Rotational alignment effects in NO(X) + Ar inelastic collisions: an experimental study

Determination of collision mechanisms at low energies using four-vector correlations

In molecular dynamics, a fundamental question is how the outcome of a collision depends on the relative orientation of the collision partners before their interaction begins (the stereodynamics of the process). The preference for a particular orientation of the reactant complex is intimately related to the idea of a collision mechanism and the possibility of control, as revealed in recent experiments. Indeed, this preference holds not only for chemical reactions involving complex polyatomic molecules, but also for the simplest inelastic atom-diatom collisions at cold collision energies. In this work, we report how the outcome of rotationally inelastic collisions between two D2 molecules can be controlled by changing the alignment of their internuclear axes under the same or different polarization vectors. Our results demonstrate that a higher degree of control can be achieved when two internuclear axes are aligned, especially when both molecules are relaxed in the collision. The possibility of control extends to very low energies, even to the ultracold regime, when no control could be achieved just by the alignment of the internuclear axis of one of the colliding partners.

Inelastic scattering of NO(A2Σ+) + CO2: rotation-rotation pair-correlated differential cross sections

A crossed beam velocity-map ion-imaging apparatus has been used to determine differential cross sections (DCSs) for the rotationally inelastic scattering of NO(A2Σ+, v = 0, j = 0.5) with CO2, as a function of both NO(A, v = 0, N') final state and the coincident final rotational energy of the CO2. The DCSs are dominated by forward-peaked scattering for all N', with significant rotational excitation of CO2, and a small backward scattered peak is also observed for all final N'. However, no rotational rainbow scattering is observed and there is no evidence for significant product rotational angular momentum polarization. New ab initio potential energy surface calculations at the PNO-CCSD(T)-F12b level of theory report strong attractive forces at long ranges with significant anisotropy relative to both NO and CO2. The absence of rotational rainbow scattering is consistent with removal of low-impact-parameter collisions via electronic quenching, in agreement with the literature quenching rates of NO(A) by CO2 and recent electronic structure calculations. We propose that high-impact-parameter collisions, that do not lead to quenching, experience strong anisotropic attractive forces that lead to significant rotational excitation in both NO and CO2, depolarizing product angular momentum while leading to forward and backward glory scattering.

Li + HF and Li + HCl Reactions Revisited I: QCT Calculations and Simulation of Experimental Results

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, l , is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

Differential Cross Sections for Pair-Correlated Rotational Energy Transfer in NO(A2Σ+) + N2, CO, and O2: Signatures of Quenching Dynamics

A crossed molecular beam, velocity-map ion-imaging apparatus has been used to determine differential cross sections (DCSs), as a function of collider final internal energy, for rotationally inelastic scattering of NO(A2Σ+, v = 0, j = 0.5f1) with N2, CO, and O2, at average collision energies close to 800 cm-1. DCSs are strongly forward scattered for all three colliders for all observed NO(A) final rotational states, N'. For collisions with N2 and CO, the fraction of NO(A) that is scattered sideways and backward increases with increasing N', as does the internal rotational excitation of the colliders, with N2 having the highest internal excitation. In contrast, the DCSs for collisions with O2 are essentially only forward scattered, with little rotational excitation of the O2. The sideways and backward scattering expected from low-impact-parameter collisions, and the rotational excitation expected from the orientational dependence of published van der Waals potential energy surfaces (PESs), are absent in the observed NO(A) + O2 results. This is consistent with the removal of these short-range scattering trajectories via facile electronic quenching of NO(A) by O2, in agreement with the literature determination of the coupled NO-O2 PESs and the associated conical intersections. In contrast, collisions at high-impact parameter that predominately sample the attractive van der Waals minimum do not experience quenching and are inelastically forward scattered with low rotational excitation.

Imaging rotational energy transfer: comparative stereodynamics in CO + N2 and CO + CO inelastic scattering

