Reaction cross section energy

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. 

Using a guided ion beam instrument the translational energy dependent reaction cross sections of endothemiic fragmentation processes can be detemiined [32]. Modelling these cross sections ultimately yields their energy tln-esholds and a great deal of valuable themiochemical infomiation has been derived with this teclmique. Precision of 0.2 eV can be obtained for reaction tln-esholds. Bimolecular reactions can also be studied and reaction enthalpies derived from the analysis of the cross section data. 

When reaction cross sections are suflSciently large over an extended energy range, the entire depth profile may be obtained using a single incident beam energy. This is referred to as nonresonant profiling. 

Much of the interest of this symposium centers on the effect of the kinetic energy of the reacting ion on the reaction cross-section. A detailed examination of the effect of energy variations is essential to the development of a comprehensive theory for the kinetics of ion-molecule reactions. 

The reaction cross-section should therefore become zero for E Ec. By taking D = 5.0 e.v. and W = 0.5 e.v. for the reactions listed in Table II, the critical energies could be calculated (13,14). 

After identifying the reactant ion, reaction cross-sections were measured as a function of average reactant ion kinetic energy. Q experimental is measured for given values of (eEl) 1/2 in the spectrometer, and experimental values of k... 

Intramolecular isotope effect studies on the systems HD+ + He, HD+ + Ne, Ar+ + HD, and Kr + + HD (12) suggest that the E l dependence of reaction cross-section at higher reactant ion kinetic energy may be fortuitous. In these experiments the velocity dependence of the ratio of XH f /XD + cross-sections was determined. The experimental results are presented in summary in Figures 5 and 6. The G-S model makes no predictions concerning these competitive processes. The masses of the respective ions and reduced masses of the respective complex reacting systems are identical for both H and D product ions. Consequently, the intramolecular isotope effect study illuminates those... 

Reactions of Complex Ions. For reactions of systems containing H2 or HD the failure to observe an E 1/2 dependence of reaction cross-section was probably the result of the failure to include all products of ion-molecule reaction in the calculation of the experimental cross-sections. For reactions of complex molecule ions where electron impact ionization probably produces a distribution of vibrationally excited states, kinetic energy transfer can readily open channels which yield products obscured by primary ionization processes. In such cases an E n dependence of cross-section may be determined frequently n = 1 has been found. 

Rare-Gas-Hydrogen Reactions. Ion-molecule reactions in the rare gas-hydrogen system are of great interest both theoretically and experimentally. The properties of the reactants and products are well known or may be calculated, and the properties of the intermediate three-body complex pose a tractable theoretical problem. Systematic studies of cross-section energy dependence and isotope effects in these systems have been undertaken by Friedman and co-workers (29, 47, 49, 67), by Koski and co-workers (2, 3), and by Giese and Maier (15, 16). 

Gustafsson and Lindholm (19) have shown the effects of translational energy on charge transfer reactions with H2, N2, and CO. They observe that endothermic reaction cross-sections increase with increasing kinetic... 

Subsequently, new PESs were constructed using ab initio calculations of the electronic energy for reactions in the CHj, BePE and NH t systems. In each case, classical mechanics was used to examine the apparent convergence of the reaction cross-sections as a function of the size of the data set. In each case convergence was demonstrated. 

Endothermic Reactions and the Determination of Bond Dissociation Energies for Organometallic Fragments. The reaction of atomic nickel ion with molecular hydrogen to yield NiH+is substantially endothermic. Reaction cross sections for this process, measured using the ion beam apparatus shown in Figure 1, are displayed in Figure 3 for reactions 1 and 2 with HD as the neutral. 

For the potential given by (5.3), it is easy to show that when b > bc the distance of closest approach is bc /21/2, whereas for b < b, the only thing preventing interpenetration is a repulsive core potential, which is not explicitly considered here. Equation (5.4) is actually the classical collision cross section for the problem. To translate this into a reaction cross section, we may assume that there is another critical separation r0 such that when r < rg chemical forces complete the reaction and no reaction takes place if r > rg. If rg is less than b /2m, then Eq. (5.4) is also the reaction cross section, since reaction definitely takes place if b < b. and it definitely does not take place if b > b.. According to this modification, the high-energy limit of the reaction cross section is nr2 rather than zero as given by (5.4). One therefore has... 

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