Spin-orbit Changing Research Articles

Differential Cross Sections for Cold, State-to-State Spin-Orbit Changing Collisions of NO(v = 10) with Neon.

Inelastic scattering processes have proven a powerful means of investigating molecular interactions, and much current effort is focused on the cold and ultracold regime where quantum phenomena are clearly manifested. Studies of collisions of the open shell nitric oxide (NO) molecule have been central in this effort since the pioneering work of Houston and co-workers in the early 1990s. State-to-state scattering of vibrationally excited molecules in the cold regime introduces challenges that test the suitability of current theoretical methods for ab initio determination of intermolecular potentials, and concomitant electronically nonadiabatic processes raise the bar further. Here we report measurements of differential cross sections for state-to-state spin-orbit changing collisions of NO (v = 10, Ω″ = 1.5, and j″ = 1.5) with neon from 2.3 to 3.5 cm-1 collision energy using our recently developed near-copropagating beam technique. The experimental results are compared with those obtained from quantum scattering calculations on a high-level set of coupled cluster potential energy surfaces and are shown to be in good agreement. The theoretical results suggest that distinct backscattering in the 2.3 cm-1 case arises from overlapping resonances.

Inelastic collision dynamics of oriented NO molecules with Kr atoms

Building on our previous work on NO + Ar, this paper presents a complete set of orientation measurements and quantum mechanical calculations for the NO + Kr collision system, including both spin-orbit conserving and changing collisions, and both side-on (x-axis) and end-on (z-axis) orientations. While many of the trends observed in the oriented differential and integral scattering distributions, as well as in the spin-orbit branching fractions, are similar to the ones seen previously for NO + Ar, a direct comparison with the Ar data reveals subtle differences in the scattering dynamics, which we rationalise with the more extended attractive regions on the NO + Kr potential energy surfaces. High-impact parameter collisions that lead to low scattering angles in the spin-orbit conserving manifold are particularly sensitive to the topology in the attractive parts of the potential, whereas more impulsive, low-impact parameter trajectories, which sample the repulsive parts of the potential, produce very similar features in the oriented differential cross sections for the Ar and Kr systems, especially for spin-orbit changing collisions.

Controlling the Spin-Orbit Branching Fraction in Molecular Collisions.

The collision geometry, that is, the relative orientation of reactants before interaction, can have a large effect on how a collision or reaction proceeds. Certain geometries may prevent access to a given product channel, while others might enhance it. In this Letter, we demonstrate how the initial orientation of NO molecules relative to approaching Ar atoms determines the branching between the spin-orbit changing and the spin-orbit conserving rotational product channels. We use a recently developed quantum treatment to calculate differential and integral branching fractions, at any arbitrary orientation, from theoretical and experimental data points. Our results show that a substantial degree of control over the final spin-orbit state of the scattering products can be achieved by tuning the initial collision geometry.

Correlations in rotational energy transfer for NO-D2 inelastic collisions.

We present a combined experimental and theoretical study of state-to-state inelastic collisions between NO (X 2Π1/2, j = 1/2, f) radicals and D2 (j = 0, 1, 2, 3) molecules at collision energies of 100 cm-1 and 750 cm-1. Using the combination of Stark deceleration and velocity map imaging, we fully resolve pair-correlated excitations in the scattered molecules. Both spin-orbit conserving and spin-orbit changing transitions in the NO radical are measured, while the coincident rotational excitation (j = 0 → j = 2) and rotational de-excitation (j = 2 → j = 0 and j = 3 → j = 1) in D2 are observed. De-excitation of D2 shows a strong dependence on the spin-orbit excitation of NO. We observe translation-to-rotation energy transfer as well as direct rotation-to-rotation energy transfer at the lowest collision energy probed. The experimental results are in good agreement with cross sections obtained from quantum coupled-channels calculations based on recent NO-D2 potential energy surfaces. The observed trends in the correlated scattering cross sections are understood in terms of the NO-D2 quadrupole-quadrupole interaction.

