Non-additivity, interaction

The self-organization may take place with significant interaction non-additivity effects nonlinearity in mathematical terms) that may lead to cooperation in forming the multilevel structure. 

Pauli blockade (p. 722) exchange-deformation interaction (p. 722) interaction non-additivity (p. 726) many-body expansion (p. 727)... 

The third virial coefficient C(7) depends upon tliree-body interactions, both additive and non-additive. The relationship is well understood [106. 107. 111]. If the pair potential is known precisely, then C(7) ought to serve as a good probe of the non-additive, tliree-body interaction energy. The importance of the non-additive contribution has been confimied by C(7) measurements. Unfortunately, large experimental uncertainties in C (7) have precluded unequivocal tests of details of the non-additive, tliree-body interaction. 

Bell R J 1970 Multipolar expansion for the non-additive third-order interaction energy of three atoms J. 

The results obtained demonstrate competition between the entropy favouring binding at bumps and the potential most likely to favour binding at dips of the surface. For a range of pairwise-additive, power-law interactions, it was found that the effect of the potential dominates, but in the (non-additive) limit of a surface of much higher dielectric constant than in solution the entropy effects win. Thus, the preferential binding of the polymer to the protuberances of a metallic surface was predicted [22]. Besides, this theory indirectly assumes the occupation of bumps by the weakly attracted neutral macromolecules capable of covalent interaction with surface functions. 

There has been considerable recent activity developing appropriate parameters to allow semi-empirical methods to describe a variety of biologically important systems, and their related properties, such as (i) enzyme reactivity, including both over- and through-barrier processes, (ii) conformations of flexible molecules such as carbohydrates, (iii) reactivity of metalloenzymes and (iv) the prediction of non-covalent interactions by addition of an empirical dispersive correction. In this review, we first outline our developing parameterisation strategy and then discuss progress that has been made in the areas outlined above. 

Roux, B. 1993. Non-additivity in Cation-peptide Interactions. A Molecular Dynamics and Ab Initio Study of Na+ in the Gramicidin Channel. Chem. Phys. Letters 212,231-240. 

Finally, as shown in Table 13, p for an aromatic ring is also strongly dependent on the other substituents at the double bond it varies from —1.6 to — 5.5 on going from a-methoxystyrenes to stilbenes. This variation, which is related to the well-known non-additivity of multiple substituent effects, and contrasts with what is observed for alkene bromination, is discussed in the next paragraph, devoted to substituent interaction and selectivity relationships in bromination. 

The treatment of non-additivity has also been applied to a large variety of multiple substituent effects on various reactions (Argile et al., 1984) and, in particular, to the bromination of X,Y-disubstituted benzenes where two substituents on the same ring interact strongly (Dubois et al, 1972b) the interaction constant q = — 7.98, associated with a very negative p-value, —12.05, is much higher than those found for the bromination of arylolefins. 

Table 15 Non-additivity of multiple substituent effects p-dependence on X for a substituent Y and interaction constants in arylolefin bromination in methanol at 25°C.

Equations (37)—(39), where the non-additivity of multiple substituent effects is described by a cross-term, express correctly the rate data for bromination and other reactions of polysubstituted substrates. The question arises, therefore has the interaction constant, q, any physicochemical meaning in terms of mechanism and transition state charge To reply to this question, selectivity relationships (42) that relate the p-variation to the reactivity change and not to any substituent constant, have been considered (Ruasse et al., 1984). 

We can also illustrate the interesting non-additivity of multiple donor-acceptor interactions involving the same monomer. For this purpose we consider the ternary NO+(C2H4)2 complex in which two ethylene molecules donate to the same... 

Note that, due to their infinite-range character, pure Coulombic potentials can actually lead to significant bond non-additivity for any proposed separation into bonded and nonbonded units. This reflects the fact that classical electrostatics is oblivious to any perceived separation into chemical units, because all Coulombic pairings (whether in the same or separate units) make long-range contributions to the total interaction energy. 

Fig.Z Adsorption isotherms of the lattice gas model with (a) nearest neighbor attractive interaction, and (b) nearest neighbor repulsion and next nearest neighbor attraction of the same strength. Only 0 < 1/2 is shown because the isotherms are antisymmetric around the point 0 = 0, + e = 0 in this case, (c) Adsorption isotherms of a lattice gas with non-additive interactions with P = 1.5 (cf. text) for fixed reduced temperature, T/T,. Dotted curve describes the two branches 0 of the coexistence curve separating the two-phase region from the one-phase region. Cases (a), (b) are taken from Binder and Landau, case (c) from Milchev and Binder. )...

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