Tensor cross sections and the collisional evolution of state multipoles: OH(XΠ2)–Ar

Semiclassical analysis of jm → j'm' transitions in rotationally inelastic collisions in cell experiments

Recent quantum calculations of rotationally inelastic collisions of NaK (A¹Σ⁺) with He or Ar in a cell experiment are analyzed using semiclassical approximations valid for large quantum numbers. The results suggest a physical interpretation of jm → j'm' transitions based on the vector model and lead to expressions that explicitly involve the initial and final polar angles of the angular momentum of the target molecule. The relation between the polar angle θ and the azimuthal quantum number m links the semiclassical results for the change in polar angle (θ → θ') to quantum results for an m → m' transition. Analytic formulas are derived that relate the location and width of peaks in the final polar angle distribution (PAD) to the K-dependence of the coefficients d_K(j, j'), which are proportional to tensor cross sections σ_K(j → j'). Several special cases are treated that lead to final PADs that are approximately Lorentzian or sinc functions centered at θ' = θ. Another interesting case, "angular momentum reversal," was observed in the calculations for He. This phenomenon, which involves a reversal of the direction of the target's angular momentum, is shown to be associated with oscillatory behavior of the d_K for certain transitions. Finally, several strategies for obtaining the d_K coefficients from experimental data are discussed.

An experimental study of OH(A2Σ+) + H2: Electronic quenching, rotational energy transfer, and collisional depolarization

Zeeman quantum beat spectroscopy has been used to determine the thermal (300 K) rate constants for electronic quenching, rotational energy transfer, and collisional depolarization of OH(A²Σ⁺) by H₂. Cross sections for both the collisional disorientation and collisional disalignment of the angular momentum in the OH(A²Σ⁺) radical are reported. The experimental results for OH(A²Σ⁺) + H₂ are compared to previous work on the OH(A²Σ⁺) + He and Ar systems. Further comparisons are also made to the OH(A²Σ⁺) + Kr system, which has been shown to display significant non-adiabatic dynamics. The OH(A²Σ⁺) + H₂ experimental data reveal that collisions that survive the electronic quenching process are highly depolarizing, reflecting the deep potential energy wells that exist on the excited electronic state surface.

Rotationally inelastic scattering of NO(A(2)Σ(+)) + Ar: Differential cross sections and rotational angular momentum polarization

We present the implementation of a new crossed-molecular beam, velocity-map ion-imaging apparatus, optimized for collisions of electronically excited molecules. We have applied this apparatus to rotational energy transfer in NO(A(2)Σ(+), v = 0, N = 0, j = 0.5) + Ar collisions, at an average energy of 525 cm(-1). We report differential cross sections for scattering into NO(A(2)Σ(+), v = 0, N' = 3, 5, 6, 7, 8, and 9), together with quantum scattering calculations of the differential cross sections and angle dependent rotational alignment. The differential cross sections show dramatic forward scattered peaks, together with oscillatory behavior at larger scattering angles, while the rotational alignment moments are also found to oscillate as a function of scattering angle. In general, the quantum scattering calculations are found to agree well with experiment, reproducing the forward scattering and oscillatory behavior at larger scattering angles. Analysis of the quantum scattering calculations as a function of total rotational angular momentum indicates that the forward scattering peak originates from the attractive minimum in the potential energy surface at the N-end of the NO. Deviations in the quantum scattering predictions from the experimental results, for scattering at angles greater than 10°, are observed to be more significant for scattering to odd final N'. We suggest that this represents inaccuracies in the potential energy surface, and in particular in its representation of the difference between the N- and O-ends of the molecule, as given by the odd-order Legendre moments of the surface.

Theoretical calculations of rotationally inelastic collisions of He with NaK(A (1)Σ(+)): Transfer of population, orientation, and alignment

We have performed extensive calculations to investigate thermal energy, rotationally inelastic collisions of NaK (A(1)Σ(+)) with He. We determined a potential energy surface using a multi-reference configuration interaction wave function as implemented by the GAMESS electronic structure code, and we have performed coupled channel scattering calculations using the Arthurs and Dalgarno formalism. We also calculate the Grawert coefficients B(λ)(j, j') for each j → j' transition. These coefficients are used to determine the probability that orientation and alignment are preserved in collisions taking place in a cell environment. The calculations include all rotational levels with j or j' between 0 and 50, and total (translational and rotational) energies in the range 0.0002-0.0025 a.u. (∼44-550 cm(-1)). The calculated cross sections for transitions with even values of Δj tend to be larger than those for transitions with odd Δj, in agreement with the recent experiments of Wolfe et al. (J. Chem. Phys. 134, 174301 (2011)). The calculations of the energy dependence of the cross sections and the calculations of the fraction of orientation and alignment preserved in collisions also exhibit distinctly different behaviors for odd and even values of Δj. The calculations also indicate that the average fraction of orientation or alignment preserved in a transition becomes larger as j increases. We interpret this behavior using the semiclassical model of Derouard, which also leads to a simple way of visualizing the distribution of the angles between the initial and final angular momentum vectors j and j'. Finally, we compare the exact quantum results for j → j' transitions with results based on the simpler, energy sudden approximation. That approximation is shown to be quite accurate.

