Quantum chemistry statement

Finally, the editors of this book would tend to agree with Cramer and Truhlar s statement that contemporary advances in the field of solvent effect representation would allow quantum chemistry to have the same revolutionary impact on condensed-phase chemistry as the last 25 years have witnessed for gas-phase chemistry. We hope this book will contribute to this end. 

If quantum theory is to be used as a chemical tool, on the same kind of basis as, say, n.m.r. or mass spectrometry, one must be able to carry out calculations of high accuracy for quite complex molecules without excessive cost in computation time. Until recently such a goal would have seemed quite unattainable and numerous calculations of dubious value have been published on the basis that nothing better was possible. Our work has shown that this view is too pessimistic semiempirical SCF MO treatments, if properly applied, can already give results of sufficient accuracy to be of chemical value and the possibilities of further improvement seem unlimited. There can therefore be little doubt that we are on the threshold of an era where quantum chemistry will serve as a standard tool in studying the reactions and other properties of molecules, thus bringing nearer the fruition of Dirac s classic statement, that with the development of quantum theory chemistry has become an exercise in applied mathematics. 

We agree totally with these statements, especially as we were able to prove by ourselves during several years how powerful a concerted use of many physical methods could be (including quantum chemistry) for conformational analysis within the field of molecular inorganic chemistry However, some limits of such approaches... 

It is our submission that failure to publish computer code, together with its documentation, and the resulting lack of open criticism and constructive use has hampered the development of computational molecular physics and quantum chemistry. It is high probable that similar statements could be made about many other areas of computational science and engineering. 

In response to a previously published analysis of orbital hybridization [17] I was castigated by an international group of theoretical chemists for not understanding the subtleties of modern quantum chemistry. Their rebuttal of my views is summarized by three statements, from an extensive e-mail message forwarded to me by their spokesman [19] ... 

William of Ockham, 141 1 century A1 Sherman, who introduced me to quantum mechanics while I was an undergraduate at the University of Wisconsin, was co-author with Van Vleck of a classic paper on quantum chemistry which contained the following significant statement ... 

IBM in Germany organized a symposium on Computational Methods in Chemistry at Bad Neuenahr in 1979 with the preface According to Graham Richards the Third Age of Quantum Chemistry has started, where the results of quantum chemical calculation can guide the experimentalists in their search for the unknown. One of the examples chosen to underline this statement was the acetylene molecule. In 1970 Kammer had made qualitatively correct predictions for the first cis ( Bu and trans ( Bu A ) bent... 

In the community of Relativistic Quantum Chemistry one often hears the opposite statement, that there is no need for a perturbation theory of relativistic effects, since it is straightforward (though admittedly not cheap ) to perform fully relativistic calculations [4]. 

In the halls of chemistry departments, we often hear how difficult it is to understand quantum chemistry. It is hard to know if this situation reflects a problem on the side of the teacher or the student. Somehow it should be easier to study quantum chemistry than classical mechanics, since so many areas of study in the 20th century have been shaped by quantum theory. In other words, the essence of quantum theory has invaded our conventional ideas. For example, we say If there is no conflict, it has to be right. The logic of this statement is obviously related to the formulation of quantum theory. One would think that it should be easier to understand a field based on contemporary logic than fields rooted in classical logic. Pedagogues often believe one should study history systematically from the past to the latest events. This does not mean that the concept of a field is easy to understand, but it reflects the fact that history is a human drama. If many people took this attitude, the study of quantum theory could become quite enjoyable. 

We recall here the opening statement of a famous book on quantum chemistry In so far as quantum mechanics is correct, chemical questions are problems in applied mathematics. Actually, the mathematics to apply to liquid systems is a hard nut to crack. Fortunately a sequence of many, but reasonable, approximations can be introduced. We shall consider and exploit them in the following section of this chapter. 

When Dirac wrote that the underlying physical laws are for the whole of chemistry are thus completely known, this was certainly revolutionary, since it implied that the only forces responsible for chemical phenomena are Coulombic, and that there is no genuine chemical force, as was still widely believed. A few years later Hellmann [15] formulated the program of quantum chemistry which claims nothing less than to predict all chemical and physical properties of matter purely theoretically based on a simple mathematical law . Some 20 years ago the present author tried to formulate a consistent and rigorous theory of the chemical bond [16] and found that there is a long way from Dirac s statement (2) to an explicit theory of chemistry on the basis of quantum mechanics . In view of the spectacular success of numerical quantum chemistry that culminated in the Nobel prize for chemistry 1998, there are hardly doubts that at least with statement 2 Dirac was right. 

In Section 2.1, the electronic problem is formulated, i.e., the problem of describing the motion of electrons in the field of fixed nuclear point charges. This is one of the central problems of quantum chemistry and our sole concern in this book. We begin with the full nonrelativistic time-independent Schrodinger equation and introduce the Born-Oppenheimer approximation. We then discuss a general statement of the Pauli exclusion principle called the antisymmetry principle, which requires that many-electron wave functions must be antisymmetric with respect to the interchange of any two electrons. 

Prefatory note This chapter and the others in Part II have been written in as non-mathematical a style as the author could manage. The theoretical validity of the various statements made without formal proof can be checked in any of the many available texts on Quantum Chemistry [1, 2, 3]. The initiate, who may be tempted to skip this and the following chapter, is urged to skim through them anyway. To paraphrase Shakespeare s Ulysses [8], the author s drift may be nothing to strain at but his position may not be altogether familiar . 

For most members of the community of physicists, it appeared that the solution of chemical problems amounted to no more than quantum-mechanical calculations. Physicists came under the spell of Dirac s reductionist program, and quantum chemistry came to be usually regarded as a success story of quantum mechanics. Although it took some time for physicists to realize that Dirac s statement was a theoretically correct but practically meaningless dictum, the first attempts to solve chemical problems in the "proper way"—that is, in the physicists way—appeared to be rather promising. These attempts started before the publication of Dirac s paper, and they may have provided some kind of justification for such a generalized statement. 

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