Statistical mechanics background

A comprehensive and up-to-date introduction to the ideas of molecular dynamics and Monte Carlo, with statistical mechanical background, advanced teclmiques and case studies, supported by a Web page for software download. 

The book consists of 14 chapters, in which we attempt to summarize the current state of the art in the field. We also offer a look into the future by including descriptions of several methods that hold great promise, but are not yet widely employed. The first six chapters form the core of the book. In Chap. 1, we define the context of the book by recounting briefly the history of free energy calculations and presenting the necessary statistical mechanics background material utilized in the subsequent chapters. 

Statistical Mechanical Background. We will present a brief review of the basic statistical mechanical concepts needed in this experiment, because standard textbooks in physical chemistry vary widely in their approach. 

Nonequilibrium molecular dynamics (NEMD) Monte Carlo heat flow simulation, 71-74 theoretical background, 6 Nonequilibrium probability, time-dependent mechanical work, 51-53 Nonequilibrium quantum statistical mechanics, 57-58... 

The formalism of the thermodynamics of solutions was described in Chapter 3. In this chapter we shall revisit the topic of solutions and apply statistical mechanics to relate the thermodynamic properties of solutions to atomistic models for their structure. Although we will not give a rigorous presentation of the methods of statistical mechanics, we need some elements of the theory as a background for the solution models to be treated. These elements of the theory are presented in Section 9.1. 

S. Adair, H. S. Sinuns, K. Linderstrom-Lang, and, especially, J. Wyman. These treatments, however, were empirical or thermodynamic in content, that is, expressed from the outset in terms of thermodynamic equilibrium constants. The advantage of the explicit use of the actual grand partition function is that it is more general it includes everything in the empirical or thermodynamic approach, plus providing, when needed, the background molecular theory (as statistical mechanics always does). 

In this chapter we summarize some background information concerning molecular collisions, dipoles and radiation, spectroscopy, and statistical mechanics that will be needed later. This Chapter should be skipped in a first reading. It is hoped that a reader who comes back to this Chapter later with specific questions will find the answers here - or, at least, some useful reference for further study. 

In 1923, Peter Debye and Erich Hiickel developed a classical electrostatic theory of ionic distributions in dilute electrolyte solutions [P. Debye and E. Hiickel. Phys. Z 24, 185 (1923)] that seems to account satisfactorily for the qualitative low-ra nonideality shown in Fig. 8.3. Although this theory involves some background in statistical mechanics and electrostatics that is not assumed elsewhere in this book, we briefly sketch the physical assumptions and mathematical techniques leading to the Debye-Hiickel equation (8.69) to illustrate such molecular-level description of thermodynamic relationships. 

We have tried, without being overly formalistic, to develop the subject in a systematic manner with attention to basic concepts and clarity of derivations. The reader is assumed to be familiar with the basic concepts of classical mechanics, quantum mechanics, and chemical kinetics. In addition, some knowledge of statistical mechanics is required and, since not all potential readers may have that, we have included an appendix that summarizes the most important results of relevance. The book is reasonably self-contained such that a standard background in mathematics, physics, and physical chemistry should be sufficient and make it possible for the students to follow and understand the derivations and developments in the book. A few sections may be a little more demanding, in particular some of the sections on quantum dynamics and stochastic dynamics. 

See, e.g., J. M. Seddon and J. D. Gale, Thermodynamics and Statistical Mechanics (The Royal Society of Chemistry, London 2001), for friendly background reading. 

For a review of the statistical backgrounds, but without any example of a surface tension computation, see D. Nicholson, N.G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press (1982). 

Originally, basically noncubic equations of state, often with some theoretical background on statistical mechanics, have been proposed for polymer systems. To date, it is generally accepted that both cubic and noncubic equations of state can be used for correlating polymer-solvent equlibria. Orbey et al. ° recently reviewed several cubic equations of state for polymers. 

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