Quantum mechanics, introduction

At present, we have many equivalent ways to describe quantum mechanics. Introduction of the varying constants into these different descriptions produces different effects. 

Molecular modeling - Introduction Quantum mechanics - Introduction Ab initio - Theory I... 

The purpose of this chapter is to provide an introduction to tlie basic framework of quantum mechanics, with an emphasis on aspects that are most relevant for the study of atoms and molecules. After siumnarizing the basic principles of the subject that represent required knowledge for all students of physical chemistry, the independent-particle approximation so important in molecular quantum mechanics is introduced. A significant effort is made to describe this approach in detail and to coimnunicate how it is used as a foundation for qualitative understanding and as a basis for more accurate treatments. Following this, the basic teclmiques used in accurate calculations that go beyond the independent-particle picture (variational method and perturbation theory) are described, with some attention given to how they are actually used in practical calculations. 

Pauling L and Wilson E B 1935 Introduction to Quantum Mechanics (New York Dover)... 

Tannor D J 2001 Introduction to Quantum Mechanics A Time Dependent Perspective (Mill Valley, CA University Science Books)... 

The appropriate quantum mechanical operator fomi of the phase has been the subject of numerous efforts. At present, one can only speak of the best approximate operator, and this also is the subject of debate. A personal historical account by Nieto of various operator definitions for the phase (and of its probability distribution) is in [27] and in companion articles, for example, [130-132] and others, that have appeared in Volume 48 of Physica Scripta T (1993), which is devoted to this subject. (For an introduction to the unitarity requirements placed on a phase operator, one can refer to [133]). In 1927, Dirac proposed a quantum mechanical operator tf), defined in terms of the creation and destruction operators [134], but London [135] showed that this is not Hermitean. (A further source is [136].) Another candidate, e is not unitary. 

For larger systems, various approximate schemes have been developed, called mixed methods as they treat parts of the system using different levels of theory. Of interest to us here are quantuin-seiniclassical methods, which use full quantum mechanics to treat the electrons, but use approximations based on trajectories in a classical phase space to describe the nuclear motion. The prefix quantum may be dropped, and we will talk of seiniclassical methods. There are a number of different approaches, but here we shall concentrate on the few that are suitable for direct dynamics molecular simulations. An overview of other methods is given in the introduction of [21]. 

Pauling, L. and Wilson, E. B., 1935. Introduction to Quantum Mechanics. McGraw-Hill, New York. Reprinted (1963). Dover, New York. 

Introduction to Quantum Mechanics, L. Pauling and E. B. Wilson, Dover Publications, Inc., New York, N. Y. (1963)- Pauling and Wilson. 

Quantum mechanics is cast in a language that is not familiar to most students of chemistry who are examining the subject for the first time. Its mathematical content and how it relates to experimental measurements both require a great deal of effort to master. With these thoughts in mind, the authors have organized this introductory section in a manner that first provides the student with a brief introduction to the two primary constructs of quantum mechanics, operators and wavefunctions that obey a Schrodinger equation, then demonstrates the application of these constructs to several chemically relevant model problems, and finally returns to examine in more detail the conceptual structure of quantum mechanics. 

W. Greiner, Quantum Mechanics An Introduction Springer, Berlin (1994). 

M. Tinkham, Group Theory and Quantum Mechanics McGraw-Hill, New York (1964). R. McWeeny, Symmetry An Introduction to Group Theory and its Applications Pergamon, New York (1963). 

Apractical introduction to molecular mechanics and semi-empirical quantum mechanics calculations, with extensive examples from the MMP2 (not in HyperChem), MINDO/3, and MNDO methods. One of the more accessible books for new computational chemists. 

Griffiths, D. J. (1995) Introduction to Quantum Mechanics, Prentice Hall, New Jersey. 

I have assumed that the reader has no prior knowledge of concepts specific to computational chemistry, but has a working understanding of introductory quantum mechanics and elementary mathematics, especially linear algebra, vector, differential and integral calculus. The following features specific to chemistry are used in the present book without further introduction. Adequate descriptions may be found in a number of quantum chemistry textbooks (J. P. Lowe, Quantum Chemistry, Academic Press, 1993 1. N. Levine, Quantum Chemistry, Prentice Hall, 1992 P. W. Atkins, Molecular Quantum Mechanics, Oxford University Press, 1983). 

These days students are presented with the four quantum number description of electrons in many-electron atoms as though these quantum numbers somehow drop out of quantum mechanics in a seamless manner. In fact, they do not and furthermore they emerged, one at a time, beginning with Bohr s use of just one quantum number and culminating with Pauli s introduction of the fourth quantum number and his associated Exclusion Principle. 

This is a crudal and frequently overlooked point about electronic configurations. They are far from being based in quantum mechanics it is precisely this theory that shows them to be an inadequate concept The notion that electron orbits and configurations really exist or "refer" is a relic of the old quantum theory and of Pauli s introduction of the exclusion prind-ple in its original and now strictly incorrect... 

Introduction.—The quantum mechanics of angular momenta has grown into a theory that is far more complex than its classical ancestor yet an understanding of it is indispensable for the student of modem physics. We, therefore, expand the rudimentary indications presented formerly,1 and present the basic techniques employed today in this useful subject. 

Chapter I has been reorganized in this edition to give readers a gentler introduction to atoms and their structure. Atoms and molecules, including discussions of quantum mechanics and molecular orbitals, provide the foundation for understanding bulk properties and models of gases, liquids, and solids. 

The error in Hiickel s treatment lies not in the quantum mechanical calculations themselves, which are correct as far as they go, but in the oversimplification of the problem and in the incorrect interpretation of the results. Consequently it has seemed desirable to us to make the necessary extensions and corrections in order to see if the theory can lead to a consistent picture. In the following discussion we have found it necessary to consider all of the different factors mentioned heretofore the resonance effect, the inductive effect, and the effect of polarization by the attacking group. The inclusion of these several effects in the theory has led to the introduction of a number of more or less arbitrary parameters, and has thus tended to remove significance from the agreement with experiment which is achieved. We feel, however, that the effects included are all justified empirically and must be considered in any satisfactory theory, and that the values used for the arbitrary parameters are reasonable. The results communicated in this paper show that the quantum mechanical theory of the structure of aromatic molecules can account for the phenomenon of directed substitution in a reasonable way. 

Reprinted from Introduction to Quantum Mechanics, with Application to Chemistry, by Linus Pauling and E. Bright Wilson, Jr., McGraw Hill, NY, Section 42, pp. 326-331 (1935). 

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