Ion-induced dipole potential

N2 - NO+ + N, compared with a theory (7) based on classical trajectories subject to an ion-induced dipole potential. The assumptions involved in calculating the measured cross-sections are noted in the text... 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

Early attempts to describe bimolecular gas phase ion-molecule reactions were based on the classical collision dynamics of a point charge and a structureless polarizable neutral molecule. The collision process is dominated by the long range attractive ion-induced dipole potential V(r) given by (16),... 

We consider the so-called Langevin model for ion-molecule reactions. An ion and a neutral non-polar molecule interact—at large distances—through an ion-induced-dipole potential... 

An application of the phase-space model to four bodies has been made by Wolf and Haller (1970). They treated reactions of type A2 + A2, i.e. cases where exchange resonance may arise. Introduction of a resonance potential to describe charge transfer in the reactant channel led to a relative increase of the non-reactive cross seection, compared with that expected from using only ion-induced dipole potentials. 

A different model, also for ion-reactions, has been proposed by Gislason (1972). It applies to (ArH2)+, for which the surfaces of Ar+(2P1/2 3/2) + H2 and of Ar + H2 (u) are assumed to cross at large distances, where they are given by ion-induced dipole potentials. Cross sections at various energies are expressed in terms of the crossing radius and the radii of Langevin s theory of ion-reactions. 

Fig, 3, Various trajectories of ions under the ion-induced dipole potential as a function of impact parameter 6 at a constant velocity u. 

At the simplest level, it is assumed that a necessary and sufficient condition for reaction is that the colliding reactants must surmount the centrifugal barrier in the effective radial potential. A model for the ion-molecule potential must then be assumed when that chosen is the ion-induced-dipole potential, this approach yields, of course, the familiar Langevin model. ... 

The significance of (36) is that, if it can be established that the ion-induced-dipole potential is an accurate representation of the ion-neutral potential for a range of separation R < r < oc, then K (R) is the upper energy limit above which the model may not be applied. 

Fig. 21. Hartree-Fock potential energy curves calculated for the Ar2 system. The ion-induced-dipole potential is shown for comparison.

The isotropic ion-induced-dipole potential discussed in the previous section is of course the simplest form of the potential to use in the computation of close-collision cross sections. Various refinements to this are considered next. 

To seek to explain the rates of ion-dipolar molecule reactions in terms of close-collision cross sections computed from the ion-dipole and ion-induced-dipole potentials, attention must be directed to rate data obtained at thermal energies. Further, Hyatt and Stanton s theoretical studyS indicate that such a description may be a gross oversimplification for linear dipolar molecules. Thus, consideration is given here to symmetric-top or quasisymmetric-top molecules. Two pairs of examples are considered, each exhibiting a different behavior. 

The extensive use by Dugan and Magee of trajectory calculations to compute close-collision cross sections for the collision of ions with polar molecules has been reviewed in Section 4.2.2d. For such calculations, a form for only the attractive part of the potential need be assumed and, in this case, a particular value of the ion-molecule separation was used to define a close collision. The form chosen for the potential was the simple, anisotropic, electrostatic ion-dipole potential plus the ion-induced-dipole potential and, for reasons discussed in that section, such a model may only be applied to ion-molecule collisions at thermal energies. 

Their model is simple enough to be tractable, yet realistic enough to be a reasonable approximation to the physical situation. The system chosen was the reaction of Ar" with H2, D2, and HD. The model is as follows. The reactants approach under the influence of the ion-induced-dipole potential during the collision, the ion and each atom are treated as hard spheres the argon hydride ion is deemed to have been formed if the relative translational energy between the two nuclei is less than the bond dissociation energy finally, the products separate subject to the relevant ion-induced-dipole potential, t... 

Ref. 272. Identical results were obtained for both the ion-induced-dipole potential and the resonance potential (see text). 

Wolf and Haller/ These authors have made the only attempt to date to use a more realistic potential than that of the ion-induced-dipole potential—a welcome development in view of the inadequacy of the latter (Section 4.2.1). Their success in predicting an excitation function which agrees so well with experiment (Fig. 6) is impressive. Nevertheless, there are three aspects of this comparison which raise serious doubts as to the validity of the comparison. These are now discussed below. 

There are two possible origins of the excess product velocity. One derives from the long-range, attractive, ion-induced dipole potential. The other results from short-range forces which would have the effect of repelling the products away from each other (or of attracting them, thus actually reducing their velocity). 

Contour maps for the angle-velocity flux of ArD+ produced in this reaction have been computed on the basis of a highly approximate potential-energy surface. The model treats Ar+ as a hard sphere and Dg as a pair of hard spheres nearly in contact. The relative motion prior to Ar -Da collision is governed by the ion-induced-dipole potential between Ar+ and D2. During collision the ion and each atom are treated as hard spheres. An ArD+ ion is presumed to have formed if the relative translational energy of the nuclei is less than the bond dissociation energy. As the products... 

The ion induced-dipole potential and the corresponding Langevin rate expression have proven to be of great value in the interpretation of numerous studies of ion-molecule reaction kinetics (see chapters 2 and 3 by Canosa et al, and by Gerlich). For neutral reactions, a f/i potential, which can be taken to represent dispersion and/or dipole induced-dipole interactions, has provided a similarly important reference potential. The Gorin model, which is based on PST like assumptions for this potential, provides a simple expression for the capture rate ... 

---