Nonadditivity of interactions

The methodology is extended accordingly for tetramers and larger complexes. Analysis of extended systems can be simplified by treating a selected group of molecules as one subsystem. For example a hydrated cation (cation plus water molecules) could be treated as one subsystem when evaluating the nonadditivity of interactions in complexes between hydrated cations and base pairs and trimers [13c]. 

The three-body extension of SAPT developed in Ref. 140 has been applied in calculations for the Ar trimer, The nonadditivity of interaction energy has been computed at more than 30 configurations and a functional form has been fitted to those values. This work provided the first complete nonadditive potential for any trimer based on an ab initio calculation which included all major physical components of the nonadditivity. 

Sc, carbon chemical shift, referred to tetramethylsilane (8 = 0) (cf. Sect. I) SCS, substituent-induced chemical shift, or substituent effect difference between S s of a given carbon atom in a monosubstituted and the respective unsubstituted parent molecule (cf. Sect. Ill) NAE, nonadditivity effect nonadditivity of individual SCSs in disubstituted molecules (cf. Sect. IV) ICS, intramolecular-interaction chemical shift = NAE (cf. Sect. IV) A, polarization effect difference in S s of sp2 carbon atoms in a double bond (cf. Sect. IV-C) LEF, linear electric field (cf. Sect. II-B-3) SEF, square electric field (cf. Sect. II-B-3). 

We present here a simple model where long-range and nonadditivity of the correlations can be studied explicitly in terms of the ligand-ligand, and ligand-site interactions. With this model we can clearly see the different behavior of the three models discussed in previous sections and, by generalization, we shall see that the same mechanism applies for correlations between particles in the liquid state. 

Nonadditivity of entropies and free energy for weak interactions,... 

Korona T, Moszynski R, Jeziorski B (1996) Convergence of symmetryadapted perturbation theory expansions for pairwise nonadditive interatomic interactions. J Chem Phys 105 8178-8186... 

The importance of selecting gravimetry instead of volumetry to measure liquid amounts in the pharmaceutical industry of liquid dosage forms is well illustrated by the volume contraction of water-ethanol and volume expansion of ethyl acetate-carbon disulfide liquid mixtures as well as a CS2-ethyl acetate system. The National Formulary (NF) diluted alcohol is a typical example of the volume nonadditivity of liquid mixtures [29], This solution is prepared by mixing equal volumes of alcohol [U.S. Pharmacopeia (USP)] USP and purified water (USP). The final volume of this solution is about 3% less than the sum of the individual volumes because of the contraction due to the mixing phenomenon [1], In addition, molecular interactions of surfactants in mixed monolayers at the air-aqueous solution interface and in mixed micelles in aqueous media also cause some contraction of volume upon mixing [30],... 

The total of all three-body interactions is -3.8 kcal/mol, as compared to -19.2 kcal/mol for the sum of all two-body interactions. When added together, the total of all pairwise and three-body interactions comes within 0.4 kcal/mol of the total interaction energy of -23.4 kcal/mol in the hexamer. With respect to the individual components, there is very little nonadditivity in ES or EX. The total nonadditivity of some 4 kcal/mol is approximately equally divided between POL and CT. 

As long as the two Ar atoms are held in equivalent equatorial positions, the interaction with each of them should, in the pairwise additive approximation, result in the same incremental shifts of the asymmetric stretch of CO2. In reality, a minute nonadditivity of shifts amounting to 0.042 cm-1 was observed by Sperhac et al. when the second Ar atom was added. 

Shimizu S, Chan HS. Temperature dependence of hydrophobic interactions a mean force perspective, effects of water density and nonadditivity of thermodynamic signatures. J. Chem. Phys. 2000 113 4683-4700. 

Harper N, Connor K, Steinberg M, et al. 1995. Immunosuppressive activity of polychlorinated biphenyl mixtures and congeners Nonadditive (antagonistic) interactions. Fundam Appl Toxicol 27 131-139. 

The intermolecular potential in gases is usually assumed to be additive. It has been pointed out, however, that the effect of potential nonadditivity on the equation of state of gases does not seem to be negligible (Kihara9). The simplest system for which the nonadditivity of the intermolecular potential plays a role is the system composed of three spherically symmetric atoms, which will be treated in Sectiqn I. The aim of Sections I. A and I. B is to investigate quantum-mechanically the van der Waals interaction between three distant atoms. By use of the results, a model of nonadditive potential is introduced in Section I. C, which model will be applied, in Part II, to the equation of state of gases. 

Except for H. azteca, lethality was observed at remarkably similar ETNT concentrations for a variety of experimental species and sediment organic carbon content. However, accurate comparisons of the toxicity of TNT-spiked sediments using different sediments and species should take into account the variable relative concentration of parent and transformation products in the different exposure sediments because of potential toxicity differences among compounds and nonadditive mixture interactions. 

We will now examine the major nonadditive components of interaction energy for four different near-equilibrium trimers. These components are displayed in Fig. 33.1. The first observation that can be made is that the ratio of the three-body component to the sum of two-body interactions changes dramatically from system to system from 0.4% for He3 to 16% for the water trimer. The total nonadditive contribution can also be of either sign, even for similar systems like rare gas trimers, cf. He3 v. Ar3. The increased role of nonadditive terms is clearly correlated with the polarity of a system the more polar a system is, the larger are the relative contributions of nonadditive terms with respect to two-body terms. 

As already stated, perturbation theory approach allows the individual components of a TT-body contribution to the interaction energy to be given a physical interpretation. Such a physical interpretation is important for several reasons. First, it allows one to better understand the mechanisms of nonadditive forces. Second, it relates components to monomer properties. Third, it makes possible to propose analytic forms of fitting functions which are the most appropriate for a given type of interactions. 

Let us now return to many-electron systems but before addressing the nonadditivity of electron correlation effects and relativistic effects we need to concern ourselves with the nature of the electron-electron interaction. 

See, for instance C. Biot, R. Wintjens, and M. Rooman, Stair motifs at protein-DNA interfaces Nonadditivity of H-bond, stacking and cation-pi interactions, J. Am. Chem. Soc., 126 (2004) 6220-6221. 

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