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Über dieses Buch

New textbooks at all levels of chemistry appear with great regularity. Some fields like basic biochemistry, organic reaction mechanisms, and chemical thermody­ namics are well represented by many excellent texts, and new or revised editions are published sufficiently often to keep up with progress in research. However, some areas of chemistry, especially many of those taught at the graduate level, suffer from a real lack of up-to-date textbooks. The most serious needs occur in fields that are rapidly changing. Textbooks in these subjects usually have to be written by scientists actually involved in the research which is advancing the field. It is not often easy to persuade such individuals to set time aside to help spread the knowledge they have accumulated. Our goal, in this series, is to pinpoint areas of chemistry where recent progress has outpaced what is covered in any available textbooks, and then seek out and persuade experts in these fields to produce relatively concise but instructive introductions to their fields. These should serve the needs of one semester or one quarter graduate courses in chemistry and biochemistry. In some cases, the availability of texts in active research areas should help stimulate the creation of new courses. New York, New York CHARLES R. CANTOR Preface This book is not a traditional quantum chemistry textbook. Instead, it represents a concept that has evolved from teaching graduate courses in quantum chemistry over a number of years, and encountering students with diverse backgrounds.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Experimental Basis of Quantum Theory

Abstract
In the years immediately following 1925, a dramatic series of theoretical developments occurred that explained for the first time the apparently anomolous experimental data then existing. Also, these developments provided a conceptual and mathematical framework that has motivated and allowed interpretation of an immense number and diversity of experiments since then. These theoretical developments, called quantum mechanics, will be the subject of our attention throughout this entire text.
Ralph E. Christoffersen

Chapter 2. Vector Spaces and Linear Transformations

Abstract
Having seen that it was necessary to construct a new theory to describe the behavior of sub-microscopic particles, it should not be surprising that mathematical techniques were introduced concurrently to aid in the development of the new theory.
Ralph E. Christoffersen

Chapter 3. Matrix Theory

Abstract
As we shall see presently, there is a mathematical technique called matrix theory that will allow us to represent many of the relations of quantum mechanics in a concise and easily manipulated form. In order to become familiar with the techniques involved in manipulating matrices, let us begin by considering some definitions and elementary properties.
Ralph E. Christoffersen

Chapter 4. Postulates of Quantum Mechanics and Initial Considerations

Abstract
In order to begin the actual study of quantum mechanics, we shall now state a set of five postulates (or axioms), which form the basic structure of the theory. These postulates provide a conceptual and mathematical framework that is strikingly different from classical mechanics in many ways. Within it, however, explanations for apparently contradictory results of early experiments such as quantization of energy and angular momentum can be achieved. In addition, it provides a framework for interpretation of future experiments, as well as additional development of the theory itself.
Ralph E. Christoffersen

Chapter 5. One-Dimensional Model Problems

Abstract
In the previous chapter, the basic ideas of quantum mechanics were introduced by means of several postulates. It was also seen that there are several possible equivalent ways of viewing quantum mechanics, commonly referred to as the Schrödinger picture, the Heisenberg picture, and the interaction picture. Since these are all equivalent views of the same phenomena, the choice of which one to employ when attempting to solve a problem of interest can be made on the basis of which one is most convenient to use.
Ralph E. Christoffersen

Chapter 6. Angular Momentum

Abstract
In Chapter 1 we saw that one of the areas where strikingly different results are found, compared to the results expected from classical considerations, is associated with the measurement of angular momentum. In particular, the allowed states of orbital angular momentum are quantized at the microscopic level, in sharp contrast to the corresponding classical analog. Also, a new kind of angular momentum, associated with the intrinsic spin of particles, is observed at the microscopic level, which has no classical analog and is also quantized. In this chapter we shall investigate the properties of angular momentum in general, and show how both spin and orbital angular momentum can be considered to be different examples of a general quantum theory of angular momentum.
Ralph E. Christoffersen

