Effect of permanent dipole on Langevin cross-section

3 EFFECT OF PERMANENT DIPOLE ON LANGEVIN CROSS-SECTION 

In the Langevin orbiting theory, only the ion-induced dipole interaction was considered as a long-range force operative between the ion—molecule pair. Thus the theory applies only to the reactions of ions with non-polar molecules. In fact, it has been pointed out that some ion—molecule reactions in which the neutral molecule has a permanent dipole have reaction cross-sections greater than those predicted by the Langevin theory [56—63]. Such ion—polar molecule reactions have also been treated classical mechanically by several authors [57, 58, 61, 64—68]. 

The dipole moment Pn interacts with ionic charge according to the potential 

The new problem now is how to obtain the average value of 6. Theard and Hamill [56] and Moran and Hamill [57] first considered these problems in interpreting their experimental data on the reactions in polar systems and used the simplifying assumption that the dipole locks in on the ion with 0 = 0. In this case, the effective potential (eqn. (57)) yields an additional term in the reaction cross-section 

Theory was compared with experimental results on ion—dipolar charge transfer [60, 61] and proton transfer [62, 63] reactions, and was found to predict very satisfactorily the rate coefficients of proton transfer reactions which are considered to proceed by a capture mechanism. The energy dependence of the proton transfer was also correctly represented by the theory. As to the charge transfer reactions, the comparison is difficult because the observed rate coefficients are considerably larger than the capture limit. This is explained by the contribution of a long range electron-jump mechanism to the rate coefficients. Even in this case, however, the trend of the dipole effect is predicted correctly by the theory. 

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