Stress electrostatic contribution

In Equations 2.17-2.19, the Boltzmann factor contains contributions arising from the different interactions considered by the molecular theory. For example, 7t(z) and /(z) represent the repulsive and electrostatic interaction fields at z. It should be stressed that these fields are unknowns for the theory and that they depend on the distribution of all the different species across the film, that is. Equations 2.17-2.19. This has two consequences. First, a self-consistent solving process must be used, which means that simplicity is sacrificed in the theory in order to study the system in all its molecular complexity. Second, their interactions in the system are highly coupled and nonlocal [157]. 

It should be stressed that the analysis presented above is general, and applies to any system. However, for the majority of Van der Waals complexes the electrostatic term E will not be as important as it is for the CO dimer. On the other hand, this analysis shows that any supermolecule method should be applied with great care, and an understanding of the supermolecule results in terms of contributions as defined by the symmetry-adapted perturbation theory is necessary. 

Finally, we feel it is worthwhile to stress one more time the importance of the kinetic inertia in the (reversible) chiral transfer and memory processes of our porphyrin systems. Inertia provides evidence that the system is trapped in an energy minimum. In the above examples the minimum is local the real minimum is that reached from the achiral system whose formation involves the same enthalpic contribution of the chiral one but a more favourable entropic contribution. In particular, the network of electrostatic interactions ensures a quite deep local energy minimum (that is a high value of EA). 

The available data support a mechanism involving catalysis by distortion in which the enzyme binds and stabilizes a transition state that is characterized by partial rotation about the C-N amide bond. The energy that is required to distort this bond out of planarity with the C=0 bond, thereby destroying the resonance stabilization of the amide linkage, is supplied by favorable transition state binding interactions between enzyme and substrate. As Lumry states (1986), mechanical distortion as a source of small-molecule reactivity is attractive as a basis for enzymatic catalysis. It is quite realistic to assume that a distorted substrate will have enhanced reactivity, either because its ground state or the activated complex for its chemical reaction or both are altered by strain and stress in the protein conformation. However, as mentioned previously, this distortion need not be the result of mechanical deformation but could also be the result of desolvation or electrostatic destabilization. In fact, the current data support contributions from all three mechanisms for distortion. 

Stress has been laid on the contribution of Debye and Hiickel (1923) to the development of the theory of ion-ion interactions. It was Debye and Hiickel who ushered in the electrostatic theory of ionic solutions and worked out predictions that precisely fitted experiments for sufficiently low concentrations of ions. It is not often realized, however, that the credit due to Debye and Hiickel as the parents of the theory of ionic solutions is the credit that is quite justifiably accorded to foster parents. The true parents were Milner and Gouy. These authors made important contributions very early in the growth of the theory of ion-ion interactions. 

In our first simple example the electrostatic potential set up by CsCl is almost but not quite a minimal surface [10]. The reason is that the Coulomb electrostatic energy is only a part of the whole electromagnetic field. Two body, three and higher order, non-additive van der Waals interactions contribute to the complete field, distributed within the crystal. This leads one to expect that the condition that the stress tensor of the field is zero, as for soap films, yields the condition for equilibrium of the crystal. Precisely that condition is that for the existence of a minimal surface. Strictly speaking the minimal surface might be defined by the condition that the electromagnetic stress tensor is zero. But in any event, we see in this manner that the occurrence of minimal surfaces, should be a consequence of equilibrium (cf. Chapter 3,3.2.4). Indeed a statement of equilibrium may well be equivalent to quantum statistical mechanics. 

Therefore, if the contributions from the outer electrons to the energy of s, p or d electrons are not very much different - as is expected to be the case if the s, p, d electrons are valence-shell electrons - then the order of penetration MS > np > nd implies an opposite order for the energies ms < np < Md. However, the problem is not as simple as it seems. In particular it should be stressed that the averaged potential energy associated with a given electrostatic interaction depends on the mean of (1/distance) and not on (1/mean distance). In addition, changes in kinetic energy must also be considered (for a recent discussion, see ref. 161 and letters that followed in the 1999 May issue of the Journal of Chemical Education). 

One of the early works on enzyme electrostatics involved a study of CPA (Hayes and Kollman, 1976). These authors stressed the importance of the MEP in understanding enzyme action. They suggested that the electrostatic environmental effects do contribute to the lowering the transition-state energy of the reaction. However, as stressed above, the actual calculations were basically unable to address this issue since they did not consider the protein dielectrics nor the fact that the reaction in solution involves major electrostatic stabilisation (what counts is the difference between the stabilisation in the enzyme and in water). Nevertheless, site-directed mutagenesis experiments have provided strong evidence that electrostatic effects play a major role in the reactions catalysed by carboxipeptidase A. 

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