Differential and integral cross sections in OH(X) + Xe collisions

Differential cross sections (DCSs) for inelastic collisions of OH(X) with Xe have been measured at a collision energy of 483 cm(-1). The hydroxyl (OH) radicals were initially prepared in the X(2)Π3/2 (v = 0, j = 1.5, f) level using the hexapole electric field selection method. Products were detected state-selectively by [2 + 1] resonance-enhanced multiphoton ionization of OH, combined with velocity-map imaging. Integral cross sections in OH(X) + Xe at a collision energy of 490 cm(-1) were also measured by laser-induced fluorescence. The results are compared with exact close-coupling quantum mechanical scattering calculations on the only available ab initio potential energy surface (PES). The agreement between experimental and theoretical results is generally very satisfactory. This highlights the ability of such measurements to test the available PES for such a benchmark open-shell system. The agreement between experiment and theory for DCSs is less satisfactory at low scattering angles, and possible reasons for this disagreement are discussed. Finally, theoretical calculations of OH(X) + He DCSs have been obtained at various collision energies and are compared with those of OH(X) + Xe. The role of the reduced mass in the DCSs and partial cross sections is also examined.

Parity-dependent oscillations in collisional polarization transfer: CN(A²Π, v = 4) + Ar

We report the first systematic experimental and theoretical study of the state-to-state transfer of rotational angular momentum orientation in a (2)Π-rare gas system. CN(X(2)Σ(+)) was produced by pulsed 266 nm photolysis of ICN in a thermal bath (296 K) of Ar collider gas. A pulsed circularly polarized tunable dye laser prepared CN(A(2)Π, v = 4) in two fully state-selected initial levels, j = 6.5 F1e and j = 10.5 F2f, with a known laboratory-frame orientation. Both the prepared levels and a range of product levels, j' F1e and j' F2f, were monitored using the circular polarized output of a tunable diode laser via cw frequency-modulated (FM) spectroscopy in stimulated emission on the CN(A-X) (4,2) band. The FM Doppler lineshapes for co-rotating and counter-rotating pump-and-probe geometries reveal the time-dependence of the populations and orientations. Kinetic fitting was used to extract the state-to-state population transfer rate constants and orientation multipole transfer efficiencies (MTEs), which quantify the degree of conservation of initially prepared orientation in the product level. Complementary full quantum scattering (QS) calculations were carried out on recently computed ab initio potential energy surfaces. Collision-energy-dependent tensor cross sections for ranks K = 0 and 1 were computed for transitions from both initial levels to all final levels. These quantities were integrated over the thermal collision energy distribution to yield predictions of the experimentally observed state-to-state population transfer rate constants and MTEs. Excellent agreement between experiment and theory is observed for both measured quantities. Dramatic oscillations in the MTEs are observed, up to and including changes in the sign of the orientation, as a function of even/odd Δj within a particular spin-orbit and e/f manifold. These oscillations, along with those also observed in the state-to-state rate constants, reflect the rotational parity of the final level. In general, parity-conserving collisions conserve rotational orientation, while parity-changing collisions result in large changes in the orientation. The QS calculations show that the dynamics of the collisions leading to these different outcomes are fundamentally different. We propose that the origin of this behavior lies in interferences between collisions that sample the even and odd-λ terms in the angular expansions of the PESs.

Reactive scattering dynamics of rotational wavepackets: a case study using the model H+H2 and F+H2 reactions with aligned and anti-aligned H2

We propose a method to steer the outcome of reactive atom-diatom scattering, using rotational wavepackets excited by strong non-resonant laser pulses. Full close-coupled quantum mechanical scattering calculations of the D+H2 and F+H2 reactions are presented, where the H2 molecule exists as a coherent superposition of rotational states. The nuclear spin selective control over the molecular bond axis alignment afforded by the creation of rotational wavepackets is applied to reactive scattering systems, enabling a nuclear spin selective influence to be exerted over the reactive dynamics. The extension of the conventional eigenstate-to-eigenstate scattering problem to the case in which the initial state is composed of a coherent superposition of rotational states is detailed, and a selection of example calculations are discussed, along with their mechanistic implications. The feasibility of the corresponding experiments is considered, and a suitable simple two pulse laser scheme is shown to strongly differentiate the reactivities of o-H2 and p-H2.

Resonances in rotationally inelastic scattering of OH(X2Π) with helium and neon

We present detailed calculations on resonances in rotationally and spin-orbit inelastic scattering of OH (X(2)Π, j = 3/2, F(1), f) radicals with He and Ne atoms. We calculate new ab initio potential energy surfaces for OH-He, and the cross sections derived from these surfaces compare well with the recent crossed beam scattering experiment of Kirste et al. [Phys. Rev. A 82, 042717 (2010)]. We identify both shape and Feshbach resonances in the integral and differential state-to-state scattering cross sections, and we discuss the prospects for experimentally observing scattering resonances using Stark decelerated beams of OH radicals.

