Woodward-Hoffman method

We can predict the outcome of pericychc reactions by considering the symmetry of the molecular orbitals of the system. The Woodward—Hoffman method requires an analysis of the symmetry of all 7t molecular orbitals as they are transformed from those in the reactants to those in the products. We will use a similar, but simpler frontier orbital method developed by K. Fukui of Kyoto University. Fukui s method considers only the orbital symmetry of the highest occupied... 

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. 

The now much-discussed Hoffman-Woodward rules provide a guide to which concerted processes may proceed via available low lying electronic states thermally, but they do not provide quantitative data on activation energies. Thermochemical data and methods permit evaluation of the energetics of the biradical paths (49). Where experimental data is available this is usually enough to decide between concerted and biradical paths. 

Woodward and Hoffman have introduced a general method to characterize a pericyclic process based on the number and type of electrons of breaking bonds and they have interpreted the formation and stereochemistry of the product by the principle of conservation of orbital symmetry. ... 

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