Woodward—Hoffmann theory

Seetion treats the spatial, angular momentum, and spin symmetries of the many-eleetron wavefunetions that are formed as anti symmetrized produets of atomie or moleeular orbitals. Proper eoupling of angular momenta (orbital and spin) is eovered here, and atomie and moleeular term symbols are treated. The need to inelude Configuration Interaetion to aehieve qualitatively eorreet deseriptions of eertain speeies eleetronie struetures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of ehemieal reaetivity is also developed. 

The application of the Woodward-Hoffmann theory 22> of electro-cyclic reactions to chemiluminescence has proved a very useful and productive approach, suggested independently by E. H. White and M. J. C. Harding 23>, F. Me Capra, D. G. Richardson, and Y. C. Chang u> 24>, and M. M. Rauhut and coworkers 25>. 

An analysis and interpretation of experimental results for the four reactions here considered in terms of the Woodward-Hoffmann theory for concerted reactions must be predicated on a clear and commonly held understanding of what that term may mean. Despite the centrality of this term and the concept it covers in recent theoretical treatments of cycloaddition and more general cycloreaction mechanisms, it seems to us to... 

When (/ )-(-)-(34) is dimerized, only the second and third isomers are formed (26%, 74%), both in dextrorotatory form, suggesting that the first isomer obtained with racemic starting material stems from a pair of enantiomers. Even though the monoinversion product (the [ir2f + irZi] product) is not the major product with either racemic or q>tically active ci.r,trur -diene, the fact that it is formed at all has been read as an indication that Woodward-Hoffmann theory has some predictive validity even for reactions which are not concerred. The normal diradical formulation rationalizes this outcome differently. 

Woodward and Hoffmann offered explanations of why some reactions are concerted and others not. They found a way to analyze reactions by determining the pathways required to maintain bonding interactions between orbital lobes as the reaction progressed. They used orbital symmetry and the aromaticity of the transition state in their analysis. The following sections take up some examples in which Woodward-Hoffmann theory is particularly useful. 

It must be admitted that the Woodward-Hoffmann theory is Med with jargon. There is nothing to do but learn it. 

The central insight of Woodward-Hoffmann theory is that one must keep track of the phase relationships of orbital interactions as a concerted reaction proceeds. If bonding overlap can be maintained throughout, the reaction is allowed if not, the reaction is forbidden by orbital symmetry. This notion leads to a variety of mechanistic explanations for reactions that can otherwise be baffling. Some of these pericyclic reactions are discussed in the section on Reactions, Mechanisms, and Tools. 

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... 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

A part of the chemical consequences of the cyclic orbital interactions in the cyclic conjngation is well known as the Hueckel rule for aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions [14]. In this section, we describe the basis for the rnles very briefly and other rules derived from or related to the orbital phase theory. The rules include kinetic stability (electron-donating and accepting abilities) of cyclic conjugate molecules (Sect. 2.2.2) and discontinnity of cyclic conjngation or inapplicability of the Hueckel rule to a certain class of conjngate molecnles (Sect. 2.2.3). Further applications are described in Sect. 4. 

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

Roald Hoffmann, a former coworker of R.B. Woodward and Nobel Prize as well for his contribution to the frontier orbital theory (the famous Woodward-Hoffmann rules concerning the conservation of molecular orbital symmetry), has also emphasised the artistic aspects of organic synthesis "The making of molecules puts chemistry very close to the arts. We create the objects that we or others then study or appreciate. That s exactly what writers, visual artists and composers do" [15a]. Nevertheless, Hoffmann also recognises the logic content of synthesis that "has inspired people to write computer programs to emulate the mind of a synthetic chemist, to suggest new syntheses". 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offiilminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4-6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

To summarize, we note two key points. Firstly, that the favourable interaction between DA and D + A in allowed reactions does not preclude barrier formation. The CM model, by its very nature, emphasizes barrier formation through the avoided crossing of reactant and product configurations. Second, the CM model gives rise to the Woodward-Hoffmann rules through consideration of the symmetry properties of the DA and D+A-configurations. This is as it should be. As we have noted previously, a key test of the CM model is whether it blends in naturally with existing theories that focus on specific areas of reactivity. 4... 

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