Probing the location of the unpaired electron in spin-orbit changing collisions of NO with Ar.

Understanding the molecular forces that drive a reaction or scattering process lies at the heart of molecular dynamics. Here, we present a combined experimental and theoretical study of the spin-orbit changing scattering dynamics of oriented NO molecules with Ar atoms. Using our crossed molecular beam apparatus, we have recorded velocity-map ion images and extracted differential and integral cross sections of the scattering process in the side-on geometry. We observe an overall preference for collisions close to the N atom in the spin-orbit changing manifold, which is a direct consequence of the location of the unpaired electron on the potential energy surface. In addition, a prominent forward scattered feature is observed for intermediate, even rotational transitions when the atom approaches the molecule from the O-end. The appearance of this peak originates from an attractive well on the A' potential energy surface, which efficiently directs high impact parameter trajectories towards the region of high unpaired electron density near the N-end of the molecule. The ability to orient molecules prior to collision, both experimentally and theoretically, allows us to sample different regions of the potential energy surface(s) and unveil the associated collision pathways.

Differential steric effects in the inelastic scattering of NO(X) + Ar: spin-orbit changing transitions.

Spin-orbit changing transitions for bond-axis oriented collisions of NO(X) with Ar have been investigated with full quantum state selection via a crossed molecular beam experiment at collision energies of 532 cm-1 and 651 cm-1. NO(X) molecules were selected in their ground rotational state (Ω = 0.5, j = 0.5, f) before being adiabatically oriented using a static electric field, such that either the N- or O-end of the molecule was directed towards the incoming Ar atom. After collision, NO(X, Ω' = 1.5, j', e) molecules were probed quantum state specifically using velocity-map ion imaging, coupled with resonantly enhanced multi-photon ionization. Differences were observed between the experimental ion images and differential cross sections for collisions occurring at the two ends of the molecule, with results that could largely be accounted for by quantum mechanical scattering calculations. The bond-axis oriented data for the spin-orbit changing collisions are compared with similar results obtained previously for spin-orbit conserving transitions, and for field free scattering of NO(X) with Ar.

Collisional excitation of interstellar CCN(X2Π) induced by He.

The CCN radical has been recently detected in the interstellar medium. Accurate modeling of its abundance in such media requires one to model its excitation by both radiation and collisions. Here, we report the first quantum mechanical close-coupling study of CCN-He collisions. Calculations of fine-structure resolved excitation cross sections of CCN(X2Π) induced by collision with He are performed for kinetic energies below 500 cm-1. The calculations are based on new two-dimensional potential energy surfaces obtained from coupled cluster approaches. We found that the inelastic cross sections for spin-orbit conserving transitions are larger than those for spin-orbit changing transitions. The new collisional data should significantly help the interpretation of interstellar CCN emission lines observed with current and future telescopes and we expect that they will allow accurate determination of the CCN abundance in the interstellar medium, which is crucial to understand the chemistry of carbon chain species in the interstellar gas.

Fine and hyperfine collisional excitation of C6H by He

Hydrogenated carbon chains have been detected in interstellar and circumstellar media and accurate modelling of their abundances requires collisional excitation rate coefficients with the most abundant species. Among them, the C6H molecule is one of the most abundant towards many lines of sight. Hence, we determined fine and hyperfine-resolved rate coefficients for the excitation of C6H(X2Π) due to collisions with He. We present the first interaction potential energy surface for the C6H–He system, obtained from highly correlated ab initio calculations and characterized by a large anisotropy due to the length of the molecule. We performed dynamical calculations for transitions among the first fine structure levels (up to J = 30.5) of both spin-orbit manifolds of C6H using the close-coupling method, and rate coefficients are determined for temperatures ranging from 5 to 100 K. The largest rate coefficients for even ΔJ transitions conserve parity, while parity-breaking rate coefficients are favoured for odd ΔJ. Spin-orbit changing rate coefficients are several orders of magnitude lower than transitions within a single manifold. State-to-state hyperfine-resolved cross-sections for the first levels (up to J = 13.5) in the Ω = 3/2 spin-orbit manifold are deduced using recoupling techniques. Rate coefficients are obtained and the propensity rule ΔJ = ΔF is seen. These new data will help determine the abundance of C6H in astrophysical environments such as cold dense molecular clouds, star-forming regions and circumstellar envelopes, and will help in the interpretation of the puzzling C6H−/C6H abundance ratios deduced from observations.

