Langevin described a model for the interaction between an ion and a neutral nearly a century ago and since then, many modifications have been introduced to adjust for specific circumstances. This work discusses the induced dipole-induced dipole interaction between an ion and a neutral without a permanent dipole and introduces an anisotropic adjustment. A point polarizable ion model (PPI) and an orientation dependent polarizable ion model (ODPI) are discussed and applied to systems where the ion is highly polarizable and the neutral is only weakly polarizable. with work outlining the attractive potential between a point charge and a point-polarizable neutral. The result was an expression for the collisional rate constant, k L , in terms of a few simple variables; e, the elementary charge, ␣ n , the polarizability of the neutral, and , the reduced mass of the ionneutral pair.The approach is appealing in its simplicity, and has been used as a standard for ion-molecule and ion-atom collisions. This method has been used extensively to calculate collision rate constants in many environments, including the interstellar medium, where atomic hydrogen, molecular hydrogen, and atomic oxygen and nitrogen are the most abundant species.Another major area of work involves the interaction of an ion and a neutral species with a permanent dipole moment. Several approaches have been taken, ranging from an orientation-fixed dipole approximation to orientation-dependent approaches which rigorously conserve angular momentum and energy. These methods have been discussed in detail [2,3]. Additional work in this area involves parameterizing the theory to obtain a solution that is easily accessible to experimentalists [4,5].Deviations from a point charge model have been described by Su et al. [9,10] and an induced dipoleinduced dipole adjustment has been discussed by Su and Bowers [11]. The possibility for large deviation is mentioned with respect to anionic systems, but due to the difficulty of acquiring ionic polarizabilities, only the Cl Ϫ and H Ϫ anions are discussed. These systems afford less than 5% deviation from the classical Langevin rate constants. In this paper we highlight the importance of the anisotropy of the induced dipole-induced dipole interaction and introduce an orientation dependent polarizable ion model. We demonstrate that these interactions, especially when anisotropy is included, have significant impact on the collision rate constants of large molecular cations and anions.
TheoryThe Langevin rate constant is derived from a potential that assumes the ion is a point charge. Two factors, the long-range nature of the potential involving ions and the way in which the random orientation of an ion causes the location of the charge to average to the center, make this approximation accurate in most cases. Deviation can occur, however, in the second of these two factors. If the charge is mobile within the ion, the average location of the charge can shift from the center, effectively increasing the critical impact parameter...