Structure-resonance theory

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

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.

The perturbational MO method of Longuet-Higgins (11) and Dewar (12), which was thoroughly reviewed by Dewar and Dougherty (6), has been the pencil-and-paper method of choice in numerous applications. More recently, a modified free-electron (MFE) MO approach (13-15) and a valence-bond structure-resonance theory (VBSRT) (7, 16, 17) have been applied to several PAH structure and reactivity problems. A new perturbational variant of the free-electron MO method (PMO F) has also been derived and reported (8, 18). Both PMO F and VBSRT qualify as simple pencil-and-paper procedures. When applied to a compilation of electrophilic substitution parameters (ct+) (19-23), the correlation coefficients of calculated reactivity indexes with cr+ for alternant hydrocarbons are 0.973 and 0.959, respectively (8). In this case, the performance of the PMO F method rivals that of the best available SCF calculations for systems of this size, and that of VBSRT is sufficient for most purposes. 

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... 

Because D and E are equivalent resonance structures, resonance theory predicts that the allyl cation should be unusually stable. Since the positive charge is located on C3 in D and on Cl in E, resonance theory also tells us that the positive charge should be delocalized over both carbon atoms. Carbon atom 2 carries none of the positive charge. The hybrid structure F includes charge and bond features of both D and E ... 

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. 

As indicated already in Chapter 2, unless stated otherwise (see for example Chapter 23), the equivalent Lewis structure resonance theory assumes that electron-pair bond wavefunctions are of the Heitler-London atomic orbital type - for example y(l)a(2) + a(l)y(2) a.nAy l)b(2) + b )a 2) for structures (6) and (7). Atomic formal charges are not indicated in the generalized valence bond structures that involve the Y, A, B, C and D atoms. 

Neuronal networks are nowadays predominantly applied in classification tasks. Here, three kind of networks are tested First the backpropagation network is used, due to the fact that it is the most robust and common network. The other two networks which are considered within this study have special adapted architectures for classification tasks. The Learning Vector Quantization (LVQ) Network consists of a neuronal structure that represents the LVQ learning strategy. The Fuzzy Adaptive Resonance Theory (Fuzzy-ART) network is a sophisticated network with a very complex structure but a high performance on classification tasks. Overviews on this extensive subject are given in [2] and [6]. 

Our first approach took resort in simple resonance theory [36, 37]. For each conjugated nr-system aU resonance structures were generated, such as those shown in Figure 7-5. 

Most of the qualitative relationships between color and structure of methine dyes based on the resonance theory were established independently during the 1940 s by Brooker and coworkers (16, 72-74) and by Kiprianov (75-78), and specific application to thiazolo dyes appeared later with the studies of Knott (79) and Rout (80-84). In this approach, the absorptions of dyes belonging to amidinium ionic system are conveyed by a group of contributing structures resulting from the different ways of localization of the 2n rr electrons on the 2n l atoms of the chromophoric cationic chain, rather than by a single formula ... 

Resonance theory tells us that molecules which cannot be adequately represented in terms of a single Lewis structure are likely to be unusually stable. What the simple theory does not tell us is the magnitude of the effect, the so-called resonance energy. This can be assessed via molecular modeling. 

Gronowitz et al. have discussed the effects of substituents on chemical reactivity and on ultraviolet (XJV), infrared (IR), and nuclear magnetic resonance (NMR) spectra in terms of simple resonance theory,They assume resonance structures (1-5) to contribute to a —I—M (Ingold s terminology) 2-substituted thiophene, resonance forms (6-10) to the structure of a drI-fM 2-substituted thiophene, forms (11-16) to a —I—M 3-substituted thiophene, and forms (17-22) to a I -M 3-substituted thiophene. 

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