Orbitals chemistry rules

As noted previously, the outstanding success of orbital symmetry rules in organic chemistry (75, 242) has led to many attempts to extend these rules to organometallic chemistry and metal-catalyzed processes. These qualitative analyses based on the principle of conservation of orbital symmetry or second-order Jahn-Teller effects have been reviewed extensively (91, 142, 143, 173, 175, 179, 221, 225) and will not be considered in any detail here. 

Theoretical chemistry rates some special mention in this context. Nowadays this activity tends to be quite mathematical [1], but history shows us that theoretical chemistry need not be mathematical at all. From the first years of the crystallization of chemistry as a subject distinct from alchemy, chemists have utilized theory, in the sense of disciplined speculation. Nonmathematical examples are found in the structural theory of organic chemistry [2] and in most applications of the powerful Woodward-Hoffman orbital symmetry rules [3]. 

The series of articles written by Woodward and Hoffmann in the middle of the 1960s caused a considerable stir in the organic chemistry community. For decades afterwards organic chemists were checking and trying out reactions proposed by the orbital symmetry rules. In 2003, the first paper of their series [14] was the 88th most cited paper in the Journal of the American Chemical Society [15],... 

The aim of the present review is to provide chemists with a general survey of the different techniques now available for the theoretical evaluation of reaction paths. Qualitative work is based nowadays mainly on orbital symmetry rules this topic is given special emphasis here, since the method is of general use in everyday chemistry. Methods that require actual computation are described in the second part of this review under the heading semi-quantitative methods, since a complete, non-approximate, quantum-mechanical calculation of a reaction rate has never yet been carried out, even for the simplest systems. 

Professors Kenichi Fukui (Kyoto University) and Roald Hoffmann (Cornell University) received the 1981 Nobel Prize in Chemistry for their quantum mechanical studies of chemical reactivity. Their applied theoretical chemistry research is certainly at the core of computational chemistry by today s yardstick. Professor Fukui s name is associated with frontier electrons, which govern the transition states in reactions, while that of Hoffmann is often hyphenated to R. B. Woodward s name in regard to their orbital symmetry rules. In addition, Professor Hoffmann s name is strongly identified with the extended Hiickel molecular orbital method. Not only was he a pioneer in the development of the method, he has continued to use it in almost all of his over 300 papers. 

Woodward saw organic synthesis as a way to advance science and to solve practical problems. One need only look to his vitamin Bj2 work to illustrate this. A reaction that Woodward had planned to use as part of the early stages of the synthesis of vitamin B12 gave a prodnct with nnexpected stereochemistry, leading the perplexed Woodward to look for similar reactions in the organic literatnre. He found them, and with Roald Hoffmann, a theoretical chemist at Harvard, formulated what are now known as the Woodward-Hoffmann mles for the conservation of orbital symmetry. These rules explained the ontcomes of a series of seemingly unrelated chemical reactions and correctly predicted the outcomes of many others. For his con-tribntions to the orbital symmetry rules, Hoffmann shared the 1981 Nobel Prize in chemistry with Kenichi Fukui of Japan, who had reached similar conclnsions independently. Woodward died before the 1981 Nobel Prize was awarded, and had he lived longer, he certainly would have received his second Nobel Prize. 

Over the years, different approaches have been developed to reveal chemical bonds. Covalent bonds are intuitively represented using conventional Lewis stractures [19]. Molecular Orbital (MO) theory has been veiy useful and successfiil for the theoretical analysis of chemical reactions and chemical reactivity. The frontier orbital theory [20] and the orbital symmetry rules of Woodward and Hoffman [21] are paradigmatic examples of the possibilities of quantum chemistry within the MO theory. 

The above examples illustrate the insight of the VBCM model to problems which range from reaction mechanisms to predictions of TS structure based on orbital selection rules. Much of our current effort is concerned with the application of the VBCM to a variety of chemical problems, especially in odd electron systems, and in organometallic chemistry. 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The modern approach to chemical education appears to be strongly biased toward theories, particularly quantum mechanics. Many authors have remarked that classical chemistry and its invaluable predictive rules have been downgraded since chemistry was put into orbit around physics. School and undergraduate courses as well as textbooks show an increasing tendency to begin with the establishment of theoretical concepts such as orbitals and hybridization. There is a continuing debate in the chemical literature on the relative merits of theory as opposed to qualitative or descriptive chemistry 1-6). To quote the late J. J. Zucker-man who supported the latter approach (3). 

In the case of the second excerpt I think I can safely say that Lowdin is wrong. The simple energy rule regarding the order of filling of orbitals in neutral atoms has now entered every textbook of chemistry, although his statement may have been partly true in 1969 when he wrote his article.1 Although Lowdin can be excused for not knowing what was in chemistry textbooks I think it is also safe to assume that he is correct in his main claim that this important rule has not been derived. Nor as I have claimed in a number of brief articles has the rule been derived to this day (Scerri, 1998). 

The last decade has witnessed an unprecedented strengthening of the bone between theory and experiment in organic chemistry. Much of this success may be credited to the development of widely applicable, unifying concepts, such as the symmetry rules of Woodward and Hoffmann, and the frontier orbital thee>ry of Eukui. Whereas the the ore tical emphasis had historically been on detailed structure and spectroscopy, the new methods are de signe d to solve pre)blems e>f special importance to organic chemists reactivity, stereochemistry, and mechanisms. 

Here, n corresponds to the principal quantum number, the orbital exponent is termed and Ylm are the usual spherical harmonics that describe the angular part of the function. In fact as a rule of thumb one usually needs about three times as many GTO than STO functions to achieve a certain accuracy. Unfortunately, many-center integrals such as described in equations (7-16) and (7-18) are notoriously difficult to compute with STO basis sets since no analytical techniques are available and one has to resort to numerical methods. This explains why these functions, which were used in the early days of computational quantum chemistry, do not play any role in modem wave function based quantum chemical programs. Rather, in an attempt to have the cake and eat it too, one usually employs the so-called contracted GTO basis sets, in which several primitive Gaussian functions (typically between three and six and only seldom more than ten) as in equation (7-19) are combined in a fixed linear combination to give one contracted Gaussian function (CGF),... 

The problem of competition of the molecular reaction (direct route) and chain reaction (complicated, multistage route) was firstly considered in the monograph by Semenov [1], The new aspect of this problem appeared recently because the quantum chemistry formulated the rule of conservation of orbital symmetry in chemical and photochemical reactions (Woodward-Hofmann rule [4]). Very often the structure of initial reactants suggests their direct interaction to form the same final products, which are also obtained in the chain reaction, and the thermodynamics does not forbid the reaction with AG < 0. However, the experiment often shows that many reactions of this type occur in a complicated manner through several intermediate stages. For example, the reaction... 

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