Ion-quadrupole interactions

It should be emphasized that none of the methods in categories (ii) and (iii) that have been used to obtain the absolute enthalpies of hydration of ions is theoretically rigorous. For example, Conway and Salomon (54) have made a detailed critique of the Halliwell—Nyburg type of treatment. If the water dipole orientation is not exactly opposite at cations and anions, as seems to be indicated by various previous calculations (55, 56), then the assumption that the difference between heats of hydration of cations and anions of the same radius originates from the ion-quadrupole interaction could be inaccurate. However, the results given in Table 7 are probably reliable to within a few kcal mole-1, despite the fact that it is impossible to assess their accuracy specifically. They indicate that an anion has a more negative absolute heat of hydration than a cation of the same crystal radius. 

For monopositive ions and the gases Ar, H2, 02, N2, and C02, the second term is between 18 and 60% as large as the first, which corresponds to the ion-induced dipole interaction. For bipositive ions, the contribution of the second term is only 5 to 15% that of the first. Thus, although the ion-quadrupole interaction is not negligible, it is small compared with the total. The pure quadrupole-quadrupole interaction is of course a much smaller contribution. The absolute maximum magnitude of the second term above is about 1300 cal. per mole for any of the above combinations (C02 and Li+) and the minimum value is about 700 cal. per mole (H2 and K+). 

For argon-Ca+2, the only case to be considered in the present study, the appropriate value of field-quadrupole interaction is approximately 1300 cal. per mole, but the ion-induced dipole-ion field interaction is nearly 6000 cal. per mole, the sum of both being directly comparable with the value derived earlier for this pair from the Kirkwood-Miiller expression. Since one may resort to complex reasoning for interpretive purposes only if a rationale cannot be achieved with simple truths (12), it is evident that we cannot a priori use the ion-quadrupole interaction to explain the results. 

AG (H ) or AG (C1 ). Later on, Alfenaar and de Ligny determined the non-electrostatic contribution to AG from the solubilities of analogous uncharged species of the same radius (as e.g. noble gases) and extrapolated the free energy of transfer of an electrolyte conected by the non-electrostatic contribution of the variable counterion as function of the reciprocal radius to r = 0. The authors attempted, furthermore, to improve the method by adding to the electrostatic and non-electrostatic terms of AG further terms proportional to r and which account for ion-dipol and ion-quadrupole interactions ... 

What is the expression for the energy of interaction between an ion of charge ZjCo and a quadrupole The derivation of a general expression requires sophisticated mathematical techniques, but when the water molecule assumes a symmetrical orientation (Fig. 2.35) to the ion, the ion-quadrupole interaction energy can easily be shown to be (Appendix 2.3)... 

Instead of presenting a sophisticated general treatment for ion-quadrupole interactions, a particular case of these interactions will be worked out. The special case to be worked out is that corresponding to the water molecule being oriented with respect to a positive ion so that the interaction energy is a minimum. 

The ion-quadrupole interaction energy is simply given by the charge on the ion times the potential v r at the site of the ion due to the charges of the quadrupole. 

When an comes in contact with water molecules, its ion-quadrupole interaction energy is -394.6 kJ mol . Calculate the quadrupole moment of water (r = 138 pm, rp- = 136 pm,n =. i D). (Contractor)... 

The interaction of the carbon dioxide molecule with the sieve includes electrostatic, induction, dispersion, and repulsion contributions. The CO2 molecule was assumed to be capable of free rotation, so that the directional interactions could be averaged over all orientations using a Boltzmann weighting factor (JJ) this causes the electrostatic ion-quadrupole interaction to depend on the temperature. Mean values were used for the polarizability (a), the diamagnetic susceptibility (x), and the equilibrium radius of the CO2 molecule. Using vector summation for the total electric field at the CO2 molecule, the total potential, c(r), at a given position r is given by ... 

The above description disregarded the possible role of quadrupole moments. These are often consid ied small and n Ugible. While this is almost certainly so for quadrupole-quadrupole interactions, dipole-quadrupole and ion-quadrupole interactions mi t be appredable. Terms like —Cj/r and can be added to... 