State-to-state rotational energy transfer in collisions of ground ro-vibrational state ¹³CO molecules with N₂ molecules has been studied using the crossed molecular beam method under kinematically equivalent conditions used for ¹³CO + CO rotationally inelastic scattering described in a previously published report (Sun et al., Science, 2020, 369, 307-309). The collisionally excited ¹³CO molecule products are detected by the same (1 + 1' + 1'') VUV (Vacuum Ultra-Violet) resonance enhanced multiphoton ionization scheme coupled with velocity map ion imaging. We present differential cross sections and scattering angle resolved rotational angular momentum alignment moments extracted from experimentally measured ¹³CO + N₂ scattering images and compare them with theoretical predictions from quasi-classical trajectories (QCT) on a newly calculated ¹³CO-N₂ potential energy surface (PES). Good agreement between experiment and theory is found, which confirms the accuracy of the ¹³CO-N₂ potential energy surface for the 1460 cm^-1 collision energy studied by experiment. Experimental results for ¹³CO + N₂ are compared with those for ¹³CO + CO collisions. The angle-resolved product rotational angular momentum alignment moments for the two scattering systems are very similar, which indicates that the collision induced alignment dynamics observed for both systems are dominated by a hard-shell nature. However, compared to the ¹³CO + CO measurements, the primary rainbow maximum in the DCSs for ¹³CO + N₂ is peaked consistently at more backward scattering angles and the secondary maximum becomes much less obvious, implying that the ¹³CO-N₂ PES is less anisotropic. In addition, a forward scattering component with high rotational excitation seen for ¹³CO + CO does not appear for ¹³CO-N₂ in the experiment and is not predicted by QCT theory. Some of these differences in collision dynamics behaviour can be predicted by a comparison between the properties of the PESs for the two systems. More specific behaviour is also predicted from analysis of the dependence on the relative collision geometry of ¹³CO + N₂ trajectories compared to ¹³CO + CO trajectories, which shows the special 'do-si-do' pathway invoked for ¹³CO + CO is not effective for ¹³CO + N₂ collisions.

Stereodynamical Control of Cold Collisions between Two Aligned D_{2} Molecules

Resonant scattering of optically state-prepared and aligned molecules in the cold regime allows the most detailed interrogation and control of bimolecular collisions. This technique has recently been applied to collisions of two aligned ortho-D_{2} molecules prepared in the j=2 rotational level of the v=2 vibrational manifold using the Stark-induced adiabatic Raman passage technique. Here, we develop the theoretical formalism for describing four-vector correlations in collisions of two aligned molecules and apply our approach to state-prepared D_{2}(v=2,j=2)+D_{2}(v=2,j=2)→D_{2}(v=2,j=2)+D_{2}(v=2,j=0) collisions, making possible the simulations of the experimental results from first principles. Key features of the experimental angular distributions are reproduced and attributed primarily to a partial wave resonance with orbital angular momentum ℓ=4.

Role of Low Energy Resonances in the Stereodynamics of Cold He + D2 Collisions

In recent experiments using the Stark-induced adiabatic Raman passage technique, Zhou et al. ( J. Chem. Phys. 2021, 154, 104309; Science 2021, 374, 960-964) measured the product's angular distribution for the collisions between He and aligned D₂ molecules at cold collision energies. The signatures of the angular distributions were attributed to an [Formula: see text] = 2 resonance that governs scattering at low energies. A first-principles quantum mechanical treatment of this problem is presented here using a highly accurate interaction potential for the He-H₂ system. Our results predict a very intense [Formula: see text] = 1 resonance at low energies, leading to angular distributions that differ from those measured in the experiment. A good agreement with the experiment is achieved only when the [Formula: see text] = 1 resonance is artificially removed, for example, by excluding the lowest energies present in the experimental velocity distribution. Our analysis revealed that neither the position nor the intensity of the [Formula: see text] = 1 resonance significantly changes when the interaction potential is modified within its predicted uncertainties. Energy-resolved measurements may help to resolve the discrepancy.

Stereodynamics of rotational energy transfer in NO(A2Σ+) + Kr collisions

A crossed molecular beam, velocity-map ion imaging apparatus has been used to determine differential cross sections (DCSs) and angle-resolved rotational angular momentum alignment moments for the state-resolved rotationally inelastic scattering of NO(A²Σ⁺, v = 0, j = 0.5 f₁) with Kr at an average collision energy of 785 cm^-1. The experimental results are compared to close-coupled quantum scattering (QS) calculations performed on a literature ab initio potential energy surface (J. Kłos et al., J. Chem. Phys., 2008, 129, 244303). DCSs are very strongly forward scattered, with weaker side and backward scattered peaks becoming progressively more important at higher-N'. Good agreement is found between experimental and QS DCSs, indicating that the PES is an accurate reflection of the NO(A)-Kr interaction energies. Partial wave analysis of the QS DCSs isolates multiple scattering mechanisms contributing to the DCSs, including L-type rainbows and Fraunhofer diffraction. Measured alignment moments are not well described by a hard-shell kinematic apse scattering model, showing deviations in the forward scattering hemisphere that are in agreement with QS calculations and arise from attractive regions of the PES. These discrepancies emphasise that established scattering mechanisms for molecules such as NO with lighter noble gases cannot be extrapolated safely to heavier, more polarisable members of the series.

