Ion-quadrupole

Note that two distinct types of interactions (ion-quadrupole and dipole-dipole) contribute to an overall R 3 dependence, and the number of distinct multipole types having similar R n dependences continues to increase with increasing n. For uncharged systems, the dipole-dipole interaction (5.23d) is expected to dominate, with an angular term that favors parallel alignment of the two dipoles. 

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) ... 

This question was addressed by use of classical trajectory techniques with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (k ). Over one million trajectories with initial conditions covering a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for are listed in the last column of Table 3 and indicate that reaction (11) for H2/H2, D2/D2, and HD /HD proceeds at essentially the classical collision rate, whereas the reported experimental rates for H2/D2 and D2/H2 reactions seem to be in error as they are significantly larger than k. This conclusion raises two questions (1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K (2) Do conditions exist where the restriction would give rise to observable kinetic effects ... 

Interestingly, for the series of zirconocene catalysts [Zr]+[MeB(C5F5)3] Marks and coworkers [307] have found no evidence of significant aggregation to ion quadrupoles, as in Eq. (21). These authors have found that the tendency to form aggregates of higher nuclearity than simple ion-pairs is dependent on whether the anion is in the inner or outer coordination sphere of the metallocenium cation [308]. 

At increasing salt concentrations the conductance of all solutions investigated shows the emergence of other equilibria involving the ions and ion-pairs triple ions, quadrupoles. .. become stable species. Althought one expects from chemical relaxation theory the appearance of more relaxation processes, experimentally only one relaxation process, whatever the concentration of salt, is observed. This odd behavior is intimately related to the nature of equlllbriun perturbation and observation of the response in the field modulation method. 

In a quadrupole device, not as accurate and precise as double-focusing instruments but fast, a quadrupolar electrical field comprising radio-frequency (RF) and direct-current components is used to separate ions. Quadrupole instruments as mass analyzers are used together with ESI as the ion source the configuration employing a three-dimensional quadrupolar RF electric field (Wolfgang Paul, University of Bonn, 1989 Nobel prize for physics) is referred to as an ion trap analyzer (see below). 

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. 

In solvents of low polarity the formation of triple ions and ion quadrupoles with an increasing concentration of ionic salts has been observed [31]. The conductance versus concentration is a function with a minimum. The increase in conductivity versus concentration (after the minimum) is due to the formation of triple ions by coulombic interaction between ion pairs and ionic species. The equation describing this equilibrium is [32]... 

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. 

Figure 11.56. Block diagram of the ion quadrupole trap apparatus used to detect magnetic resonance and hyperfine spectra of the Hj ion [108].

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)... 

Thequantity Ef represents the energy of interaction between one water molecule and one ion. If, however, four water molecules surround one ion and one considers a mole of ions, the heat change involved in the formation of a primary solvated ion through the agency of ion-quadrupole forces is given by... 

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... 

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)... 

An important point to recall regarding the dissolution of an ionic crystal (Chapter 2) is that ionic lattices consist of ions even before they come in contact with a solvent. In fact, all that a polar solvent does is to use ion-dipole (or ion-quadrupole) forces to disengage the ions from the lattice sites, solvate them, and disperse them in solution. 

Water, it may be recalled (Chapters 2 and 4), has two modes of solvent action, depending on the nature of the added electrolyte. The water can contact an ionic crystal (e.g., NaCl), detach the ions from the lattice through the operation of ion-dipole (or ion-quadrupole) forces, and convert them to hydrated ions (Chapter 2). 

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 ... 

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