Woodward-Hoffmann orbital symmetry concept

The ring-chain tautomerism between cyclobutene and butadiene is perhaps the most famUiar example of an allowed Woodward-Hoffmann process. This transformation invariably is discussed in every attempt to rationalize or teach the Woodward-Hoffmann orbital symmetry concepts. This popularity is due in large part to the existence of a geometrically well defined (and easily visualized) alternate, forbidden, electrocyclic pathway. Thus it is exceedingly simple to set up a nonaUowed strawman, the disrotatory ring opening, and... 

Prior to the delineation of the concept of conservation of orbital symmetry by Woodward and Hoffmann, Bachmann and Deno reported that all Diels-Alder reactions... 

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. 

In 1969 R.B. Woodward and R. Hoffmann developed a general theory of concerted reactions which proceed through a cyclic transition state process which they turned pericyclic. They used the concept of orbital symmetry to predict which types of cyclic transition state are energetically feasible. 

Woodward-Hoffmann rule org chem A concept which can predict or explain the stereochemistry of certain types of reactions in organic chemistry it is also described as the conservation of orbital symmetry. wCid-ward haf-mon, rul ... 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

McWeeny has written a tribute to the valence-bond theory pioneers of 1927-1935.362 Shavitt has outlined the history and evolution of Gaussian basis sets as employed in ah initio molecular orbital calculations.363 Hargittai has interviewed Roald Hoffmann (b. 1937)364 of Cornell University and Kenichi Fukui (1918-1998)365 of Kyoto University, who were jointly awarded the Nobel Prize in Chemistry in 1981. Fukui developed the concept of frontier orbitals and recognized the importance of orbital symmetry in chemical reactions, but his work was highly mathematical and its importance was not appreciated until Robert Woodward (1917-1979) and Hoffmann produced their rules for the conservation of orbital symmetry from 1965 onwards.366... 

Both the Woodward-Hoffmann approach and the Hiickel-Mobius concept are useful for predicting the course of concerted reactions. They both have their limitations as well. The application of the Hiickel-Mobius concept is probably preferable for systems with low symmetry. On the other hand, this concept can only be applied when there is a cyclic array of orbitals. The conservation of orbital symmetry approach does not have this limitation. 

Symmetry and stability analysis. The semi-empirical unrestricted Hartree-Fock (UHF) method was used for symmetry and stability analysis of chemical reactions at early stage of our theoretical studies.1,2 The BS MOs for CT diradicals are also expanded in terms of composite donor and acceptor MOs to obtain the Mulliken CT theoretical explanations of their electronic structures. Instability in chemical bonds followed by the BS ab initio calculations is one of the useful approaches for elucidating electronic structures of active reaction intermediates and transition structures.2 The concept is also useful to characterize chemical reaction mechanisms in combination with the Woodward-Hoffman (WH) orbital symmetry criterion,3 as illustrated in Figure 1. According to the Woodward-Hoffmann rule,3 there are two types of organic reactions orbital-symmetry allowed and forbidden. On the other hand, the orbital instability condition is the other criterion for distinguishing between nonradical and diradical cases.2 The combination of the two criteria provides four different cases (i) allowed nonradical (AN), (ii) allowed radical (AR), (iii) forbidden nonradical (FN), and (iv) forbidden radical (FR). The charge and spin density populations obtained by the ab initio BS MO calculations are responsible for the above classifications as shown in Fig. 1. 

From 1965, the ideas of symmetry begin also to penetrate gradually into the theory of chemical reactions. The principle of orbital symmetry conservation formulated by Woodward and Hoffmann [13] became a powerful incentive to the development of the theoretical group concepts of the quantum theory of chemical reactions. Hence, it should be expected, proceeding from the general tendencies of science development, that the theoretical chemistry of the future will follow mathematics and physics and will be to a considerable extent a science on symmetry or, in other words, a science about the harmony of nature . 

A key to understanding the mechanisms of the concerted pericyclic reactions was the recognition by Woodward and Hoffmann that the pathway of such reactions is determined by the symmetry properties of the orbitals that are directly involved. Specifically, they stated the requirement for conservation of orbital symmetry. The idea that the symmetry of each participating orbital must be conserved during the reaction process dramatically transformed the understanding of concerted pericyclic reactions and stimulated much experimental work to test and extend their theory. The Woodward and Hoffmann concept led to other related interpretations of orbital properties that are also successful in predicting and interpreting the course of concerted... 

These results are in accord with orbital symmetry principles. Indeed, examples found in the study of vitamin D provided the initial examples of the dichotomy between thermal and photochemical processes that led to development of the concepts underlying the Woodward-Hoffmann rules for photochemical reaction. It was found that the triene precalciferol gave ergosterol on photocyclization, but the stereoisomer lumisterol on heating. 

Huisgen s general concept was not only fruitful for synthetic applications after 1960, but also for thorough evaluations of the mechanism of 1,3-dipolar cycloadditions, carried out simultaneously. Within three years, Huisgen came to quite remarkable conclusions (1963 a, b) with respect to stereochemistry and orbital control of these reactions they fitted very well to the principle of conservation of orbital symmetry (Hoffmann and Woodward, 1965). 

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