Collisional angular momentum depolarization of OH(A) and NO(A) by Ar: A comparison of mechanisms

Two-color polarization spectroscopy measurements of Zeeman state-to-state collision induced transitions of nitric oxide in binary gas mixtures

We investigated collision induced transitions in the (0, 0) band of the A2Σ+-X2Π electronic transition of nitric oxide (NO) using two-color polarization spectroscopy (TCPS). Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295 K and 1 atm, were obtained with the pump beam tuned to the R11(11.5) and OP12(1.5) transitions. The buffer gases were He, Ar, and N2. The probe was scanned while the pump beam was tuned to the line center. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. A model for collisional transfer from an initial to a final Zeeman state was developed based on the difference in cosine of the rotational quantum number J projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the A2Σ+ level of NO is almost zero for rotational quantum numbers ≥8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra.

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Non-adiabatic quantum dynamics of the electronic quenching OH(A2Σ+) + Kr

The quantum dynamics is investigated in full dimensionality, using three PESs and all the non-adiabatic couplings of a total Hamiltonian.

Experimental and theoretical studies of the Xe-OH(A/X) quenching system

New multi-reference, global ab initio potential energy surfaces (PESs) are reported for the interaction of Xe atoms with OH radicals in their ground X²Π and excited A²Σ⁺ states, together with the non-adiabatic couplings between them. The 2A' excited potential features a very deep well at the collinear Xe-OH configuration whose minimum corresponds to the avoided crossing with the 1A' PES. It is therefore expected that, as with collisions of Kr + OH(A), electronic quenching will play a major role in the dynamics, competing favorably with rotational energy transfer within the 2A' state. The surfaces and couplings are used in full three-state surface-hopping trajectory calculations, including roto-electronic couplings, to calculate integral cross sections for electronic quenching and collisional removal. Experimental cross sections, measured using Zeeman quantum beat spectroscopy, are also presented here for comparison with these calculations. Unlike similar previous work on the collisions of OH(A) with Kr, the surface-hopping calculations are only able to account qualitatively for the experimentally observed electronic quenching cross sections, with those calculated being around a factor of two smaller than the experimental ones. However, the predicted total depopulation of the initial rovibrational state of OH(A) (quenching plus rotational energy transfer) agrees well with the experimental results. Possible reasons for the discrepancies are discussed in detail.

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.

Rotationally inelastic scattering of methyl radicals with Ar and N2

The rotationally inelastic scattering of methyl radical with Ar and N2 is examined at collision energies of 330 ± 25 cm(-1) and 425 ± 50 cm(-1), respectively. Differential cross sections (DCSs) were measured for different final n' rotational levels (up to n' = 5) of the methyl radicals, averaged over k' sub-levels, using a crossed molecular beam machine with velocity map imaging. For Ar as a collision partner, we present a newly constructed ab initio potential energy surface and quantum mechanical scattering calculations of state-resolved DCSs. These computed DCSs agree well with the measurements. The DCSs for both Ar and N2 collision partners are strongly forward peaked for all spectroscopic lines measured. For scattering angles below 60°, the theoretical CD3-Ar DCSs show diffraction oscillations that become less pronounced as n' increases, but these oscillations are not resolved experimentally. Comparisons are drawn with our recently reported DCSs for scattering of methyl radicals with He atoms.

Rate constants for collisional quenching of NO (A(2)Σ(+), v = 0) by He, Ne, Ar, Kr, and Xe, and infrared emission accompanying rare gas and impurity quenching

The quenching rates of NO (A(2)Σ(+), v = 0) with He, Ne, Ar, Kr and Xe have been studied at room temperature by measurements of the time dependence of the fluorescence decay following laser excitation. The rates are slow, with upper limits of rate constants determined as between 1.2 and 2.0 × 10(-14) cm(3) molecule(-1) s(-1), considerably lower than those reported before in the literature. Such slow rates can be markedly influenced by impurities such as O2 and H2O which have quenching rate constants close to gas kinetic values. Time resolved Fourier transform infrared emission has been used to observe the products of the quenching processes with the rare gases and with impurities. For He, Ne Ar and Kr there is no difference within experimental error of the populations in NO (X(2)Π v ≥ 2) produced with and without rare gas present, but the low quantum yields of such quenching (of the order of 5% for an atmosphere of rare gas) preclude quantitative information on the quantum states being obtained. For quenching by Xe the collisional formation of electronically excited Xe atoms dominates the emission at early times. Vibrationally excited NO (X(2)Π, v) and products of reactive quenching are observed in the presence of O2 and H2O.

