Ion-dipole energy

Relations between Heats and Cation Radii. For any cation—water pair, the ion-dipole energy should vary inversely as the square of the center-to-center distance between ion and water molecule—i.e., as (+ 1.40)", where Vc is the cation radius in A and 1.40A is taken as the radius of water. Accordingly, correlations might be sought between qn, Qi, or Quo and (r + 1.40)" or Tc. Such plots proved qualitatively the same whether (fc + 1.40)" or was the abcissa. Figures 4 and 5 show several of the observed relations with for zeolites X and Y and for chabazite. 

Salomon have shown that if Verwey s model of cation solvation is considered (see Fig. 2.11.1), then the orientation of a water molecule at the cation is 52° to the radial direction. If anions lie along this direction, then the difference in ion-dipole energy is fie(l — cos S2°)jR which is the term included in eqn. 2.11.25. By fitting the conventional enthalpies to a least square power series... 

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

Ion-dipole interactions interact over longer distances. Their mean interaction energy 0id decreases with r-4 3) ... 

The curve marked ion-dipole is based on the classical cross-section corresponding to trajectories which lead to intimate encounters (9, 13). The measured cross-sections differ more dramatically from the predictions of this theory than previously measured cross-sections for exothermic reactions (7). The fast fall-off of the cross-section at high energy is quite close to the theoretical prediction (E 5 5) (2) based on the assumption of a direct, impulsive collision and calculation of the probability that two particles out of three will stick together. The meaning of this is not clear, however, since neither the relative masses of the particles nor the energy is consistent with this theoretical assumption. This behavior is, however, probably understandable in terms of competition of different exit channels on the basis of available phase space (24). 

A low energy drop-off in the cross-section is also consistent with recent afterglow measurements of the apparent rate constant (4), 3 X 10-12 cc. sec.-1, which is well below the predicted (9, 13) ion-dipole rate, 9.7 X 10-10 cc. sec.-1... 

When the multiplicity of a complex is the same for ionic or ion-dipole bonds and for covalent bonds, the decision as to which extreme bond type is the more closely approached in any actual case must be made with the aid of less straightforward arguments. Sometimes theoretical energy diagrams can be constructed with sufficient accuracy to decide the question. A discussion of crystals based on the Born-Haber thermochemical cycle has been given by Rabinowitsch and Thilo3), and more accurate but less extensive studies have been made by Sherman and Mayer4). 

There is evidence, both experimental and theoretical, that there are intermediates in at least some Sn2 reactions in the gas phase, in charge type I reactions, where a negative ion nucleophile attacks a neutral substrate. Two energy minima, one before and one after the transition state, appear in the reaction coordinate (Fig. 10.1). The energy surface for the Sn2 Menshutkin reaction (p. 499) has been examined and it was shown that charge separation was promoted by the solvent.An ab initio study of the Sn2 reaction at primary and secondary carbon centers has looked at the energy barrier (at the transition state) to the reaction. These minima correspond to unsymmetrical ion-dipole complexes. Theoretical calculations also show such minima in certain solvents, (e.g., DMF), but not in water. "... 

The 3-21+G reaction path to 13 is illustrated in Figure 7 and involves the intermediacy of the ion-dipole complex 12. As shown in Figure 5, the well-depth for 12 is reduced to 14.3 kcal/mol since the chloride ion is kept by the methyl group about 1.5 A farther from the carbonyl carbon than in 9. This interaction energy for Ci" CH3C0Ci compares favorably with the value of 11 kcal/mol estimated by Asubiojo and Brauman from their ICR experiments (4). 

Taking all of these results together, some general patterns emerge. Foremost, the tetrahedral adducts 1 are found to be energy minima when the substituents X and Y are both first-row elements. However, when X and Y are both second-row elements, the tetrahedral species is a transition state and the only minima are ion-dipole complexes, 1. Clearly, two key factors in the formation of the tetrahedral adduct 1 are the difference in gas-phase basicities for the two anions (X" and 1) and the difference... 

A second trajectory was also studied as indicated by the dashed curves in Figure 10. In this case, the OCO angle was fixed at its value of 127 at the transition state for all separations beyond r(C0) - 2.39 A. The more tetrahedral approach corresponds to traditional ideas about approach vectors in addition reactions (33). The ion-dipole minimum no longer occurs for this trajectory, though the energy surface has a relatively flat region between r(C0) - 1.9 and 2.4 A. 

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