The fully quantum state-resolved inelastic scattering of NO(X) + Ne: experiment and theory

Fully Λ-doublet quantum state-resolved differential cross-sections for collisions of NO(X) with neon at a collision energy of 540 cm−1 are presented. Initial state selection of the Ω = 0.5, j = 0.5, f Λ-doublet level of the NO(X) was achieved using hexapole focussing. Both spin-orbit level conserving and spin-orbit level changing transitions have been studied. The experimental results are compared with those obtained from quantum scattering calculations and are shown to be in excellent agreement. Quantum scattering calculations have also been performed on a modified potential energy surface with the attractive region removed, to determine the effects this has on the differential cross-sections. Comparisons are also made with the inelastic scattering of NO(X) with He and Ar.

The effect of parity conservation on the spin–orbit conserving and spin–orbit changing differential cross sections for the inelastic scattering of NO(X) by Ar

The fully Λ-doublet resolved state-to-state differential cross sections (DCSs) for the collisions of NO(X, (2)Π, v = 0, j = 0.5) with Ar have been shown to depend sensitively on the conservation of the total parity of the NO molecular wavefunction. Parity changing collisions exhibit a single maximum only in the DCS, while parity conserving transitions exhibit multiple rainbow peaks. This behaviour is shown to arise directly from the constructive or destructive interference of collisions impacting on the two pointed ends and on the flatter middle of the NO molecule. A simple hard shell, four path model has been employed to determine the relative phase shifts of the paths contributing to the scattering amplitude. The model calculations using the V(sum) potential, together with the results of a quasi-quantum treatment, provide good qualitative agreement with the experimental spin-orbit conserving (ΔΩ = 0) DCSs, suggesting that the dynamics for all but the lowest Δj transitions are determined largely by the repulsive part of the potential. The collisions leading to spin-orbit changing transitions (ΔΩ = 1) have been also found to be dominated by repulsive forces, even for the lowest Δj values. However, they are less well reproduced by hard shell calculations, because of the crucial participation of the V(diff) potential in determining the outcome of these collisions.

Fully Λ-doublet resolved state-to-state differential cross-sections for the inelastic scattering of NO(X) with Ar

Fully Λ-doublet resolved state-to-state differential cross-sections (DCSs) for the collisions of the open-shell NO(X, (2)Π(1/2), ν = 0, j = 0.5) molecule with Ar at a collision energy of 530 cm(-1) are presented. Initial state selection of NO(X, (2)Π(1/2), j = 0.5, f) was performed using a hexapole so that the (low field seeking) parity of ε = -1, corresponding to the f component of the Λ-doublet, could be selected uniquely. Although the Λ-doublet levels lie very close in energy to one another and differ only in their relative parities, they exhibit strikingly different DCSs. Both spin-orbit conserving and spin-orbit changing collisions have been studied, and the previously unobserved structures in the fully quantum state-to-state resolved DCSs are shown to depend sensitively on the change in parity of the wavefunction of the NO molecule on collision. In all cases, the experimental data are shown to be in excellent agreement with rigorous quantum mechanical scattering calculations.

