Über die Autorin bzw. den Autor

Christopher Cramer, Professor of Computational Chemistry Department of Chemistry, University of Minnesota,Minneapolis, USA

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Essentials of Computational Chemistry, Theories and Models, Second Edition provides an accessible introduction to this fast developing subject. Extensively revised and updated, the Second Edition has been carefully developed to encourage student understanding and to establish seamless

connections with the primary literature for the advanced reader. The book opens with a presentation of classical models, before gradually moving on to increasingly more complex quantum mechanical and dynamical theories. Coverage and examples are drawn from inorganic, organic and biological chemistry.

• evolving topics like density functional theory, continuum solvation models, and computational thermochemistry brought firmly up-to-date
• carefully guides the reader through key equations, providing background information and placing each in context.

• numerous examples and applications with selected case studies designed as a basis for classroom discussion.
• supplementary website with exercises problems and updates: www.pollux.chem.umn.edu/8021/

Invaluable to all students taking a first course in computational chemistry, molecular modelling, computational quantum chemistry or electronic structure theory. This book will also be of interest to postgraduates, researchers and professionals needing an up-to-date, accessible introduction to this subject.

Reviews of the First Edition

"This is an excellent text for graduates or advanced undergraduates in any field of chemistry……the text provides an excellent introduction to the field for students and researchers in any area of chemistry" Theoretical Chemistry Accounts, 2003

"…..this book has a lot to recommend to undergraduate students as a way of getting them involved in computational chemistry…Professor Cramer has done a superb job and deserves congratulating" The Alchemist, 2003

" ‘Essentials’ is a useful tool not only for teaching and learning but also as a quick reference, and thus will most probably become one of the standard text books for computational chemistry"

Journal of Chemical Information and Computer Science, 2003

Aus dem Klappentext

Essentials of Computational Chemistry, Theories and Models, Second Edition provides an accessible introduction to this fast developing subject. Extensively revised and updated, the Second Edition has been carefully developed to encourage student understanding and to establish seamless

connections with the primary literature for the advanced reader. The book opens with a presentation of classical models, before gradually moving on to increasingly more complex quantum mechanical and dynamical theories. Coverage and examples are drawn from inorganic, organic and biological chemistry.

• evolving topics like density functional theory, continuum solvation models, and computational thermochemistry brought firmly up-to-date
• carefully guides the reader through key equations, providing background information and placing each in context.

• numerous examples and applications with selected case studies designed as a basis for classroom discussion.
• supplementary website with exercises problems and updates: www.pollux.chem.umn.edu/8021/

Invaluable to all students taking a first course in computational chemistry, molecular modelling, computational quantum chemistry or electronic structure theory. This book will also be of interest to postgraduates, researchers and professionals needing an up-to-date, accessible introduction to this subject.

Reviews of the First Edition

"This is an excellent text for graduates or advanced undergraduates in any field of chemistry……the text provides an excellent introduction to the field for students and researchers in any area of chemistry" Theoretical Chemistry Accounts, 2003

"…..this book has a lot to recommend to undergraduate students as a way of getting them involved in computational chemistry…Professor Cramer has done a superb job and deserves congratulating" The Alchemist, 2003

" ‘Essentials’ is a useful tool not only for teaching and learning but also as a quick reference, and thus will most probably become one of the standard text books for computational chemistry"

Journal of Chemical Information and Computer Science, 2003

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Essentials of Computational Chemistry

John Wiley & Sons

Chapter One

1.1 Definition of Terms

A clear definition of terms is critical to the success of all communication. Particularly in the area of computational chemistry, there is a need to be careful in the nomenclature used to describe predictive tools, since this often helps clarify what approximations have been made in the course of a modeling 'experiment'. For the purposes of this textbook, we will adopt a specific convention for what distinguishes theory, computation, and modeling.

In general, 'theory' is a word with which most scientists are entirely comfortable. A theory is one or more rules that are postulated to govern the behavior of physical systems. Often, in science at least, such rules are quantitative in nature and expressed in the form of a mathematical equation. Thus, for example, one has the theory of Einstein that the energy of a particle, E, is equal to its relativistic mass, m, times the speed of light in a vacuum, c, squared,

E = m]c.sup.2] (1.1)

The quantitative nature of scientific theories allows them to be tested by experiment. This testing is the means by which the applicable range of a theory is elucidated. Thus, for instance, many theories of classical mechanics prove applicable to macroscopic systems but break down for very small systems, where one must instead resort to quantum mechanics. The observation that a theory has limits in its applicability might, at first glance, seem a sufficient flaw to warrant discarding it. However, if a sufficiently large number of 'interesting' systems falls within the range of the theory, practical reasons tend to motivate its continued use. Of course, such a situation tends to inspire efforts to find a more general theory that is not subject to the limitations of the original. Thus, for example, classical mechanics can be viewed as a special case of the more general quantum mechanics in which the presence of macroscopic masses and velocities leads to a simplification of the governing equations (and concepts).

