Resonance energies constants

Resonance energies of ca. 90, 182 and 330 kJ moF have been estimated for pyrrole, indole and carbazole respectively by comparing their protonation constants with those for selected model compounds (72C1(L)335, 72TL5019). 

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. 

The discussion in section (c), page 373, regarding the quantitative agreement of the calculations with experiment has to be altered somewhat in accordance with the corrected values of the free radical resonance energies. The calculated dissociation constant of hexabiphenylethane now becomes... 

By equating to zero the differential of this with respect to r, we find the equilibrium distance as a function of x and the ratio of force constants C2/C1. For Q/Ci = 3, r2 = 1.34, and f = 1.54, this function is that given by Equation 1. The value 3 for the ratio of force constants is somewhat larger than that indicated by Badger s rule, which is about 2.3 it is probable that this increase is needed to compensate for the neglect of resonance energy in the assumed potential function. 

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. ... 

Equations such as this were normally solved by graphing before the days in which a calculator removed the need for such tedious techniques. Using numerical techniques, the roots can be found to be x = — 2.55, —1.15, —0.618, 1.20, and 1.62. The three lowest energy states are populated with six electrons (nitrogen is presumed to contribute two electrons to the bonding). Therefore, the resonance energy is 6a + 7.00/3 — (6a + 8.64/3) = - 1.64/3. After the constants ax. .. as are evaluated, the wave functions can be shown to be... 

The presence of the electron acceptor site adjacent to the donor site creates an electronic perturbation. Application of time dependent perturbation theory to the system in Figure 1 gives a general result for the transition rate between the states D,A and D+,A. The rate constant is the product of three terms 1) 27rv2/fi where V is the electronic resonance energy arising from the perturbation. 2) The vibrational overlap term. 3) The density of states in the product vibrational energy manifold. 

The definition used depends on the phenomenon under study. For instance, the intensity-averaged lifetime must be used for the calculation of an average colli-sional quenching constant, whereas in resonance energy transfer experiments, the amplitude-averaged decay time or lifetime must be used for the calculation of energy transfer efficiency (see Section 9.2.1). 

The Forster resonance energy transfer can be used as a spectroscopic ruler in the range of 10-100 A. The distance between the donor and acceptor molecules should be constant during the donor lifetime, and greater than about 10 A in order to avoid the effect of short-range interactions. The validity of such a spectroscopic ruler has been confirmed by studies on model systems in which the donor and acceptor are separated by well-defined rigid spacers. Several precautions must be taken to ensure correct use of the spectroscopic ruler, which is based on the use of Eqs (9.1) to (9.3) ... 

Very large rate constants have been found for near resonant energy transfer between infrared active vibrations in CO2 Such near-resonant transitions and their dependence on temperature have also been studied for collisions between vibrationally excited CO2 and other polyatomic molecules as CH4, C2H4, SF et al. The deactivation cross-sections range from 0.28 for CH3F to 4.3 for SFs at room temperature, and decrease with increasing temperature. 

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. 

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