Woodward-Hoffmann rules definition

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]. 

Obviously, the appropriate application of the Woodward-Hoffmann rules to transition metal complex reactions involving metal carbon bonds requires information about the mechanistic and stereochemical details which is not easy to come by and definitely not yet sufficiently available for photochemical cycloaddition reactions of complexed olefinic systems. 

The selection rules for chemical reactions derived by using symmetry arguments show a definite pattern. Woodward and Hoffmann generalized the selection rules on the basis of orbital symmetry considerations applied to a large number of systems [89], Two important observations are summarized here we refer to the literature for further details [90, 91],... 

With these descriptors in hand, we can look at the generalized orbital symmetry rule. There is a definite binary nature to the theory of pericyclic reactions. For cycloadditions, [2-f2] is forbidden (all suprafacial), whereas [4-F2] is allowed (all suprafacial). Continuing with the series, [6+2] is forbidden, and [8+2] is allowed. We will also encounter patterns in the other kinds of pericyclic reactions presented electrocyclic reactions, sigmatropic shifts, etc. Based on patterns such as these. Woodward and Hoffmann proposed the following rule for all pericyclic reactions ... 

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