Resonance energies empirical

There appear to be no ERE data for pyridones and related compounds, and although Dewar and co-workers18 have calculated the heats of atomization for a number of structures of this type, the results were used for a discussion of tautomeric equilibria rather than for deriving values for the Dewar resonance energies. Empirical studies on tautomeric equilibria have, however, been used to estimate the difference in ERE of pyridones and pyridine (Section II,A, 4). Beak et al 1 studied the gas-phase 1-methyl-2-pyridone 2-methoxypyridine equilibrium and compared the result with the equilibrium constant for the jV-methylvalerolactam ... 

Secondly, the use of a value of the resonance integral yS derived from empirical resonance energies in other contexts is not justifiable. 

Table 35 Empirical Resonance Energy Data (kj mol ) for Azoles ...

This treatment could be applied to anthracene and phenanthrene, with 429 linearly independent structures, and to still larger condensed systems, though not without considerable labor. It is probable that the empirical rule6 of approximate proportionality between the resonance energy and the number of benzene rings in the molecule would be substantiated. 

These authors proposed a uniform mean-field HF (UMHF) procedure which involves orbital occupancy constraints and correction of resonance energy by non-empirical factors. This UMHF method yields the dissociation energies of three-electron systems in satisfactory agreement with accurate calculation performed in the same basis set. 

It is true that the idea of resonance energy was then provided by quantum mechanics. . . but the theory of resonance in chemistry has gone far beyond the region of application in which any precise quantum mechanical calculations have been made, and its great extension has been almost entirely empirical.. . . The theory of resonance in chemistry is an essentially qualitative theory, which, like the classical structure theory, depends for its successful application largely upon a chemical feeling that is developed through practice. 46... 

This assessment may be based on the so-called empirical resonance energies determined from thermodynamic parameters of reactions characterized by retention of structural type or on various indices of structural stability and reactivity, such as the HOMO-LUMO energy gap. 

Of special importance are tautomeric equilibria of two forms in which proton jumps lead to a change of the type of conjugation. Katritzky (72KGS1011 91H329) has developed a useful approach to estimating the empirical resonance energies from the constants of tautomeric equilibria which, in their turn, are determined from the pKa values of suitable compounds properly modeling individual tautomers. 

Relatively low RE values, compared to that of benzene, of pyridazine, s-triazine, and s-tetrazine (see Table VII) are explained, primarily, by changes in the cr-system that occur in passing from the conjugated system to the reference system, i.e., by the factors, such as the compression energy, that were noted in the discussion of the so-called empirical resonance energies. 

Pyridine and benzene conform to Hiickers rule, which predicts that planar cyclic polyenes containing (4n + 2) -electrons ( = 0, or an integer) should show added stability over that anticipated for theoretical polyenes composed of formal alternate single and double bonds. This difference is sometimes called the empirical resonance energy. For example, benzene, where n = 1, is estimated to be 150 kJ moT more stable than the hypothetical molecule cyclohexatriene (Box 1.8) for pyridine, the empirical resonance energy is 107 kJ mol . ... 

Empirical Values of Resonance Energies.—The tables of bond energies permit the calculation of values of the heats of formation of molecules to which a single valence-bond structure can be assigned that agree with the experimental values to within a few kcal/mole. On carrying out a similar calculation for a resonating molecule on the... 

The difference between the observed heat of formation and that calculated for a single valence-bond structure for a molecule with use of the table of bond energies is an empirical value of the resonance energy of the molecule relative to the assumed valence-bond structure. 

The empirical resonance-energy values8 given in Table 6-2 are discussed in the following sections of this chapter and in later chapters. 

The three structures C, Z), and E are less stable than the Kekul6 structures and make much smaller contributions to the normal state of the benzene molecule. They increase the resonance energy from 0.9a to 1.11a. By equating this to the empirical resonance energy of benzene, 37 kcal/rncle, a is found to have the value 33 kcal/mole. 

A similar treatment of naphthalene17 leads to the value 2.04a, which on equation to the empirical resonance energy 75 kcal/mole fixes a at 37 kcal/mole, in approximate agreement with the result for benzene. Calculations for anthracene and phenanthrene1 lead to 2.95a and 3.02a, respectively, for the resonance energy, giving a = 36 and 35 kcal/mole on comparison with the empirical values. 

The agreement of the two treatments with each other and with the empirical resonance-energy values makes it probable that the point of view presented above regarding the structure of aromatic molecules will not need extensive revision in the future, although it may be subjected to further refinement. 

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