Model of exchange interactions

The analysis of Fig. (5.1) shows that the analytical description of A y may be effectively used for / > 11 a.u. Naturally, for shorter R the analytical values of APg, y are noticeably differ from ab initio values due to exchange interactions appeared in this range. It is also noticeable that the exchange interaction is the most important for the Afi component. Such behavior of Aj is consistent with results of the asymptotic model of exchange interactions for van der Waals complexes [54, 60]. The strong anisotropy of the exchange effects was also observed for the case of collision-induced dipole moments and dipole polarizabilities in ion-atom pairs [61]. 

M.A. Buldakov, V.N. Cherepanov, Asymptotic model of exchange interactions for polarizability calculation of van der Waals complexes. J. Comp. Meth. Sci. Eng. 10, 1-16 (2010)... 

Further development and application of the submolecule model of exchange interaction. 

Buldakov and Cherepanov employed the asymptotic model of exchange interactions to calculate the interaction polarizability of the Fle-Fle, Ar-Ar, Kr-Xe and Xe-Xe systems. The model is valid only for a weak overlap of the valence electrons of the interacting atoms. The authors have derived analytical expressions that take into account induction, dispersion and exchange contributions. The interaction-induced dipole polarizability was calculated for a wide range of internuclear separations. 

Our treatment so far has dealt with non-interacting electrons, yet we know for sure that electrons do interact with each other. Dirac (1930b) studied the effects of exchange interactions on the Thomas-Fermi model, and he soon discovered that this effect could be modelled by adding an extra term... 

The theoretical model [130] was developed as an extension of the classical theory of dipolar broadening in dilute solid solutions in the absence of exchange interactions [16]. It was suggested in [130] how to determine the dipolar part in the line width by subtraction of the calculated input of Heisenberg exchange interaction of pairs of exchange-coupled ions. Equations were written for the three cubic lattices as a function of ion s concentration for various numbers of cationic sites included in a sphere of radius Rc with the assumption that clustering effects were absent. The results were compared well with experimental data on Cr3+ in MgO powders. 

This, in turn, accounts for the deviation from Curie-law behavior in many paramagnetic materials, as described in the last section. Before a discussion on the nature of exchange interactions, a phenomenological model of ferromagnetic behavior by Weiss is presented, which precedes the understanding of its quantum mechanical origin. 

The magnetic properties of Cs4Ni3CdF12 (12R) and Cs5Ni4CdF15 (10H) were shown to agree with a model of exchange-coupled units, on a large temperature scale [3]. The interactions are well-described by the Heisenberg Hamiltonian... 

Fig. 38. Magnetic behavior of Ba2CaCuFe2F14. The theoretical curve for a model of exchange-coupled trimers (5/2-1/2-5/2) is displayed as a dashed line. The decay of x-T observed at low temperature is provided by intercluster interactions...

Chromia gel behaves as a typical paramagnetic substance, the susceptibility of which may be represented by the Curie-Weiss law, with a moderate value for the Weiss constant. This indicates a moderate degree of exchange interaction between adjacent Cr+++ ions, and from this it is possible to deduce a model for the gel which is consistent with the very large specific surface often shown by these substances Chromia gel is thus in sharp contrast... 

The crystal structure of demetallized concanavalin A has been determined, at a resolution of 3.2Observed differences between the native and demetallized proteins have formed the basis for a mechanistic model of the interactions in solution between the two metal-binding sites. Intact sub-units of concanavalin A have been isolated after ion-exchange chromatography of the lectin in the presence of H4-edta. ... 

The Bean-Rodbell model (Bean Rodbell, 1962) adds a phenomenological description of magneto-volume effects to the classical molecular mean-field model of Weiss. The dependence of exchange interaction on interatomic spacing is then considered, taking into account three new parameters fi, which corresponds to the dependence of ordering temperature on volume, and also the volume compressibility, K and thermal expansion ai-The formulation behind the model is as follows ... 

The exponential decay of transfer rate indicates that the exchange interaction is very sensitive to distance. The exchange transfer prefers the nearest or the second nearest D-A pairs. Such a behavior of exchange interaction is similar to the Perrin model, in which the transfer rate is assumed to be constant if A exists within a critical distance and is zero outside the range. This model is thought to be the most applicable to the exchange interaction. In the Perrin model, the steady-state luminescence of D as a function of concentration of A is simply written as [4]... 

It should be noted that the suggested model allowing to take into account the effects related to the overlap of shells of valence electrons is based on the point model of interacting molecules and can be apphed only to small molecules. Such limitation is due to the fact, that the parameters of exchange interaction Pa and p are defined only by the ionization potentials of molecules and take into account neither the form nor the size of interacting molecules. 

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