Resonance energy values, table

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 standard enthalpy of formation of C02(g) is—394 kJ mole" , and that of CS2(g) is +115 kJ mole Calculate the enthalpies of formation of the molecules from the monatomic elements (Table V-3). By comparison with the C=0 and C=S bond-energy values (Table V-2), calculate the resonance energy for each of these molecules. (Answer 157, 204 kJ mole". )... 

With this value of Eq we have calculated some theoretical resonance energies. In Table I they are compared with the empirical values. Besides the case of benzene which apparently plays a singular part in the group of aromatic hydrocarbons, the coincidence is very good. This is an astonishing effect because until now caloric and spectroscopic energy values within the Hiickel theory differed by a factor of 3. 

From Table III we see that the difference between the free radical resonance energies of tribiphenylmethyl and triphenylmethyl is 0.07a. Hence X]/X2 = 37 = 2.2 X103. Ziegler and Ewald8 found that at 20°C the value of the dissociation constant for hexaphenylethane in benzene solution is 4.1 X10-4 and consequently we calculate for hexabiphenylethane a value of X = 2.2X103 X4.1 X 10 4 = 0.90. This value is probably too low as the compound is reported to be completely dissociated the error may not be large, however, since a dissociation constant of 0.90 would lead to 91 percent dissociation in 0.05M solution. 

Data are given in Table IV for heterocyclic compounds. For piperidine there is no difference between E and E, showing that the bond energies used are applicable to saturated heterocyclic molecules. Pyridine and quinoline differ from benzene and naphthalene only by the presence of one N in place of CH and, as expected, the values 1.87 v.e. and 3.01 v.e., respectively, of the resonance energy are equal to within 10 percent to the values for the corresponding hydrocarbons. 

The data given in Table VII for the quinones show large extra resonance energies of 0.57 v.e. in quinone, 1.42 v.e. in anthraquinone, and 1.4 v.e. in phenanthraquinone, in addition to the resonance energy of two benzene rings in the last two compounds. These large values we at-... 

In Table III are given calculated values of the resonance energy for straight conjugated chains containing two, three, and four double bonds and a branched chain with three double bonds (the list could be easily extended). In each case the secular equation was solved as a quadratic, all first-excited structures being given the same... 

A corresponding correlation is obtained for the rate constants of a,a -phenyl substituted alkanes 26 (R1 = C6H5, R2 = H, R3 = alkyl) (see Fig. 1 )41). It has, however, a different slope and a different axis intercept. When both correlations are extrapolated to ESp = 0, a difference of about 16 kcal/mol in AG is found. This value is not unexpected because in the decomposition of a,a -phenyl substituted ethanes (Table 5, no. 22—27) resonance stabilized secondary benzyl radicals are formed. From Fig. 1 therefore a resonance energy of about 8 kcal/mol for a secondary benzyl radical is deduced. This is of the expected order of magnitude54. ... 

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. 

Those familiar with the long history of the attacks on the question of the resonance energy of benzene may be somewhat surprised at the small numbers in Table 15.3. The energy differences that are given there are for just the sort of process that might be expected to yield a theoretical value for the resonance energy, but experimental determinations deld numbers in the range 1.7-2.3 eV. This is an important question, which we will take up in Section 15.3, where it will turn out that some subtleties must be dealt with. 

When we look at the energies from Table 15. 10, perhaps the most striking fact is that the correlation energy in the n system makes so little difference in the Ai values. As we indicated above, the experimental value for the resonance energy from heats of hydrogenation is —1.54 eV, in quite satisfactory agreement with the result in Table 15.10. The fact that our value is a little lower than the experimental one may be attributed to the small amoimt of residual resonance remaining in the cyclohexatriene, whereas the isolated double bonds in the experiment are truly isolated in separate molecules. ... 

The Bronsted correlation for five-membered rings shows that effects of structure on reactivity and on acidity are related. Variations in rate constants for quaternization and in pKa values (Table III) are understandable in terms of resonance and inductive effects of the heteroatom X.120 The effects on the energy of a transition state leading to quaternized product are similar but smaller than those on the energy of protonated material. The following considers in more detail the influence of benzo-fusion. 

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