Nonadditive effects

LarA68 Larsen, A. H., Pings, C. J. Counting graphs of interest in statistical mechanics including nonadditivity effects. J. Chem. Phys. 49 (1968) 72-80. 

Caldwell, J.W. and Kollman, P.A. (1995). Cation-7t interactions nonadditive effects are critical in their accurate representation. J. Am. Chem. Soc. 117, 4177-4178... 

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). 

This approach is admissible because SCSs are well known to be additive unless (i) the conformational equilibrium of the molecule is altered by progressive substitution, and/or (ii) there is no intramolecular substituent interaction whatsoever. Thus, if application of eq. [18] to a rigid molecular system affords ICS values other than zero, such an interaction must exist. In earlier publications (216,221) the abbreviation NAE (nonadditivity effect)—a merely descriptive term—was employed. 

Geminal substituents in multiply substituted compounds present the situation of closest mutual proximity. For that reason it is often difficult, if not impossible, to separate steric from electronic contributions to nonadditivity effects (NAEs, ICSs). A predominance of steric contributions to the ICS is expected when at... 

In two-site systems, there is only one correlation function which characterizes the cooperativity of the system. In systems with more than two identical sites, for which additivity of the higher-order correlations is valid, it is also true that the pair correlation does characterize the cooperativity of the system. This is no longer valid when we have different sites or nonadditivity effects. In these cases there exists no single correlation that can be used to characterize the system, hence the need for a quantity that measures the average correlation between ligands in a general binding system. There have been several attempts to define such a quantity in the past. Unfortunately, these are valid only for additive systems, as will be shown below. 

Factorial designs, in which n chemicals are tested at x dose levels (x treatment groups) have been suggested by the US-EPA (US-EPA 1986) as a statistical approach for risk assessment of chemical mixmres. A 2 factorial design has been used to describe interactions between the carcinogenic activity of five polycyclic aromatic hydrocarbons at two dose levels (Nesnow 1994) and a 5 design to identify nonadditive effects of three chemicals on developmental toxicity at five dose levels (Narotsky et al. 1995). 

In a three-atom clusters, the nonadditive effects are completely described by the 3-body forces. 

TABLE 1. Summary of the supermolecular calculations of the nonadditive effects around the three equilibrium He2Br2 structures. Energy is in cm and distances in A. 

Chalasinski G, Cybulski SM, Szczesniak MM, Scheiner S (1989) Nonadditive effects in HF and HC1 trimers. J Chem Phys 91 7048-7056... 

And, admitting some additional complexities and nonadditivity effects ... 

An opposite situation arises for a collinear form. Orthogonalizing two monomers gets in the way of orthogonalizing the third monomer. Instead of cooperating, the monomers now compete. Eventually, the net repulsion is larger than the sum of all three pair repulsions. The nonadditive effect is repulsive. 

In this cluster the three-body effect was detected via the observation of the asymmetric stretching frequency of CO2 by Sperhac et al. [82]. Recent ab initio calculations confirmed the experimental predictions [83], The exciting aspect of this cluster is that the nonadditive effect on the stretching frequency may be obtained directly with a very good accuracy. The reason is the well defined structure of the A CC cluster, shown in Fig.l 1... 

Besides the initial object of CARS as a tool for the determination of molecular energy levels and its application to combustion studies and related areas, there are several other scientific applications of academic interests. These include spectral lineshape studies, collisional effects, Dicke narrowing, nonadditivity effects, and motional narrowing. CARS turned out to be an excellent method for these studies (Berger et al., 1992 and references therein). 

It is concluded that total nonadditive effects are dominated by SCF terms, which are directly attributed to electric polarization. However, since the polarization is constrained by the Pauli exclusion principle, classical models which neglect exchange phenomena may incur certain errors, especially in regions of strong overlap between electron clouds of the monomers. Correlation contributions to nonadditivity do appear small enough that they can be safely ignored, with efforts better concentrated on an accurate portrayal of the SCF phenomena. 

Tachikawa, M., and Iguchi, K., Nonadditivity effects in the molecular interactions ofH O and HF trimers by the symmetry-adapted perturbation theory, J. Phys. Chem. 101, 3062-3072... 

It was established that the use of diffusion vortex affecting on heterogenous system, composed from a liquid medium and composite sorbing materials allows to reach nonadditive effect it lies in abnormal raise of an extent of hydrocarbon fuel purification from admixtures, as in case of a stream passage through fixed sorbent layers, as in case as sorbent of composition mixture each component separately. 

Nonadditive effects are characteristic for the processes of water purification from oil (Fig 3) and benzene [S], also hydrocarbon fuel from toxic admixtures [6] (Fig.4 ). 

The nonadditivity effect of the introduction of a-benzyldioximate fragments instead of dimethylglyoximate ones in the NMR spectra of the Ca-nonsymmetric mixed a-benzyldioximate-dimethylglyoxi-mate complexes was clearly observed the introduction of the first fragment increases chemical shifts of the methyl protons by approximately 0.2 ppm, while the appearance of the second diphenyl chelate ring increases the shifts by only 0.06 ppm (Table 17) [64]. 

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