Computational quantum mechanics Hiickel theory

The definition of "concepts" must be accompanied by explicit recipes for computing them is actual cases. There is no more space in theoretical chemistty for "driving forces", "effects, etc. not accompanied by specific rules for their quantification. The impact of a new "concept will be greater if the rules of quantifications are not restricted to ad hoc methods, but related to methods of general use in molecular quantum mechanics. A concept based exclusively on some specific features of a given method, e g. the extended Hiickel method, is less robust than a concurrent concept which may be quantified also using other levels of the theory. 

Abstract A historical view demystifies the subject. The focus is strongly on chemistry. The application of quantum mechanics (QM) to computational chemistry is shown by explaining the Schrodinger equation and showing how this equation led to the simple Hiickel method, from which the extended Hiickel method followed. This sets the stage well for ab initio theory, in Chapter 5. 

These successes did not go unnoticed by industry. Several pharmaceutical companies (1963-1964) became interested in applications of it-electron theory to biochemistry. While it was admittedly premature, it was felt that quantum chemistry was both the wave of the future and the very matrix for rational drug design. Hiickel energies of cephalosporins could be correlated with their biological activities.While companies were applying some mathematical methods of correlation techniques in quantitative structure-activity relationships (QSAR), it was chiefly the Hiickel theory and various forms of semiempirical quantum mechanics that was using a large share of computer time on the IBM 7094 mainframe in 1966. 

Ab initio calculations can be extremely expensive in terms of the computer resources required. Nevertheless, improvements in computer hardware and the availability of easy-to-use programs have helped to make ab initio methods a widely used computational tool. The approximate quantum mechanical methods require significantly less computational resources. Indeed, the earliest approximate methods such as Hiickel theory predate computers by many years. Moreover, by their incorporation of parameters derived from experimental data some approximate methods can calculate certain properties more accurately then even the highest level of ab initio methods. 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

This situation prompts a theoretical investigation of the problem. So far, the only available computation was carried out for the isolated molecule by the extended Hiickel Theory (51) and it predicts as the most stable conformation of the free zwit-terion the completely extended one. Because of known limitations of this methodology which lead frequently to erroneous results we have reinvestigated the problem by more refined quantum mechanical procedures. We have also distinguished explicitly between the study of the free molecule and the molecule in solution. 

We then present ab initio molecular orbital theory. This is a well-defined approximation to the full quantum mechanical analysis of a molecular system, and also the basis of an array of powerful and popular computational approaches. Molecular orbital theory relies upon the linear combination of atomic orbitals, and we introduce the mathematics and results of such an approach. Then we discuss the implementation of ab initio molecular orbital theory in modern computational chemistry. We also describe a number of more approximate approaches, which derive from ab initio theory, but make numerous simplifications that allow larger systems to be addressed. Next, we provide an overview of the theory of organic TT systems, primarily at the level of Hiickel theory. Despite its dramatic approximations, Hiickel theory provides many useful insights. It lies at the core of our intuition about the electronic structure of organic ir systems, and it will be key to the analysis of pericyclic reactions given in Chapter 15. 

Molecular orbital (MO) theory includes a series of quantum mechanical methods for describing the behavior of electrons in molecules by combining the familiar s, p, d, and / atomic orbitals (AOs) of the individual atoms to form MOs that extend over the molecule as a whole. The accuracy of the calculations critically depends on the way the interactions between the electrons (electron correlation) are handled. More exact treatments generally require more computer time, so the problem is to find methods that give acceptable accuracy for systems of chemical interest without excessive use of computer time. For many years, the extended Hiickel (EH) method was widely used in organometallic chemistry, largely thanks to the exceptionally insightful contributions of Roald Hoffmann. The EH method allowed structural and reactivity trends to be discussed in terms of the interactions of specific molecular orbitals. Fenske-Hall methods also proved very useful in this period. ... 

In 1927, Heitler and London used valence bond theory to treat the H2 molecule but to treat larger molecules, further simplifications were needed. In 1931, Erich Hiickel introduced an extremely simple approximation which could be used to treat the 7i-electrons in flat organic molecules such as benzene, napthaline, and so on. This approximation yielded matrices to be diagonalized, and it is a measure of the state of computers at that time to remember that during World War II, Alberte Pullman sat in a basement room in Paris diagonalizing Hiickel matrices with a mechanical desk calculator, while her husband-to-be Bernard drove a tank with the Free French Forces in North Africa. Alberte s hand-work led to the publication of the Pullmans early book Quantum Biochemistry. ... 

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