Ion-dipole dynamics

Abstract

A unified semi-classical theory applicable to ion-polar molecule reaction kinetics and electron-dipole spectroscopy is presented within a planar ion/ point-dipole model. The forms of the trapped periodic orbits that constitute dividing surfaces between internal and external regions of phase space are determined and their properties are shown to be well represented by a semianalytical adiabatic theory. Subsequent applications of the adiabatic theory to electron-dipole dynamics (a) yield a good approximation to the critical dipole for electron capture and (b) predict an exponential gap law for the excited states of electron/fixed dipole states, in good agreement with recent ab initio calculations. Extension of the theory to include dipoles of finite length, d, provides a correlation of the critical strength with d/I 1/2 where I is the molecular moment of inertia.

Gyroscopic Effect in Low-Energy Classical Capture of a Rotating Quadrupolar Diatom by an Ion

“…〈S cq AC,( (T)〉 ) ∫ S h cq AC,( (E) exp(-E/kT)E dE/(kT) 2 ) for the ion-anisotropically polarizable (anisotropic Langevin) diatom interaction, 29,30 ion-dipolar diatom interaction, 31 and the anisotropic Langevin interaction supplemented with a shortrange repulsion. 32,33 The parameter space of the models studied was not very wide which allowed one to get some analytical insight into the problem.…”

“…This study falls into the category of works devoted to analysis of trajectories in the classical capture for systems with two degrees of freedom. Earlier papers addressed the planar capture for the ion−anisotropically polarizable (anisotropic Langevin) diatom interaction, , ion−dipolar diatom interaction, and the anisotropic Langevin interaction supplemented with a short-range repulsion. , The parameter space of the models studied was not very wide which allowed one to get some analytical insight into the problem. Our paper addresses three-dimensional capture for the charge−quadrupole (cq) interaction under the additional assumption of adiabatic conditions with respect to transitions between rotational states of the diatom.…”

“…In this respect, this paper is complimentary to the earlier ones. [28][29][30][31][32][33] The final expression for the capture rate constant contains, besides the trivial factor (qQ/k B T), three dimensionless parameters: the rotational quantum number of the diatom (in the quantum correction to the classical cq AC rate coefficient), the reduced intrinsic momentum (in the gyroscopic correction to the cq AC rate coefficient), and the reduced strength of the isotropic Langevin interaction (in the Langevin correction to the cq AC rate coefficient). The assumption about the PR approximation, adopted in this paper, can be relaxed within the same formalism, provided that one is prepared to introduce one more parameter, which will include the rotational constant of the diatom.…”

Adiabatic decoupling of the reaction coordinate

“…At large enough values of the separation coordinate r , the neutral fragment undergoes free rotation in the field of the ion. If, furthermore, the total angular momentum is assumed to be zero, the Hamiltonian of a two‐dimensional system writes 25–27 where I denotes the moment of inertia of the neutral fragment and m red is the reduced mass of the ion‐neutral pair. Three commonly used electrostatic potentials have been examined: where q denotes the charge of the ion, μ, the magnitude of the permanent electric dipole of the neutral fragment, θ its orientation, α its polarizability, and Q its quadrupole moment.…”

Adiabatic invariance along the reaction coordinate

“…Using the Jacobi system of coordinates, the interaction between a point particle and a diatomic fragment is represented by the following classical Hamiltonian: 22,27,31 H͑r,p r , ,p ͒ = 1…”