Ion-quadrupole model

Thus, the ion-quadrupole model of ion-solvent interactions predicts that if the experimentally available differences AW. trel) - A/ x-lrel) in the relative heats of solvation of oppositely charged ions or equal raaii r are plotted against (r,. -e r ) , one should get a straight line with a slope -E4A( ZjeoP. From Fig. 2.36, it can be seen that... 

The results of energy partitioning in Li+... OH2 obtained with a number of different basis sets are listed in Table 3. Since intermolecular overlap is small in these kind of complexes (Table 1), we expect the electrostatic model to be a good approximation for classical contributions to the total energy of interaction. Indeed, ZlE cou is to a good approximation proportional to the dipole moment of the water molecule calculated with the same basis set. This can be seen even more clearly in Table 4 where zIEcou is compared with ion-dipole and ion-quadrupole energies obtained from the classical expression of the multipole expansion series 45,95-97) ... 

It can therefore be concluded that by considering a quadrupole model for the water molecule, one can not only explain why oppositely charged ions of equal radius have differing heats of hydration (Fig. 2.32), but can also quantitatively predict the way these differences in the heats of hydration will vary with the radius of the ions concerned. 

Buckingham s attempt to sum all the significant terms in Table 2.11.1 has led to several new approaches to the problem. Buckingham attributed the differences in solvation enthalpies of anions and cations of equal size to the ion-quadrupole interaction energy. Referring to Fig. 2.11.1, Buckingham used models (c) and (d) as the basis of his calculations. 

The motion of ions in a buffer gas is governed by diffusive forces, the external electric field and the electrostatic interactions between the ions and neutral gas molecules. Ion-dipole or ion-quadrupole interactions, as well as ion-induced dipole interactions, can lead to attractive forces that will slow the ion movement, mainly due to clustering effects. The interaction potential can be calculated according to different theories, and three such approaches—the hard-sphere model, the polarization limit model, and the 12,4 hard-core potential model— were introduced here. Under... 

For the Li -H2 system, the Hartree-Fock interaction energy, which includes the effect of overlap forces, becomes comparable to that calculated from a perturbative treatment of the electrostatic (ion-quadrupole) and inductive (ion-induced-dipole) contributions when the interaction energy is O.l eV. In this case, however, the Langevin model may not even be used at thermal energies since the ion-quadrupole interaction energy is comparable to that due to the ion-induced-dipole interaction in the relevant range of separation ( SA). ... 

The Ar2 potential curve is shown in Fig. 21. Considering for the present only the attractive state, the Hartree-Fock interaction energy only becomes comparable to that of the polarization potential when the interaction energy is of the order of 0.1 eV. Once again, such considerations restrict the use of the Langevin model to thermal energies. Here, there is no possible ion-quadrupole contribution and in both these cases, dispersion forces are negligible. 

Both these studies on methane as a target molecule, involving reactive collisions of CH4 and nonreactive collisions of CH5, C2H5, etc., may well provide support for the validity of the Langevin model in this case. While there is no ion-quadrupole term in this system, CH4 possessing no quadrupole moment, it is clear as always that the ion-induced-dipole component is not the only term contributions from the ion-induced-quadrupole term and the dispersion term have been estimated to increase the cross section by... 

While the potential selected for this very simple model is appropriately the simplest, it should be remembered, from the discussion in Section 4.2.1, that it is quite unrealistic, as evidenced by the discontinuity discussed above. Moreover, it should be remembered that, even at those low collision energies when the electrostatic potential is a reasonable approximation for the calculation of close-collision cross sections, the ion-quadrupole potential plays a significant role, the resultant potential exhibiting dramatic differences for the various M,J states of the deuterium molecule rotor. While it would be interesting to explore the effect of employing a more realistic potential in this calculation, such refinements are contrary to the spirit of the model, which enquires how adequate the simplest possible model may be. 

The Born model is only a rough approximation. Improvements of the method take into account a local permittivity e and effective ionic radii fl= a -I- 5 , where Si is the distance between an ion and an adjacent solvent dipole. More elaborate models include in the calculation the energy of formation of a spherical cavity in the pure solvent into which an ion and its solvation shells can be transferred from the vacuum. Further interactions that can be taken into account result from ion-quadrupole, ion-induced dipole, dipole-dipole, dispersion, and repulsion forces. For nonaqueous electrolyte solutions most of the molecular and structural data needed for this calculation of the solvation energy are unknown, and ab initio calculations have not so far been very successful. Actual information on ion solvation in nonaqueous solutions is based almost exclusively on semiempirical methods and/or the extrathermodynamic assumptions quoted in Section II.C. 

In conclusion, it appears that quantitative tests of the electronic distortion model for the quadrupole relaxation resulting from ion-solvent interactions are presently not possible since neither the field gradient nor the correlation time may be reliably estimated. A more fruitful approach of investigating if electronic distortion effects contribute to halide ion quadrupole relaxation at infinite dilution would probably be to test the predicted relationship between... 

No attempts, corresponding to those described above for the alkali halides, have been made to separate the relaxation rates for the alkaline earth halides into ion-ion and ion-solvent contributions and to analyze these in terms of the electrostatic and electronic distortion models of ion quadrupole relaxation. To do so, certain presently lacking information would be needed such as halide ion chemical shift data. It can, however, be said from the well-established structure-stabilizing effect on water of the alkaline earth ions and from studies of water translational [281] and rotational motions [79] in aqueous alkaline earth halide solutions that a modification of the ion-solvent contribution to halide ion relaxation due to the cations is of great importance. In line with this, in their analyses based on the macroscopic viscosity, Deverell et al. [52] found the ion-ion contributions to Br relaxation to be small at least at not too high electrolyte concentration. Such an interpretation is also suggested by the... 

As demonstrated in Ref. [327] both slow overall and fast local motions may, on the basis of an electrostatic model, produce relaxation rates of the observed order of magnitude. It is to be expected that in particular studies of the change in counterion relaxation rate with phase structure and length of the surfactant ion, as well as comparisons between quadrupole splittings and quadrupole relaxation rates, will come to be very helpful in attempts to elucidate the detailed relaxation mechanism in surfactant systems. It can finally be noted that electronic distortion effects on relaxation, as was discussed above for simple halides, have not been considered for halide ion quadrupole relaxation in surfactant systems. It appears that the electronic distortion model (see above) cannot provide a good rationalization of the observations quoted above. 

Different types of interaction exist for sorbate molecules in a micropore. For example, van der Vaals type of interaction or dispersive force, inductive interactions, and electrostatic interactions (e.g., ion-dipole or ion-quadrupole) can exist depending on the nature of the adsorbent surface as well as the physical properties of the adsorbate molecule. For the sake of simplicity, only the van der Vaals type of interaction (computed by LJ equations) have been considered in the HK model. 

The general influence of covalency can be qualitatively explained in a very basic MO scheme. For example, we may consider the p-oxo Fe(III) dimers that are encountered in inorganic complexes and nonheme iron proteins, such as ribonucleotide reductase. In spite of a half-filled crystal-field model), the ferric high-spin ions show quadrupole splittings as large as 2.45 mm s < 0, 5 = 0.53 mm s 4.2-77 K) [61, 62]. This is explained... 

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