Chapter 7. The Hydrogen Atom, Rigid Rotor, and the H 2 + Molecule

Abstract
After developing the notions of angular momentum in the previous chapter, we are now ready to use these ideas to help solve some important applications. As a first example, we shall examine the hydrogen atom and hydrogen-like atoms. It should be noted that the hydrogen atom is not only an important historical contribution to theoretical chemistry. As we shall see later, a substantial number of the qualitative and quantitative concepts that are used concerning complex atoms and molecules are couched in terms of hydrogenic orbitals. Consequently, it is of importance to study the eigenfunctions and associated eigenvalues of the hydrogen atom in some detail.1
Ralph E. Christoffersen

Chapter 8. The Molecular Hamiltonian

Abstract
In Chapter 4 a set of postulates for the study of quantum mechanics was introduced, including the Schrödinger equation plus a prescription for forming the quantum mechanical Hamiltonian for a time-independent, field-free, conservative system in which relativistic effects are ignored. Although such a Hamiltonian is indeed a restricted one compared to the circumstances found in many experiments, use of it has allowed a number of important principles to be established using one-dimensional and other examples, as well as the introduction of angular momentum from a quantum mechanical point of view.
Ralph E. Christoffersen

Chapter 9. Approximation Methods for Stationary States

Abstract
In several of the preceding chapters we have discussed application of the postulates of quantum mechanics to several important types of examples. Although these applications were varied, there is one common characteristic shared by all of them. In each case, the Schrödinger equation could be solved exactly for the eigenvalues and associated eigenfunctions. If this were possible for all problems of interest to chemists, our insight into the nature of chemical phenomena would certainly be increased enormously. However, the fact is that only a very few problems are solvable exactly. In particular, it has not yet been possible to obtain an exact solution to the Schrödinger equation for any system containing more than one electron. Consequently, our knowledge of chemistry as revealed through quantum mechanics has been restricted primarily to that obtainable from an examination of approximate solutions to the Schrödinger equation. However, the advent of large-scale computers has greatly expanded both the accuracy and the scope of approximate solutions that can be obtained. We shall now discuss some of the methods that are available for obtaining approximate solutions to the Schrödinger equation for stationary states, and that form the basis for most applications of quantum mechanics to chemical problems.
Ralph E. Christoffersen

Chapter 10. General Considerations for Many Electron Systems

Abstract
Thus far our considerations have in general been limited to systems containing only a single electron. While we have seen that many important principles and techniques can be developed using those cases, we shall now see that a major new concept is needed for systems containing more than one electron. That concept (the Pauli Exclusion Principle) will be developed in the sections to follow, along with a number of analyses and techniques that are of substantial importance in contemporary applications of quantum mechanics to chemistry. Before doing that, however, it is useful to introduce several conceptual approaches to many electron systems that were developed early, as well as the basic concepts of group theory. These will help us to understand and motivate the discussions to follow, as well as to provide useful tools for incorporating and understanding symmetry properties of molecules and wavefunctions.
Ralph E. Christoffersen

Chapter 11. Computational Techniques for Many-Electron Systems Using Single Configuration Wavefunctions

Abstract
In the last chapter we found that one-electron orbitals can be used as a basis for describing multielectron systems. Furthermore, the use of Slater determinants of these one-electron orbitals forms a convenient means of satisfying the Pauli Exclusion principle as well as creating eigenfunctions of operators such as S2, L2, etc. In this chapter and the next we shall develop these ideas further in ways that are important both from a conceptual and practical point of view.
Ralph E. Christoffersen

Chapter 12. Beyond Hartree-Fock Theory

Abstract
In the previous chapter we saw that Hartree-Fock theory provides a remarkably good description of molecular systems, especially when the conceptual simplicity of the model is considered. Many properties are accurately predicted, and total energies can be obtained that are accurate to within > 99% of the experimental value. However, we have also seen that the 1% error (i.e., the “correlation energy error”) results in incorrect conclusions in a number of important cases such as dissociation energies, electronic spectra, and potential surfaces.
Ralph E. Christoffersen

Backmatter

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