Capture Theory Models: An overview of their development, experimental verification, and applications to ion-molecule reactions

Since Arrhenius first proposed an equation to account for the behaviour of thermally activated reactions in 1889, significant progress has been made in our understanding of chemical reactivity. A number of capture theory models have been developed over the past several decades to predict the rate coefficients for reactions between ions and molecules-ranging from the Langevin equation (for reactions between ions and non-polar molecules) to more recent fully quantum theories (for reactions at ultra-cold temperatures). A number of different capture theory methods are discussed, with the key assumptions underpinning each approach clearly set out. The strengths and limitations of these capture theory methods are examined through detailed comparisons between low-temperature experimental measurements and capture theory predictions. Guidance is provided on the selection of an appropriate capture theory method for a given class of ion-molecule reaction and set of experimental conditions-identifying when a capture-based model is likely to provide an accurate prediction. Finally, the impact of capture theories on fields such as astrochemical modelling is noted, with some potential future directions of capture-based approaches outlined.

Adiabatic and diabatic invariants in ion-molecule reactions

A point charge interacting with a dipole (either induced or permanent) constitutes a completely integrable dynamical subsystem characterized by three first integrals of the motion (E, p(phi), and either l(2) or a Hamilton-Jacobi separation constant beta). An ion-molecule reaction (capture or fragmentation) can be seen as an interaction between such a subsystem and a bath of oscillators. This interaction is a perturbation that destroys some of the first integrals. However, the perturbation depends on the separation between the fragments and the destruction is gradual. The mathematical simplicity of the long-range electrostatic interaction potential leads to useful simplifications. A first-order perturbation treatment based on the structured and regular nature of the multipole expansion is presented. The separating integrals valid in the asymptotic limit are found to subsist at intermediate distances, although in a weaker form. As the reaction coordinate decreases, i.e., as the fragments approach, the asymptotic range is followed by an outer region where (i) the azimuthal momentum p(phi) remains a constant of the motion; (ii) the square angular momentum l(2) or the separation constant beta transform into a diabatic invariant in regions of phase space characterized by a high value of the translational momentum p(r); (iii) for low values of p(r), it is advantageous to use the action integral contour integral(p(theta)d theta), which is an adiabatic invariant. The conditions under which an effective potential obtained by adding centrifugal repulsion to an electrostatic attractive term can be validly constructed are specified. In short, the dynamics of ion-molecule interactions is still regular in parts of phase space corresponding to a range of the reaction coordinate where the interaction potential deviates from its asymptotic shape.

Nonadiabatic transitions between lambda-doubling states in the capture of a diatomic molecule by an ion

The low-energy capture of a dipolar diatomic molecule in an adiabatically isolated electronic state with a good quantum number Omega (Hund's coupling case a) by an ion occurs adiabatically with respect to rotational transitions of the diatom. However, the capture dynamics may be nonadiabatic with respect to transitions between the pair of the Lambda-doubling states belonging to the same value of the intrinsic angular momentum j. In this work, nonadiabatic transition probabilities are calculated which define the Lambda-doubling j-specific capture rate coefficients. It is shown that the transition from linear to quadratic Stark effect in the ion-dipole interaction, which damps the T(-1/2) divergence of the capture rate coefficient calculated with vanishing Lambda-doubling splitting, occurs in the adiabatic regime with respect to transitions between Lambda-doubling adiabatic channel potentials. This allows one to suggest simple analytical expressions for the rate coefficients in the temperature range which covers the region between the sudden and the adiabatic limits with respect to the Lambda-doubling states.

Low temperature capture of open shell dipolar molecules by ions: the capture of rotationally selected NO((2)Pi(1/2), j) by C(+)

The low-energy capture of dipolar diatomic molecules in an open electronic state by ions is usually considered to be induced by the first-order charge-permanent dipole interaction with other terms of the long-range potential playing a minor role. If the molecular dipole moment is anomalously small (as is the case for slightly asymmetrical molecules), however, the situation changes, and the capture dynamics is strongly affected by higher orders of the charge-permanent dipole, charge-permanent quadrupole, and charge-induced dipole interactions. The interplay of different terms in the interaction potential manifests itself in complicated temperature dependence of the rotationally state-specific capture rate coefficients. These features of the capture are studied by way of example for NO(X (2)Pi(1/2), j) + C(+) collisions in the temperature range 10(-2)-20 K where the dynamics is adiabatic with respect to rotational and fine-structure transitions and sudden with respect to transitions between Lambda doubling and hyperfine states. The theoretical rate coefficient, which depends on the translational and rotational temperature, agrees with the experimental one measured at T(tr) = 0.6 K and T(rot) = 20 K.

Gyroscopic effect in low-energy classical capture of a rotating quadrupolar diatom by an ion

The low-energy capture of homonuclear diatoms by ions is due mainly to the long-range part of the interpartner potential with leading terms that correspond to charge-quadrupole interaction and charge-induced dipole interaction. The capture dynamics is described by the perturbed-rotor adiabatic potentials and the Coriolis interaction between manifold of states that belong to a given value of the intrinsic angular momentum. When the latter is large enough, it can noticeably affect the capture cross section calculated in the adiabatic channel approximation due to the gyroscopic property of a rotating diatom. This paper presents the low-energy (low-temperature) state-selected partial and mean capture cross sections (rate coefficients) for the charge-quadrupole interaction that include the gyroscopic effect (decoupling of intrinsic angular momentum from the collision axis), quantum correction for the diatom rotation, and the correction for the charge-induced dipole interaction. These results complement recent studies on the gyroscopic effect in the quantum regime of diatom-ion capture (Dashevskaya, E. I.; Litvin, I.; Nikitin, E. E.; Troe, J. J. Chem. Phys. 2004, 120, 9989-9997).