I. Litvin

Low-temperature behavior of capture rate constants for inverse power potentials

The energy dependence of the capture cross section and the temperature dependence of the capture rate constants for inverse power attractive potentials V∝−R−n is considered in the regime where the quantum character of the relative motion of colliding partners is important. For practically interesting cases n=4 and n=6, a simple formula for the cross section is suggested which interpolates between the classical and the quantum Bethe limits. We have shown that the classical approximation for the capture cross section performs well far below the simple estimations of the onset the quantum regime. This seemingly “classical” feature of the cross section and the rate constant is due to the large quantum effects of the waves in transmission through and reflection above the centrifugal potential barriers.

Electron capture by polarizable dipolar targets: Numerical and analytically approximated capture probabilities.

Numerically accurate and analytically approximated partial wave probabilities for the capture of a charged particle by a stationary polarizable dipole are presented over wide ranges of collision energies. The results facilitate the analysis of electron-molecule attachment in terms of capture rates, contributions from electron-phonon coupling, and kinetic properties when metastable anions are formed.

Rates of complex formation in collisions of rotationally excited homonuclear diatoms with ions at very low temperatures: Application to hydrogen isotopes and hydrogen-containing ions

State-selected rate coefficients for the capture of ground and rotationally excited homonuclear molecules by ions are calculated, for low temperatures, within the adiabatic channel classical (ACCl) approximation, and, for zero temperature, via an approximate calculation of the Bethe limit. In the intermediate temperature range, the accurate quantal rate coefficients are calculated for j = 0 and j = 1 states of hydrogen isotopes (H2, HD, and D2) colliding with hydrogen-containing ions, and simple analytical expressions are suggested to approximate the rate coefficients. For the ground rotational state of diatoms, the accurate quantal rate coefficients are higher compared to their ACCl counterparts, while for the first excited rotational state the reverse is true. The physical significance of quantum effects for low-temperature capture and the applicability of the statistical description of capture are considered. Particular emphasis is given to the role of Coriolis interaction. The relevance of the present capture calculations for rates of ortho-para conversion of H2 in collisions with hydrogen-containing ions at low temperatures is discussed.

Locking of the intrinsic angular momentum in the capture of quadrupole diatoms by ions.

The capture dynamics of rotationally polarised homonuclear diatoms in low-energy collisions with ions is studied theoretically. The interaction potential includes charge-quadrupole and charge-induced dipole terms. The former, taken in the perturbed rotor approximation, exhibits an R −3 anisotropic dependence and causes an only gradual locking of the intrinsic angular momentum of the diatom to the collision axis. As a result, the capture occurs in a regime of incomplete locking, and the passage over centrifugal barriers is accompanied by considerable gyroscopic effects. The j-specific capture cross-sections for rotationally-aligned diatoms show a marked dependence on the polarisation state which is not described by the conventional adiabatic channel model. The latter, however, provides a fair approximation for the cross-sections of unpolarised diatoms. These features are due to a considerable angle of rotation of the collision axis before the barrier is reached and to a small angle of rotation during the passage across the barrier. The numerically determined, scaled, capture cross-sections are represented by an approximate analytical expression that interpolates between two limiting cases, very small (adiabatic channel model) and very large (fly-wheel model) gyroscopic effects of the rotating diatom.

Quantum scattering and adiabatic channel treatment of the low-energy and low-temperature capture of a rotating quadrupolar molecule by an ion

The capture rate coefficients of homonuclear diatomic molecules (H(2) and N(2)) in the rotational state j=1 interacting with ions (Ar+ and He+) are calculated for low collision energies assuming a long-range anisotropic ion-induced dipole and ion-quadrupole interaction. A comparison of accurate quantum rates with quantum and state-specific classical adiabatic channel approximations shows that the former becomes inappropriate in the case when the cross section is dominated by few partial contributions, while the latter performs better. This unexpected result is related to the fact that the classical adiabatic channel approximation artificially simulates the quantum effects of tunneling and overbarrier reflection as well as the Coriolis coupling and it suppresses too high values of the centrifugal barriers predicted by a quantum adiabatic channel approach. For H2(j=1)+Ar+ and N(2)(j=1)+He+ capture, the rate constants at T-->0 K are about 3 and 6 times higher than the corresponding values for H2(j=0)+Ar+ and N(2)(j=0)+He+ capture.

Quantum and Classical Fall of a Charged Particle onto a Stationary Dipolar Target

The quantum dynamics of the fall of a charged particle (i.e., the capture of a charged particle) onto a stationary dipolar target is considered. Extending previous approaches for the calculation of rate coefficients in the lowest channels, we now determine rate coefficients for all channels until the quantum rate coefficients converge to their classical counterpart. The results bridge the gap between the capture of light particles (electrons) and heavy particles (ions) in the limit of sudden dynamics, when the collision time is short in comparison to the rotational period of the molecular target. The quantum-classical correspondence is discussed in terms of semiclassical numbers of channels which are open for capture in effective potentials formed by charge-dipole attraction and centrifugal repulsion. The quantum capture rate coefficients are presented through classical rate coefficients and correction factors that converge to unity for high temperatures and whose behavior at ultralow temperatures, for not too small values of the dipole moment, is determined by semiclassical numbers of capture channels.

Mutual Capture of Dipolar Molecules at Low and Very Low Energies. II. Numerical Study

The low-energy rate coefficients of capture of two identical dipolar polarizable rigid rotors in their lowest nonresonant (j(1) = 0 and j(2) = 0) and resonant (j(1) = 0, 1 and j(2) = 1, 0) states are calculated accurately within the close-coupling (CC) approach. The convergence of the quantum rate coefficients to their quantum-classical counterparts is studied. A comparison of the present accurate numerical with approximate analytical results (Nikitin, E. E.; Troe, J. J. Phys. Chem. A 2010, 114, 9762) indicates a good performance of the previous approach which was based on the interpolation between s-wave fly wheel quantal and all-wave classical adiabatic channel limits. The results obtained apply as well to the formation of transient molecular species in the encounter of two atoms at very low collision energy interacting via resonance dipole-dipole interaction.

Threshold behavior and analytical fitting of partial wave capture probabilities for attractive R(-n) potentials.

Numerically accurate analytical fittings for partial wave capture probabilities in the field of R(-n) potentials (n = 4 and 6) are presented across practically interesting ranges of probabilities. The results demonstrate the performance of the Bethe and Wigner threshold laws at low collision energies and should be useful for practical applications.

Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.

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 (Hunds 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.