Parity-dependent rotational energy transfer in CN(A(2)Π, ν = 4, j F(1)ε) + N2, O2, and CO2 collisions

We report state-resolved total removal cross sections and state-to-state rotational energy transfer (RET) cross sections for collisions of CN(A(2)Π, ν = 4, j F1ε) with N2, O2, and CO2. CN(X(2)Σ(+)) was produced by 266 nm photolysis of ICN in a thermal bath (296 K) of the collider gas. A circularly polarized pulse from a dye laser prepared CN(A(2)Π, ν = 4) in a range of F1e rotational states, j = 2.5, 3.5, 6.5, 11.5, 13.5, and 18.5. These prepared states were monitored using the circularly polarized output of an external cavity diode laser by frequency-modulated (FM) spectroscopy on the CN(A-X)(4,2) band. The FM Doppler profiles were analyzed as a function of pump-probe delay to determine the time dependence of the population of the initially prepared states. Kinetic analysis of the resulting time dependences was used to determine total removal cross sections from the initially prepared levels. In addition, a range of j' F1e and j' F2f product states resulting from rotational energy transfer out of the j = 6.5 F1e initial state were probed, from which state-to-state RET cross sections were measured. The total removal cross sections lie in the order CO2 > N2 > O2, with evidence for substantial cross sections for electronic and/or reactive quenching of CN(A, ν = 4) to unobserved products with CO2 and O2. This is supported by the magnitude of the state-to-state RET cross sections, where a deficit of transferred population is apparent for CO2 and O2. A strong propensity for conservation of rotational parity in RET is observed for all three colliders. Spin-orbit-changing cross sections are approximately half of those of the respective conserving cross sections. These results are in marked disagreement with previous experimental observations with N2 as a collider but are in good agreement with quantum scattering calculations from the same study ( Khachatrian et al. J. Phys. Chem. A 2009 , 113 , 3922 ). Our results with CO2 as a collider are similarly in strong disagreement with a related experimental study ( Khachatrian et al. J. Phys. Chem. A 2009 , 113 , 13390 ). We therefore propose that the previous experiments substantially underestimated the spin-orbit-changing cross sections for collisions with both N2 and CO2, suggesting that even approximate quantum scattering calculations may be more successful for such molecule-molecule systems than was previously concluded.

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.

New findings regarding the NO angular momentum orientation in Ar-NO(2Π(1/2)) collisions

This article reports a theoretical study of the stereodynamics of Ar + NO(X(2)Π, v = 0, j = 1/2, Ω = 1/2, ε = ±1) rotationally inelastic collisions. First, quantum scattering data are used to calculate all differential polarisation moments of the reagent and product molecules; this leads to the observation that the orientations of the reagent and product angular momenta are very strongly correlated. Next, canonical collision mechanisms theory [Aldegunde et al., Phys. Chem. Chem. Phys., 2008, 10, 1139] is used to separate and characterise the stereodynamics of the two independent collision mechanisms that contribute to the collision dynamics; this leads to the observation that the average product orientation is determined by the relative contributions of the two canonical mechanisms, which have comparable importance but are associated with starkly contrasting angular momentum orientations. These observations lead to a new and rigorous explanation of the experimental results reported a decade ago by Lorenz et al. [Science, 2001, 293, 2063]. The central fact of the new explanation is the incoherent, interference-free superposition of two independent collision mechanisms. This makes the new explanation radically different from the only one previously suggested, namely that the experimental observations might be due to quantum interference in a single collision mechanism.

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.