Woodward-Hoffmann diagrams

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 Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

A key step in one route to the synthesis of hexamethyl Dewar benzene is the cycloaddition of 2-butyne to tetramethylcyclobutadiene (stabilized by A1 cation). Using the parent compounds (no methyls), develop a Woodward-Hoffmann orbital correlation diagram for the reaction and determine whether the reaction is thermally allowed. 

This question requires you to construct an orbital correlation diagram of the Woodward-Hoffmann type. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

The second principle, which has been used earlier (page 194) in constructing the correlation diagrams for the Woodward-Hoffmann rules, and which has its ultimate origin in the phenomenon of configuration interaction (page 179) is called the noncrossing rule ... 

Refer to the molecular orbital diagrams of allyl cation (Figure 10.13) and those presented earlier in this chapter for ethylene and 1,3-butadiene (Figures 10.9 and 10.10) to decide which of the following cycloaddition reactions are allowed and which are forbidden according to the Woodward-Hoffmann rules. 

This argument demonstrates in an entirely general way that the number of phase inversions in the interaction diagram for a simply connected pericyclic transformation is zero if the number of antarafacial components is even and one if the number of antarafacial components is odd. In order to complete the link between the Woodward-Hoffmann and Dewar-Zimmerman points of view, it remains only to find the total number of electrons in the completed ring. A 4q system contains an even number of pairs and a 4q + 2 system an odd number of pairs therefore any system obtained by joining components will have a total number of electrons satisfying the formula 4q (even number of pairs total) if there are an even number of 4q + 2 components and a total number satisfying 4 + 2 (odd number of pairs total) if there are an odd number of 4q + 2 components. 

The Woodward-Hoffmann pericyclic reaction theory has generated substantial interest in the pathways of forbidden reactions and of excited state processes, beginning with a paper by Longuet-Higgins and Abrahamson,54 which appeared simultaneously with Woodward and Hoffmann s first use of orbital correlation diagrams.55 We have noted in Section 11.3, p. 586, that the orbital correlation diagram predicts that if a forbidden process does take place by a concerted pericyclic mechanism,56 and if electrons were to remain in their original orbitals, an... 

Fortunately, all the conclusions that can be drawn laboriously from correlation diagrams can be drawn more easily from a pair of rules, known as the Woodward-Hoffmann rules, which distil the essence of the idea into two statements governing all pericyclic reactions, one rule for thermal reactions... 

VBSCDs without the VB mixing of the state curves. It is seen that in both cases, the promotion gap is given by the sum of the singlet-to-triplet excitation of the two reactants, while pairing up all the spins into a total singlet spin (see later for a discussion of the meaning of forbiddenness vs. allowedness in the Woodward—Hoffmann sense, in terms of the VB diagram). 

Very often, as in the case of the Woodward-Hoffmann rules, the crossing between the diabatic curves can be predicted without resorting to complicated calculations. A simple and interesting review on VB correlation diagrams has been recently given by Shaik and Shurki [7] (see also other useful Chapters in this volume). 

The Woodward-Hoffmann rules give a more satisfying description and we shall follow the routine outlined for cycloadditions. Note that for stage 3, we can use the three-dimensional diagram we have already made. 

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