Herndon structure-resonance theory

Fig. 2 Graf ical modeling of the generation of permutation integrals of Herndon [12] structure-resonance theory in case of an ra-cene yj involves permutation of (4i + 2), pi-electtons.

We will not explore the computational details of VB theory, but it is worth noting some results that can be obtained with it. Recall that one of the features of HMO theory is that it is possible to make useful predictions, such as the relative stabilities of cyclic n systems or the locations of impaired electron density in a conjugated radical, without actually doing the HMO calculations. Similarly, it is not necessary to carry out a complete valence bond calculation to obtain useful quantitative predictions of resonance energies and some other properties of conjugated n systems. Herndon described a structure-resonance theory (SRT) method that enables one to calculate resonance energies using only Kekule structures The methods described in the references present... 

M. Randic, B. Ruscic, and N. Trinajstic, Herndon s structure-resonance theory—On the valence structure cormt for conjugated radicals, Croat. Chem. Acta 54 (1981) 295-308. 

It may be of interest that isoconjugate benzenoid hydrocarbons necessarily have the same RE in Herndon s resonance theory VB model as in the conjugated circuits model, but generally they will have different RE in the HMO model and the TRE model, mentioned earlier. This clearly points to not only numerical but also conceptual differences between different graph theoretical models those based on the adjacency matrix (HMO) and that based on Kekule valence structures and conjugated circuits (VB). 

Experimental log k2 values were correlated with Brown para-localization energies, Dewar reactivity numbers, Herndon structure count ratios, Hess-Schaad resonance energy differences, indices of free valence, and second-order perturbation stabilization energies. The latter are based on Fukui s frontier orbital theory [67] which classifies the Diels-Alder reaction of benzenoid hydrocarbons with maleic anhydride as mainly HOMO (aromatic hydrocarbon)-LUMO (maleic anhydride) controlled. However, the corresponding orbital interaction energy given by... 

Herndon, W.C. (1974b). Resonance Theory and the Enumeration of Kekul6 Structures. J.Chem. Educ.,51,10-15. 

Can more elaborate VB calculations (those that are above the resonance theory of Herndon in the diagram shown in Figure 50, which represents the hierarchical relationship between different VB models according to Klein et al. ) be cast in an alternative but mathematically equivalent formalism based on the decomposition of Kekule valence structures in conjugated circuits, rather than using Kekule valence structures ... 

Herndon, W. C. Resonance Theory and the Enumeration of Kekuld Structures. J. Chem. Educ. 1974, 51, 10-15. Longuet-Higgins, H. C. J. Chem. Phys. 1950, 18, 265. Karabunarliev, S. Tyutyulkov, N. Theor. Chim. Acta 1989, 764, 65. 

---