [Pg.249]

Chemical studies usually deal with a solute which can be a single molecule or a molecular complex or transition state in a chemical reaction. In such systems, the role of the solvent is mainly a physical perturbation which can be simulated at a lower theoretical level than that required for the study of the subsystem of chemical interest. The success of continuum models confirms this statement. In order to describe the solution at the molecular level and to perform full statistical mechanics computations on a model of macroscopic sample, one may set up some computationally efficient approaches by limiting the quantum chemical study to the solute and using one of the usual classical force-fields to represent the solvent molecules. The computation of the statistical averages can be done by means of either Monte Carlo or molecular dynamics algorithms. The so-called QM/MM models are now widely used in such chemical studies. [Pg.566]

A new opportunity, which creates good prospects for avoiding many problems eoimected with the theoretical description of adsorption on heterogeneous surfaces, has appeared as a result of the introduction of computer simulation methods [17,18]. Over the last three deeades, computer simulations have grown into a third fundamental discipline of research in addition to experiment and theory. The study of adsorption on heterogeneous solid surfaces has especially benefited fi om the molecular simulation method, first of aU, because of the complexity of interactions of adsorbate molecules with differently distributed active centers that are not easily described by the methods of statistical mechanics. Computer simulation can, in principle at least, provide an exact solution of the assumed model. [Pg.108]

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