Such simplifications of general theories under special circumstances can be key to getting anything useful done! One would certainly not want to design the pendulum for a mechanical clock using the fairly complicated mathematics of quantal theories, for instance, although the process would ultimately lead to the same result as that obtained from the simpler equations of the more restricted classical theories. Furthermore, at least at the start of the twenty-first century, a generalized 'theory of everything' does not yet exist. For instance, efforts to link theories of quantum electromagnetics and theories of gravity continue to be pursued.

Occasionally, a theory has proven so robust over time, even if only within a limited range of applicability, that it is called a 'law'. For instance, Coulomb's law specifies that the energy of interaction (in arbitrary units) between two point charges is given by

E = [q.sub.1][q.sub.2]/[epsilon][r.sub.12] (1.2)

where q is a charge, [epsilon] is the dielectric constant of a homogeneous medium (possibly vacuum) in which the charges are embedded, and [r.sub.12] is the distance between them. However, the term 'law' is best regarded as honorific - indeed, one might regard it as hubris to imply that experimentalists can discern the laws of the universe within a finite span of time.

Theory behind us, let us now move on to 'model'. The difference between a theory and a model tends to be rather subtle, and largely a matter of intent. Thus, the goal of a theory tends to be to achieve as great a generality as possible, irrespective of the practical consequences. Quantum theory, for instance, has breathtaking generality, but the practical consequence is that the equations that govern quantum theory are intractable for all but the most ideal of systems. A model, on the other hand, typically involves the deliberate introduction of simplifying approximations into a more general theory so as to extend its practical utility. Indeed, the approximations sometimes go to the extreme of rendering the model deliberately qualitative. Thus, one can regard the valence-shell-electron-pair repulsion (VSEPR; an acronym glossary is provided as Appendix A of this text) model familiar to most students of inorganic chemistry as a drastic simplification of quantum mechanics to permit discrete choices for preferred conformations of inorganic complexes. (While serious theoreticians may shudder at the empiricism that often governs such drastic simplifications, and mutter gloomily about lack of 'rigor', the value of a model is not in its intrinsic beauty, of course, but in its ability to solve practical problems; for a delightful cartoon capturing the hubris of theoretical dogmatism, see Ghosh 2003.)

Another feature sometimes characteristic of a quantitative 'model' is that it incorporates certain constants that are derived wholly from experimental data, i.e., they are empirically determined. Again, the degree to which this distinguishes a model from a theory can be subtle. The speed of light and the charge of the electron are fundamental constants of the universe that appear either explicitly or implicitly in Eqs. (1.1) and (1.2), and we know these values only through experimental measurement. So, again, the issue tends to be intent. A model is often designed to apply specifically to a restricted volume of what we might call chemical space. For instance, we might imagine developing a model that would predict the free energy of activation for the hydrolysis of substituted -lactams in water. Our motivation, obviously, would be the therapeutic utility of these species as antibiotics. Because we are limiting ourselves to consideration of only very specific kinds of bond-making and bondbreaking, we may be able to construct a model that takes advantage of a few experimentally known free energies of activation and correlates them with some other measured or predicted quantity. For example, we might find from comparison with X-ray crystallography that there is a linear correlation between the aqueous free energy of activation, [DELTA][G.sup.[double dagger]], and the length of the lactam C-N bond in the crystal, [r.sub.CN] (Figure 1.1). Our 'model' would then be

[DELTA][G.sup.[double dagger]] = [r.sub.CN] + b (1.3)

where a would be the slope (in units of energy per length) and b the intercept (in units of energy) for the empirically determined correlation.

Equation (1.3) represents a very simple model, and that simplicity derives, presumably, from the small volume of chemical space over which it appears to hold. As it is hard to imagine deriving Eq. (1.3) from the fundamental equations of quantum mechanics, it might be more descriptive to refer to it as a 'relationship' rather than a 'model'. That is, we make some attempt to distinguish between correlation and causality. For the moment, we will not parse the terms too closely.

An interesting question that arises with respect to Eq. (1.3) is whether it may be more broadly applicable. For instance, might the model be useful for predicting the free energies of activation for the hydrolysis of [gamma]-lactams? What about amides in general? What about imides? In a statistical sense,...