Doublet rotational energy transfer of the SH (X 2Π, v′′ = 0) state by collisions with Ar

The rotational energy transfer (RET) by Ar collisions within the SH X (2)Π (v'' = 0, J'' = 0.5-10.5) state is characterized. The integral cross sections as a function of collision energy for each rotational transition are calculated using a quantum scattering method in which the constructed potential energy functions are based on a ground state potential energy surface (PES) reported previously. On the other hand, a laser-induced excitation fluorescence technique is employed to monitor the relaxation of the rotational population as a function of photolysis-probe delay time following the photodissociation of H(2)S at 248 nm. The rotational population evolution is comparable to its theoretical counterpart based on calculated Λ-resolved RET rate constants. The propensity in Λ-resolved RET transitions is found to approximately resemble the case of OH(X (2)Π, v'' = 0) + Ar. The Λ-averaged RET collisions are also analyzed and result in several propensity rules in the transitions. Most propensity rules are similar to those observed in the collisions of SH(A (2)Σ(+)) by Ar. However, the behavior of the conserving ratio, defined as rate constants for spin-orbit conserving transition divided by those for spin-orbit changing transition, shows distinct difference from those described by Hund's case (b).

Parity-dependent rotational rainbows in D2–NO and He–NO differential collision cross sections

The (j', Omega', epsilon') dependent differential collision cross sections of D2 with fully state selected (j = 12, Omega = 12, epsilon = -1) NO have been determined at a collision energy of about 550 cm(-1). The collisionally excited NO molecules are detected by (1+1') resonance enhanced multiphoton ionization combined using velocity-mapped ion-imaging. The results are compared to He-NO scattering results and tend to be more forward scattered for the same final rotational state. Both for collisions of the atomic He and the molecular D2 with NO, scattering into pairs of rotational states with the same value of n = j' - epsilon epsilon'2 yields the same angular dependence of the cross section. This "parity propensity rule" remains present both for spin-orbit conserving and spin-orbit changing transitions. The maxima in the differential cross sections-that reflect rotational rainbows-have been extracted from the D2-NO and the He-NO differential cross sections. These maxima are found to be distinct for odd and even parity pair number n. Rainbow positions of parity changing transitions (n is odd) occur at larger scattering angles than those of parity conserving transitions (n is even). Parity conserving transitions exhibit-from a classical point of view-a larger effective eccentricity of the shell. No rainbow doubling due to collisions onto either the N-end or the O-end was observed. From a classical point of view the presence of a double rainbow is expected. Rotational excitation of the D2 molecules has not been observed.

Steric asymmetry and lambda-doublet propensities in state-to-state rotationally inelastic scattering of NO(2Π1/2) with He

Relative integrated cross sections are measured for rotationally inelastic scattering of NO(2Pi(1/2)),hexapole selected in the upper lambda-doublet level of the ground rotational state (j = 0.5), in collisions with He at a nominal energy of 514 cm(-1). Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, [formula: see text], which is equal to within a factor of (- 1) to the molecular steric effect, S(i-->f) is identical with (sigma(He-->NO) - (sigma(He-->ON))/(sigma(He-->NO) + sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming lambda-doublet component is also observed as a function of the final rotational (j'), spin-orbit (omega'), and lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of omega'. However, the lambda-doublet propensities are very different for [omega=0.5(F1)-->omega'= 1.5(F2)] and [omega=0.5(F1)-->omega'=0.5(F1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO(2Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R.Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry S(i-->f) of the inelastic cross sections at Etr= 514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F1-->Fl) and spin-manifold changing (F1 --F2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at Etr = 508 cm(-1) are compared to the experimental data of Joswig et al. [J. Chem. Phys.85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy Etr= 491 cm(-1) is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F1 (j = 0.5) -F1f (j' = 3.5).

