Energy stabilization

Figure 20, The potential surface near the degeneracy point of a degenerate E state that distorts along two coordinates and Q. The parameter is the stabilization energy of the ground state (the depth of the moat ), [Adapted from [70]].

Resonance stabilization energies are generally assessed from thermodynamic data. If we define to be the resonance stabilization energy of species i, then the heat of formation of that species will be less by an amount ej than for an otherwise equivalent molecule without resonance. Likewise, the AH for a reaction which is influenced by resonance effects is less by an amount Ae (A is the usual difference products minus reactants) than the AH for a reaction which is otherwise identical except for resonance effects ... 

In writing the second version of this, the proportionality constant has been set equal to unity as a simplification. Note that the resonance stabilization energy of the reference radical Ri- also cancels out of this expression. 

Each exponential involves the difference between the resonance stabilization energy of the radical and monomer of a particular species. 

We might be hard pressed to estimate the individual resonance stabilization energies in Eqs. (7.23) and (7.24), but the qualitative apphcation of these ideas is not difficult. Consider once again the styrene-vinyl acetate system ... 

Define styrene to be monomer 1 and vinyl acetate to be monomer 2. The difference in resonance stabilization energy ep. - > 1, since... 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Both thermochemical and MO approaches agree that benzene is an especially stable molecule and are reasonably consistent with one another in the stabilization energy which is assigned. It is very significant that MO calculations also show a destabilization of certain conjugated cyclic polyenes, cyclobutadiene in particular. The instability of cyclobutadiene has precluded any thermochemical evaluation of the extent of destabilization. Compounds that are destabilized relative to conjugated noncydic polyene models are called antiaro-maticf ... 

Many completely conjugated hydrocarbons can be built up from the annulenes and related structural fragments. Scheme 9.2 gives the structures, names, and stabilization energies of a variety of such hydrocarbons. Derivatives of these hydrocarbons having heteroatoms in place of one or more carbon atoms constitute another important class of organic compounds. 

Scheme 9.2. Stabilization Energies of Some Conjugated Hydrocarbons"...

It is of interest to consider at this point some of the specific molecules in Scheme 9.2 and compare their chemical properties with the calculated stabilization energies. Benzo-cyclobutadiene has been generated in a number of ways, including dehalogenation of... 

The hydrocarbon phenalene is the precursor of both a highly stabibzed anion and a highly stabilized cation. The Huckel MO diagram is shown in Fig. 9.7. The single orbital at the nonbonding level is the LUMO in the cation and the HOMO in the anion. The stabilization energy calculated for both would be the same and is 0.41/3 by the HMO comparison. ... 

Scheme 9.S. Stabilization Energies and Index of Aromaticity for Heteroaromatic Structures Isoelectronic with Benzene or Naphthalene "...

Table 12.4. Substituent Effects on Radical Stability from Measurements of Bond Dissociation Energies and Theoretical Calculations of Radical Stabilization Energies...

Total radical stabilization energy of 19.8 kcal/mol implies 10 kcal/mol of excess radical stabilization relative to the combined substituents. CH—N(CH3)2 rotational barrier is > 17 kcal/mol, implying strong resonance interaction. 

Table 12.7. Thermochemical Stabilization Energies for Some Substituted Radicals...

According to these data, which structural features provide stabilization of radial centers Determine the level of agreement between these data and the radical stabilization energies given in Table 12.7 if the standard C—H bond dissociation energy is taken to be 98.8 kcal/mol. (Compare the calculated and observed bond dissociation energies for the benzyl, allyl, and vinyl systems.)... 

Let us now turn to the surfaces themselves to learn the kinds of kinetic information they contain. First observe that the potential energy surface of Fig. 5-2 is drawn to be symmetrical about the 45° diagonal. This is the type of surface to be expected for a symmetrical reaction like H -I- H2 = H2 -h H, in which the reactants and products are identical. The corresponding reaction coordinate diagram in Fig. 5-3, therefore, shows the reactants and products having the same stability (energy) and the transition state appearing at precisely the midpoint of the reaction coordinate. 

At best, van der Waals interactions are weak and individually contribute 0.4 to 4.0 kj/mol of stabilization energy. ITowever, the sum of many such interactions within a macromolecule or between macromolecules can be substantial. For example, model studies of heats of sublimation show that each methylene group in a crystalline hydrocarbon accounts for 8 k[, and each C—IT group in a benzene crystal contributes 7 k[ of van der Waals energy per mole. Calculations indicate that the attractive van der Waals energy between the enzyme lysozyme and a sugar substrate that it binds is about 60 k[/mol. 

Both attractive forces and repulsive forces are included in van der Waals interactions. The attractive forces are due primarily to instantaneous dipole-induced dipole interactions that arise because of fluctuations in the electron charge distributions of adjacent nonbonded atoms. Individual van der Waals interactions are weak ones (with stabilization energies of 4.0 to 1.2 kj/mol), but many such interactions occur in a typical protein, and, by sheer force of numbers, they can represent a significant contribution to the stability of a protein. Peter Privalov and George Makhatadze have shown that, for pancreatic ribonuclease A, hen egg white lysozyme, horse heart cytochrome c, and sperm whale myoglobin, van der Waals interactions between tightly packed groups in the interior of the protein are a major contribution to protein stability. 

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