Cation interactions

It was pointed out in Chapter II that the Heisenberg exchange Hamiltonian of equation 90, which can be directly related to the Weiss field parameters at T = 0°K by equation 94, is an excellent formal expression for the interactions between atomic spins (or moments) of neighboring atoms. There remains the problem of establishing the various spin-dependent mechanisms that contribute to the Jij. In general, there are two types of interaction cation- -cation and cation-anion-cation (or even cation-anion-anion-cation) interactions. 

With R RC the Coulomb repulsion of the electrons when they are on the same ion is the dominant electron-interaction term, so that the lowest states correspond to an exact number of electrons on each ion rather than to running waves. Although the mutual repulsion of electrons on the same ion prevents the permanent occupation of 

Where s (R, r) and s(R, r) are fermion creation and annihilation operators for an electron spin r at position R or R. The transfer integral is a matrix element connecting one-electron functions  

Anderson (20) has shown that equation 160 reduces to AE = const. + 2I6r-r,12 Sr-Sk  

Physically, the antiferromagnetic character of this superexchange effect follows from the fact that the transfer integrals 6,y carry an electron without change of spin. Since the overlapping orbitals are 

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Low sulfate selectivity of the ion-selective electrodes (ISE) based on lipophilic quaternary ammonium salts (QAS) is usually explained by unfavorable ratio of sulfate hydration and solvation energies. We have been shown that another reason does exist as well namely, low efficiency of sulfate-QAS cation interaction caused by steric hindrance for simultaneous approach of two QAS cations, containing four long-chain hydrocarbon substituents, to sulfate ion. 

Equal amounts of the two crowns were also formed when BU4NOH was used as base, but both rate and yield were considerably reduced. Greene noted that such a template effect would actually involve binding between the open-chained intermediates and cations and these interactions are known to be weak relative to crown-cation interactions. Nevertheless, evidence for such interactions exists (see also Chap. 7) ... 

Figure 10. Adsorbed cation coverage as a function of electrode potential, assuming a cation interaction parameter / = 6.18 The solid line is the steady-state solution, whereas the broken line is the quasi-steady solution. Open circles indicate the unstable area. (From G. L. Griffin, J. Electrochettu Soc. 131, 18, 1984, Fig. 1. Reproduced by permission of The Electrochemical Society, Inc.)...

The proposed intramolecular solvation is not the only feature differentiating between the polystyryl and polymethyl methacrylate salts. The former are classified as the salts of carbanions, whereas the latter are ambident salts having the character of allylic enolates with the cation interacting with the partially negatively charged carbon and oxygen atoms. The degree to which the one or the other interaction is favored is affected by the size of the cation. 

The results obtained by Brutin and Tadrist (2003) showed a clear effect of the fluid on the Poiseuille number. Figure 3.14 shows results of experiments that were done in the same experimental set-up for hydraulic diameters of 152 and 262 pm, using distilled water and tap water. The ion interactions with the surface can perhaps explain such differences. Tap water contains more ions such as Ca +, Mg +, which are 100 to 1,000 times more concentrated than H3O+ or OH . In distilled water only H30 and OH exist in equal low concentrations. The anion and cation interactions with the polarized surface could modify the friction factor. This is valid only in the case of a non-conducting surface. 

XAFS (EXAFS and XANES) methods X-ray diffraction method Biological investigations Flydrolysis of [OrganotinllV)]" Cations Interactions of [OrganotinllV)]" with Biological Molecules... 

Although two closed-shell metal cations with the same charge would normally be expected to repel each other, evidence has been obtained for an entire family of cation-cation interactions in dlh or s2 systems.570 This attraction is now shown to originate from dispersion (van der Waals)... 

Chipot, C. Maigret, B. Pearlman, D. A. Kollman, P. A., Molecular dynamics potential of mean force calculations a study of the toluene-ammonium 7r-cation interactions, J. Am. Chem. Soc. 1996,118, 2998-3005. 

Molecular simulation methods can be a complement to surface complexation modeling on metal-bacteria adsorption reactions, which provides a more detailed and atomistic information of how metal cations interact with specific functional groups within bacterial cell wall. Johnson et al., (2006) applied molecular dynamics (MD) simulations to analyze equilibrium structures, coordination bond distances of metal-ligand complexes. 

The influence of pressure has also been used to tune the ST properties of these ID chain compounds. Application of hydrostatic pressure ( 6 kbar) on [Fe(hyptrz)3] (4-chlorophenylsulfonate)2 H20 (hyptrz=4-(3 -hydroxypro-pyl)-l,2,4-triazole) provokes a parallel shift of the ST curves upwards to room temperature (Fig. 5) [41]. The steepness of the ST curves along with the hysteresis width remain practically constant. This lends support to the assertion that cooperative interactions are confined within the Fe(II) triazole chain. Thus a change in external pressure has an effect on the SCO behaviour comparable to a change in internal electrostatic pressure due to anion-cation interactions (e.g. changing the counter-anion). Both lead to considerable shifts in transition temperatures without significant influence on the hysteresis width. Several theoretical models have been developed to predict such SCO behaviour of ID chain compounds under pressure [50-52]. Figure 5 (bottom) also shows the pressure dependence of the LS fraction, yLS, of... 

The next nearest neighbours to the central M+ are 12 M+ at distance V2r. The repulsive cation-cation interaction term is given as... 

Complex cations interactions) (C5H5)2Rh2Cl2CBi H12 <2Rh-H f M (Ph2PCH2)2CH2Pd (2Pd-H, 2Pd-B)372 ... 

PCTsensors in which the bound cation interacts with an electron-donating group... 

Fig. 10.19. Crown-containing PCT sensors in which the bound cation interacts with the donor group (PCT-1 Bourson J. and Valeur B. (1989) J. Phys. Chem. 93, 3871. PCT-2 and PCT-3 Letard J. F. et al. (1993) Pure Appl. Chem. 65, 1705. PCT-4 Ushakov E. N. et al. (1997) Izv.

In contrast to the above-described systems, there are only few systems in which the bound cation can interact with the acceptor part of charge-transfer probes. The case of coumarins linked to crowns (Figure 10.24) is of special interest because the cation interacts directly with the electron-withdrawing group, i.e. the carbonyl group, in spite of the spacer between the fluorophore and the crown. An important consequence is the increase in stability constant of the complexes with respect to the same crown without external complexing atoms. 

Fig. 10.25. Calixarene-based PCTsensor in which the bound cation interacts with the acceptor group (PCT-22 Leray I. et al. (1999) Chem. Commun. 795. PCT-23 Leray I. et al., Chem. Fur. J. 7, 4590-8).

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