Spin-orbit Conserving and Changing Transitions in Inelastic Scattering of NO(2Π) + Ar

State-resolved differential cross sections (DCSs) of NO (j'' = 0.5, Ω'' = 1/2) + Ar → NO (j', Ω' = 1/2, 3/2) + Ar have been measured at a collision energy of 516 cm-1 by means of the crossed molecular beam velocity-map ion-imaging method. DCSs were obtained for twenty final (j', Ω') states including spin-orbit conserving (ΔΩ = 0) and changing (ΔΩ = 1) transitions, and compared with the results of full close-coupling scattering calculations based on ab initio potential energy surfaces. Remarkable agreement between theory and experiment was seen in the DCSs for the ΔΩ = 0 transitions, while small discrepancies were found for the ΔΩ = 1 transitions.

Rotationally inelastic collisions of OH(X 2Π)+Ar. I. State-to-state cross sections

Inelastic collisions of OH(X 2Π)+Ar at an energy of 746 cm−1 have been studied in a crossed molecular beam experiment. The OH(X 2Π) radicals were prepared in the v=0, Ω=32, J=32, f state by hexapole state selection. Parity-resolved integral state-to-state cross sections for rotational excitation have been determined up to the Ω=32, J=92 and Ω=12, J=52 states. A strong preference is found for spin–orbit manifold conserving transitions to final states of e symmetry. The experimental results are compared to quantum scattering calculations on ab initio potential energy surfaces developed by Degli-Esposti and Werner [J. Chem. Phys. 93, 3351 (1990)] and by Klos et al. [J. Chem. Phys. 112, 4952 (2000)]. The overall agreement between experiment and theory is very good; however, the calculated cross sections for spin–orbit changing transitions are a bit larger than the experimental values. The results are also compared to previous experiments at a collision energy of 451 cm−1.

Investigation of steric effects in inelastic collisions of NO(X 2Π) with Ar

Cross sections were determined for collisions of Ar with oriented NO(X 2Π), based on full close-coupled calculations and new ab initio potential energy surfaces (PESs). Collisions in which the NO molecules are initially oriented so that the O end preferentially points toward the Ar atom are more effective in promoting spin–orbit changing transitions. The magnitude of the steric asymmetry is consistent with earlier calculations based on a previous PES, and agrees well with experiment. Various modifications of the full PESs were used to explore the origin of the observed features in the steric asymmetries, in particular the striking oscillatory pattern seen in the variation of the steric asymmetry with final state.

Polarization and steric effects in inelastic collisions of NO(X 2Π) with Ar and He

Differential mj resolved cross-sections were determined for collisions of NO(X2Π) with Ar and He based on full close-coupled calculations and abinitio potential energy surfaces. As a function of the scattering angle, the predicted alignment becomes increasingly negative as the scattering angle increases. Integrated over all scattering angles, the sign of the product alignment becomes increasingly negative as Δj increases. For collisions with Ar, the product alignment is more negative for spin–orbit changing, as compared to spin–orbit conserving, transitions. For collisions with He, the calculated product alignment, both differential and integral, is in excellent agreement with experiment.

A crossed-beam study of the state-resolved integral cross sections for the inelastic scattering of OH(X 2Π) with CO and N2

State-resolved cross sections for the inelastic scattering of OH(X 2Π) with CO and N2 have been measured in a crossed molecular beam apparatus over the energy range from 0.5 to 5.5 kcal mol−1. The magnitude and shape of the excitation functions for the same OH final states were virtually independent of the two targets except near threshold. Both spin–orbit conserving and spin–orbit changing transitions have been investigated. Cross sections for spin–orbit changing transitions of large ΔN were approximately the same magnitude as those for spin–orbit conserving transitions. For small ΔN, however, the spin–orbit conserving transitions became more favorable. The Λ-doublet ratio, Π(A′)/Π(A″), in the Π3/2 (F1) manifold differed from unity only for the N2 target for which the ratio became increasingly larger than unity as N′ increased. The observed fine-structure effects were nearly the same as those from the corresponding (reverse) reactive collisions, and a close connection between the inelastic and reactive events has been conjectured.