The other limiting case of the interaction liierarchy 6 Uo between the fine splitting of atom levels and ion-quadrupole interaction potenticil leads to the (juasimoleculc quantum numbers JMj, where M is the projection of the atom angulcir momentum onto the qua.simolecule axis. In this limiting case formula (22) for the ion-atom exchange interaction potential takes the form for the process (28)... 

Schwabacher et al. have studied the directionality of the cation-tr effect by measuring the association constants of guests of various sizes with cationic and anionic water-soluble macrocycles (Figure 103) [133]. These studies have provided support for ion-quadrupole interactions contributing to the binding in the anionic host. 

Evaluations of both contributions yield values of the same order of magnitude, i.e. several hundreds of kJ mole . For an exact evaluation some further contributions must be considered, namely the ion quadrupole Interaction and an additional ion dipole interaction induced by the electric field of the ion. Further details of these derivations are given in ref. [2]. 

Ion-quadrupole interactions vary with the inverse eighth power of the separation distance and the quadrupole-quadrupole interactions vary with the inverse tenth power of the separation distance. The effect of quadruple moments on thermodynamic properties is already much less than that of dipole moments and the effect of higher multipoles is usually negligible. In general, neither ion-dipole nor dipole-dipole forces can produce long-range alignment effects in liquids. 

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. 

DeLigny and Alfenaar - suggested that the extrapolation based on eqns. 2.11.32 and 2.11.33 could be improved by considering the neutral part of the free energy of transfer. They also attempted to account for ion-dipole and ion-quadrupole interactions by use of the relations... 

In addition to the diffusive forces and effects of an external electric field mentioned, ion motion in an IMS drift tube is affected by the electrostatic interactions between the ion and the gas molecules of the supporting atmosphere. The electron cloud surrounding the neutral gas molecule is polarized by the ion, thus inducing a dipole moment in the neutral molecule. This results in an electrostatic interaction between the ion and the neutral molecule the ion-induced dipole effect. Furthermore, molecules that have permanent dipole or quadrupole moments will be attracted to the ion through ion-dipole or ion-quadrupole interactions. 

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). ... 

For the current discussion, RVS analysis has been carried out on cation-jt complexes of benzene-metal complexes. An overview of the results obtained for the RVS analysis carried out at the HF/6-31G level on the cation-jt complexes of benzene with monovalent and bivalent metal ions such as LP, Na, K, Mg and Ca + is presented in Figure 15.5. Generally, cation- t complexes are held by pure electrostatic effects due to strong attraction between opposite charges. Hence, bivalent metal ions show stronger interaction than the monovalent metal ions. However, the contribution of ion-quadrupole interactions in complex stabilization is still being... 

Sorption affinity of fluid components with molecular sieves is governed by the type of their mutual interactions, i.e., fluid-solid interactions, on the microphysical level. For the sorption systems given, besides van der Waals-type atom-atom dispersion interactions of all types of molecules involved, with the solid, zeolitic ion-dipole interactions for H2O, H2S and COS as well as zeolitic ion-quadrupole interaction for CO2 have to be taken into account. A measure of the overall strength of interaction energy is the isosteric heat of sorption, qisosteric-This quantity differs from the differential heat of sorption or sorption enthalpy, - AH, usually measured calorimetrically, by the mechanical work term, RT qisosteric AH -t RT. 

The temis on the left-hand side correspond to neutral species, and hence are available from measurements, and those on the right-hand side pertain to the ion-dipole and ion-quadrupole interactions. Plots of the left-hand side against extrapolated to infinitely large ion size, although not linear (due to the br term), then yield 2 H (Na, W S) as the ordinate intercept. 

The reaction is, however, much more complex. It turns out that the ion-quadrupole interactitMi is the most important term in the long range potential, especially at low temperatures, where the variational transitimi state occurs at large intemuclear separations [15], Assuming that only the ion-quadrupole interaction is important, Klippenstein et al. [15] showed that the rate coefficient is given by ... 

Also, neutral species can possess a sizable electric quadrupole moment (similar to a dipole but involving the spatial arrangement of four charges) so ion-quadrupole interactions can be significant. Su and Bowers introduced the average quadrupole orientation (AQO) formalism to describe these cases. 

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