Cross sections close-collision

We consider first the question of collision mechanism first, that the calculation of a close-collision cross section places no mechanistic constraints on the ensuing reaction and second, the important corollary that mechanistic statements may not be deduced from the shape of excitation functions. Next, the validity of the potential is examined,f this necessarily setting an upper bound to the energy at which the model may be applied. Various applications of the model are then considered and its success evaluated. Finally, the various explanations which have been advanced to rationalize its failure are discussed. 

Accordingly, the term Langevin cross section or close-collision cross section is to be preferred over such alternatives as capture cross sec-tion or orbiting cross section/ The former, used correctly... 

Fig. 22. Excitation function for the total charge-transfer cross section for the reactants Ar + CH4. Open circles refer to data obtained by the longitudinal tandem/pulsed ejection technique illustrated in Fig. 3. Solid circles refer to data obtained by the single-source impulse technique discussed in Section 3.4.4c. The relative excitation function of Koski is also shown and is normalized to Masson s absolute excitation function at 10 eV. Shown as a dashed line is the close-collision cross section predicted from the Langevin theory.

If the Langevin cross section or any other close-collision cross section is to be used to set an upper bound on the cross section of a charge-transfer reaction, it must be shown, by velocity analysis of the products, or from their angular distribution, that the trajectories responsible did indeed cross the centrifugal barrier. 

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. 

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 potential is constructed using a model which considers the H2 as an atomic ion and the H2 as an atom, to give two potential curves, one attractive and one repulsive (corresponding to the and states of H2 for example). The treatment amounts to approximating H4 hypersurfaces by effective two-body potentials. It is by no means clear to the present author that there can be a repulsive hypersurface of H4 which correlates with the H2- and H2 reactants in their ground electronic states. If there is not, the contributions to chemical reaction from this repulsive state is a fiction. If there is, this has profound implications for the calculation of close-collision cross sections for such systems using models for the interparticle potential (see Section 4.2.1c). 

Use of electrostatic potentials to calculate close-collision cross sections is a gross oversimplification, particularly at suprathermal energies (Section 4.2). Rather, this must be approached using trajectory studies over potential hypersurfaces. Information about these hypersurfaces is beginning to appear, both from ab initio calculations and nonreactive scattering studies. 

A low ion pair yield of products resulting from hydride transfer reactions is also noted when the additive molecules are unsaturated. Table I indicates, however, that hydride transfer reactions between alkyl ions and olefins do occur to some extent. The reduced yield can be accounted for by the occurrence of two additional reactions between alkyl ions and unsaturated hydrocarbon molecules—namely, proton transfer and condensation reactions, both of which will be discussed later. The total reaction rate of an ion with an olefin is much higher than reaction with a saturated molecule of comparable size. For example, the propyl ion reacts with cyclopentene and cyclohexene at rates which are, respectively, 3.05 and 3.07 times greater than the rate of hydride transfer with cyclobutane. This observation can probably be accounted for by a higher collision cross-section and /or a transmission coefficient for reaction which is close to unity. 

For applications where IM is used to obtain structural information about the ion, such as those in structural proteomics and biophysics, the IM separations are performed using weak electrostatic fields ca. 20-30 V cm torr ). Provided the field strength is sufficiently weak, or under so-called low-field conditions, a closed equation for the ion-neutral collision cross section can be expressed from the kinetic theory of gases see Note 1). When the IM separations are performed in low-field conditions, i.e., constant 7C, the mobility is related to the collision cross section of the ion-neutral pair ... 

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