Electronically nonadiabatic mechanism of the vibrational relaxation of NO in Ar: Rate coefficients from ab initio potentials and asymptotic coupling.

In this paper, the electronically nonadiabatic Landau-Zener (LZ) mechanism for the vibrational relaxation v = 1 → v = 0 of NO(X2Π) in collisions with Ar(S01) is discussed. It corresponds to nonadiabatic transitions between two crossing vibronic potential energy surfaces (PESs) originating from vibrational states of the collision complex and supported by two coupled electronic PESs. The LZ rate coefficients k10LZ are calculated within the uniform Airy approach in the reaction coordinate approximation with parameters derived from ab initio PESs and an asymptotic estimation of the Franck-Condon factor in the nonadiabatic coupling region. The rate coefficients are close to the experimental rate coefficients available over the range of 900-2500 K, where the electronically adiabatic Landau-Teller (LT) mechanism with the rate coefficients k10LT does not make a noticeable contribution to the total relaxation rate. The ratio k10LZ/k10LT increases with temperature and the LZ and LT mechanisms have comparable rates at about 4000 K.

Relocking of intrinsic angular momenta in collisions of diatoms with ions: Capture of H2(j = 0,1) by H2.

Rate coefficients for capture of H2(j = 0,1) by H2+ are calculated in perturbed rotor approximation, i.e., at collision energies considerably lower than Bhc (where B denotes the rotational constant of H2). The results are compared with the results from an axially nonadiabatic channel (ANC) approach, the latter providing a very good approximation from the low-temperature Bethe-Wigner to the high temperature Langevin limit. The classical ANC approximation performs satisfactorily at temperatures above 0.1 K. At 0.1 K, the rate coefficient for j=1 is about 25% higher than that for j = 0 while the latter is close to the Langevin rate coefficient. The Bethe-Wigner limit of the rate coefficient for j = 1 is about twice that for j = 0. The analysis of the relocking of the intrinsic angular momentum of H2 during the course of the collision illustrates the significance of relocking in capture dynamics in general.

Further insight into the tunneling contribution to the vibrational relaxation of NO in Ar.

Tunneling corrections to Landau-Zener rate coefficients for the vibrational relaxation NO(X(2)Π, v = 1) + Ar → NO(X(2)Π, v = 0) + Ar between 300 and 2000 K are determined employing ab initio potential energy surfaces calculated by the code provided by Alexander [J. Chem. Phys. 111, 7426 (1999)]. The calculations use a reaction coordinate approach and lead to vibronically nonadiabatic transition probabilities within the generalized Airy approximation as extended to the WKB underbarrier Landau-Lifshitz limit. The calculations confirm experimental evidence for an onset of major tunneling contributions to the relaxation rate at temperatures below about 900 K and rationalize large tunneling contributions at 300 K. These effects increase the rate coefficients by several orders of magnitude over the uncorrected Landau-Zener values and remove the large gap between the latter and experimental results.

The vibrational relaxation of NO in Ar: tunneling in a curve-crossing mechanism.

Experimental data for the vibrational relaxation NO(X(2)Π, v = 1) + Ar → NO(X(2)Π, v = 0) + Ar between 300 and 2000 K are analyzed. The measured rate coefficients k10 greatly exceed Landau-Teller values (LT)k10. This observation can be attributed to a mechanism involving curve-crossing of the (A'', v = 1) and (A', v = 0) vibronic states of the collision system. At high temperatures, the rate coefficients k10 are well represented by the thermally averaged Landau-Zener rate constant (LZ)k10 with an apparent Arrhenius activation energy Ea/kB near 4500 K. At intermediate temperatures, around T = 900 K, the measured k10 values are a factor of two higher than the extrapolated (LZ)k10 values. This deviation is attributed to tunneling in nonadiabatic curve-crossing transitions, which are analyzed within the Airy approximation (linear model for crossing diabatic curves) and an effective mass approach. This suggests a substantial contribution of hindered rotation of NO to the nonadiabatic perturbation. The extrapolation of the Airy probabilities to even lower temperatures (by the Landau-Lifshitz WKB tunneling expression for simple nonlinear model potentials) indicates a further marked increase of the tunneling contribution beyond the extrapolated (LZ)k10. Near 300 K, the k10 can be two to three orders of magnitude higher than the extrapolated (LZ)k10. This agrees with the limited available experimental data for NO-Ar relaxation near room temperature.

Quantum effects in the capture of charged particles by dipolar polarizable symmetric top molecules. II. Interplay between electrostatic and gyroscopic interactions.

Within the general axially nonadiabatic channel approach described in Paper I of this series [M. Auzinsh, E. I. Dashevskaya, I. Litvin, E. E. Nikitin, and J. Troe, J. Chem. Phys. 139, 084311 (2013)], the present article analyzes the simultaneous manifestation of electrostatic and gyroscopic interactions in the quantum capture of dipolar polarizable symmetric top molecules by ions. As a demonstration, the rate coefficients for capture of CH3D and CD3H by H(+), D(+), and H3(+) are calculated.

Quantum effects in the capture of charged particles by dipolar polarizable symmetric top molecules. I. General axially nonadiabatic channel treatment.

The rate coefficients for capture of charged particles by dipolar polarizable symmetric top molecules in the quantum collision regime are calculated within an axially nonadiabatic channel approach. It uses the adiabatic approximation with respect to rotational transitions of the target within first-order charge-dipole interaction and takes into account the gyroscopic effect that decouples the intrinsic angular momentum from the collision axis. The results are valid for a wide range of collision energies (from single-wave capture to the classical limit) and dipole moments (from the Vogt-Wannier and fly-wheel to the adiabatic channel limit).

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.

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.

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.

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.

Lambda-doublet specificity in the low-temperature capture of NO(X 2Pi(1/2)) in low rotational states by C+ ions.

Following our general approach to Lambda-doubling specificity in the capture of dipolar molecules by ions [M. Auzinsh et al., J. Chem. Phys. 128, 184304 (2008)], we calculate the rate coefficients for the title process in the temperature range 10(-4)

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.

Modelling low-energy electron-molecule capture processes.

Cross sections and rate coefficients for capture of low-energy electrons with polar and polarizable target molecules are calculated in the framework of Fabrikant and Hotop's extended version of the Vogt-Wannier model and an extension of this approach is given in the present article. Analytical approximations are derived in order to facilitate the application to experiments. A comparison with a selection of experimental electron attachment rate coefficients provides insight into the competition between anion formation through electron capture and scattering processes which do not follow this pathway.

Interpretation of the vibrational relaxation of H2 in H2 within the semiclassical effective mass approach.

The temperature dependence of the rate coefficients for vibrational relaxation of H2 in neat H2 is interpreted within the semiclassical effective mass approach. Across the temperature range of 80-3000 K, the experimental rate coefficients vary by five orders of magnitude and fall onto a strongly nonlinear Landau-Teller plot. This behavior is explained by the nonclassical nature of the energy release and by a substantial participation of rotation of the colliding partners in inducing the vibrational transition. A single fitting parameter, the optimal reduced mass, permits one to represent the temperature dependence of the rate coefficient within a factor of 2. This parameter is found to be close to that obtained from a simple model suggested by Sewell et al. [J. Chem. Phys. 99, 2567 (1993)].

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.

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.

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.

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.