Interaction stabilization energies

Table IV. Interaction Stabilization Energies of Benzoic Acid Dimers (kcal /mole)...

Fig. 9.9 The scheme of defining deformation, interaction, stabilization energies and in complexes...

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. 

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. 

Table IV. Comparison of stability and structure of Ain clusters between ab initio and parameterized interaction results with two- and three-body terms (2+3-b) as well as using only the two-body (2-b) interaction. Binding energies (Dc in eV) per atom, and bond distances (rg in ao) are given...

The behaviour, which is not controlled by the topochemical rule but is greatly influenced by non-topochemical factors, is discussed in Section 2 in terms of molecular mobility, stabilization energy by orbital interaction and energy transfer in the crystals. 

The general relation which must be satisfied in order to bring about an appreciable stabilization energy in the chemical interaction has been given by Eq. (3.20) and Eq. (3.25 b). Such relations frequently provide a selection rule for the occurrence of stereoselective reactions. 

Particular interactions between energy levels could stabilize supra-facial-suprafacial [2+2] concerted reactions, [2.ns- - ig, 57) or supra-facial-antarafacial modes, [2Jts-hn a]- Other interactions might be favorable toward biradical reactions. These diagrams will be discussed in detail in Section VI. 

Solvent interactions with solute molecules are mainly electrostatic and it is usually the differences between the electrostatic stabilization energies of ground and excited states that contribute to the relative intensities and spectral positions of fluorescence in different solvents. 

Of the 17 kcal mol-1 total error, about half is estimated to arise from the single hp— h[ j sigma-type interaction shown in Fig. 2.8, while the remainder arises from weaker pi-type interactions (2-3 kcal mol-1 each). For example, we can carry out a partially localized variational calculation, similar to that described above but with only h prevented from delocalizing into tip (hisleads to a stabilization energy (at 7 = 1.6 A)... 

Equation (2.18) establishes an important relationship connecting E, jJ2) (the stabilization energy) and Q, Jt (the charge transferred) in a general donor-acceptor interaction. Since Ac is typically a large energy separation (of order unity in a.u., 1 a.u. = 627.5 kcal mol-1), we can express this relationship in the approximate form... 

Sigma- and pi-type donor acceptor interactions Further details of the leading hp —hM donor-acceptor interactions are gathered in Table 2.5 and Figure 2.21. For each such interaction the table shows the hybrid form of the donor (hp)23 and acceptor (hM) orbitals, the occupancy of the acceptor, and the second-order estimate (cf. Eq. (1.35) or (2.7)) of the donor-acceptor stabilization energy. Let us now discuss some of the trends displayed in Table 2.5. 

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