Depolarization of rotational angular momentum in CN(A2Π, v = 4) + Ar collisions

Angular momentum depolarization and population transfer in CN(A(2)Π, v = 4, j, F(1)e) + Ar collisions have been investigated both experimentally and theoretically. Ground-state CN(X(2)Σ(+)) molecules were generated by pulsed 266-nm laser photolysis of ICN in a thermal (nominally 298 K) bath of the Ar collision partner at a range of pressures. The translationally thermalized CN(X) radicals were optically pumped to selected unique CN(A(2)Π, v = 4, j = 2.5, 3.5, 6.5, 11.5, 13.5, and 18.5, F(1)e) levels on the A-X (4,0) band by a pulsed tunable dye laser. The prepared level was monitored in a collinear geometry by cw frequency-modulated (FM) spectroscopy in stimulated emission on the CN(A-X) (4,2) band. The FM lineshapes for co- and counter-rotating circular pump and probe polarizations were analyzed to extract the time dependence of the population and (to a good approximation) orientation (tensor rank K = 1 polarization). The corresponding parallel and perpendicular linear polarizations yielded population and alignment (K = 2). The combined population and polarization measurements at each Ar pressure were fitted to a 3-level kinetic model, the minimum complexity necessary to reproduce the qualitative features of the data. Rate constants were extracted for the total loss of population and of elastic depolarization of ranks K = 1 and 2. Elastic depolarization is concluded to be a relatively minor process in this system. Complementary full quantum scattering (QS) calculations were carried out on the best previous and a new set of ab initio potential energy surfaces for CN(A)-Ar. Collision-energy-dependent elastic tensor and depolarization cross sections for ranks K = 1 and 2 were computed for CN(A(2)Π, v = 4, j = 1.5-10.5, F(1)e) rotational/fine-structure levels. In addition, integral cross sections for rotationally inelastic transitions out of these levels were computed and summed to yield total population transfer cross sections. These quantities were integrated over a thermal collision-energy distribution to yield the corresponding rate constants. A complete master-equation simulation using the QS results for the selected initial level j = 6.5 gave close, but not perfect, agreement with the near-exponential experimental population decays, and successfully reproduced the observed multimodal character of the polarization decays. On average, the QS population removal rate constants were consistently 10%-15% higher than those derived from the 3-level fit to the experimental data. The QS and experimental depolarization rate constants agree within the experimental uncertainties at low j, but the QS predictions decline more rapidly with j than the observations. In addition to providing a sensitive test of the achievable level of agreement between state-of-the art experiment and theory, these results highlight the importance of multiple collisions in contributing to phenomenological depolarization using any method sensitive to both polarized and unpolarized molecules in the observed level.

Rotationally elastic and inelastic dynamics of NO(X2Π, v = 0) in collisions with Ar

A combined theoretical and experimental study of the depolarization of selected NO(X(2)Π, v = 0, j, F, ɛ) levels in collisions with a thermal bath of Ar has been carried out. Rate constants for elastic depolarization of rank K = 1 (orientation) and K = 2 (alignment) were extracted from collision-energy-dependent quantum scattering calculations, along with those for inelastic population transfer to discrete product levels. The rate constants for total loss of polarization of selected initial levels, which are the sum of elastic depolarization and population transfer contributions, were measured using a two-color polarization spectroscopy technique. Theory and experiment agree qualitatively that the rate constants for total loss of polarization decline modestly with j, but the absolute values differ by significantly more than the statistical uncertainties in the measurements. The reasons for this discrepancy are as yet unclear. The lack of a significant K dependence in the experimental data is, however, consistent with the theoretical prediction that elastic depolarization makes only a modest contribution to the total loss of polarization. This supports a previous conclusion that elastic depolarization for NO(X(2)Π) + Ar is significantly less efficient than for the electronically closely related system OH(X(2)Π) + Ar [P. J. Dagdigian and M. H. Alexander, J. Chem. Phys. 130, 204304 (2009)].

Dependence of elastic depolarization cross sections on the potential: OH(X 2Pi)-Ar and NO(X 2Pi)-Ar

Elastic tensor and depolarization cross sections are computed for the collision of two exemplary diatomic molecules with (2)Pi electronic ground states-OH and NO-with argon. The interaction of a diatomic molecule in a Pi state with a spherical collision partner must be described by two potential energy surfaces (PESs), corresponding to the two asymptotically degenerate electronic states, of A(') and A(") symmetry. Quantum scattering calculations are most naturally based on the average (V(sum)) and half-difference (V(dif)) of these two PESs. When V(dif) is neglected, the OH(X (2)Pi)-Ar depolarization cross sections are found to be significantly reduced in magnitude, while the NO(X (2)Pi)-Ar cross sections are relatively unaffected. In addition, treating the molecules as closed-shell (1)Sigma(+) species with a corresponding rotational level structure and using (V(sum)) to model the PES, we predict depolarization cross sections which differ significantly from those based on full inclusion of the electronic degeneracy and fine structure of these (2)Pi molecules. This indicates that any single-PES-based simulation of the collisional depolarization of these two molecules would be subject to significant error.