Orientation and Alignment dynamics of polar molecule driven by shaped laser pulses

We review the theoretical status of intense laser induced orientation and alignment-a field of study which lies at the interface of intense laser physics and chemical dynamics and having potential applications such as high harmonic generation, nano-scale processing and control of chemical reactions. The evolution of the rotational wave packet and its dynamics leading to orientation and alignment is the topic of the present discussion. The major part of this article primarily presents an overview of recent theoretical progress in controlling the orientation and alignment dynamics of a molecule by means of shaped laser pulses. The various theoretical approaches that lead to orientation and alignment such as static electrostatic field in combination with laser field(s), combination of orienting and aligning field, combination of aligning fields, combination of orienting fields, application of train of pulses etc. are discussed. It is observed that the train of pulses is quite an efficient tool for increasing the orientation or alignment of a molecule without causing the molecule to ionize. The orientation and alignment both can occur in adiabatic and non-adiabatic conditions with the rotational period of the molecule taken under consideration. The discussion is mostly limited to non-adiabatic rotational excitation (NAREX) i.e. cases in which the pulse duration is shorter than the rotational period of the molecule. We have emphasised on the so called half-cycle pulse (HCP) and square pulse (SQP). The effect of ramped pulses and of collision on the various laser parameters is also studied. We summarize the current discussion by presenting a consistent theoretical approach for describing the action of such pulses on movement of molecules. The impact of a particular pulse shape on the post-pulse dynamics is also calculated and analysed. In addition to this, the roles played by various laser parameters including the laser frequency, the pulse duration and the system temperature etc. are illustrated and discussed. The concept of alignment is extended from one-dimensional alignment to three-dimensional alignment with the proper choice of molecule and the polarised light. We conclude the article by discussing the potential applications of intense laser orientation and alignment.

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 ²Π_1/2, 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.

Steric Effects in the Inelastic Scattering of NO(X) + Ar: Side-on Orientation

The rotationally inelastic collisions of NO(X) with Ar, in which the NO bond-axis is oriented side-on (i.e., perpendicular) to the incoming collision partner, are investigated experimentally and theoretically. The NO(X) molecules are selected in the |j = 0.5, Ω = 0.5, ε = -1, f⟩ state prior to bond-axis orientation in a static electric field. The scattered NO products are then state selectively detected using velocity-map ion imaging. The experimental bond-axis orientation resolved differential cross sections and integral steric asymmetries are compared with quantum mechanical calculations, and are shown to be in good agreement. The strength of the orientation field is shown to affect the structure observed in the differential cross sections, and to some extent also the steric preference, depending on the ratio of the initial e and f Λ-doublets in the superposition determined by the orientation field. Classical and quantum calculations are compared and used to rationalize the structures observed in the differential cross sections. It is found that these structures are due to quantum mechanical interference effects, which differ for the two possible orientations of the NO molecule due to the anisotropy of the potential energy surface probed in the side-on orientation. Side-on collisions are shown to maximize and afford a high degree of control over the scattering intensity at small scattering angles (θ < 90°), while end-on collisions are predicted to dominate in the backward scattered region (θ > 90°).

Observation of Rainbows in the Rotationally Inelastic Scattering of NO with CH4

Using a combination of velocity-map imaging and resonance-enhanced multiphoton ionization detection with crossed molecular beam scattering, the dynamics of rotational energy transfer have been examined for NO in collisions with CH₄ at a mean collision energy of 700 cm^-1. The images of NO scattered into individual rotational (j_NO^') and spin-orbit (Ω) levels typically exhibit a single broad maximum that gradually shifts from the forward to the backward scattering direction with increasing rotational excitation (i.e., larger Δj_NO). The rotational rainbow angles calculated with a two-dimensional hard ellipse model show reasonable agreement with the observed angles corresponding to the maxima in the differential cross sections extracted from the images for higher Δj_NO transitions, but there are clear discrepancies for lower Δj_NO (in particular, final rotational levels with j_NO^' = 7.5 and 8.5). The sharply forward scattered angular distributions for these lower Δj_NO transitions better agree with the predictions of an L-type rainbow model. The more highly rotationally excited NO appears to coincide with low rotational excitation of the co-product CH₄, indicating a degree of rotational product-pair anticorrelation in this bimolecular scattering.

Stereodynamical Control of a Quantum Scattering Resonance in Cold Molecular Collisions

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

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.

Direct observation of product-pair correlations in rotationally inelastic collisions of ND3 with D2

We present a combined experimental and theoretical study of state-to-state inelastic scattering of ND₃(j = 1₁^-) with D₂ (j = 0, 1, 2, 3) molecules at collision energies around 800 cm^-1. Using a crossed molecular beam apparatus which employs the combination of Stark deceleration and velocity map imaging, we observe the correlated rotational excitations of both collision partners. For D₂, both elastic (Δj_D2 = 0), inelastic excitation (j = 0 →j = 2) and inelastic de-excitation (j = 2 →j = 0) processes are observed. For a number of final ND₃ states, inelastic channels in which D₂ is rotationally excited or de-excited appear surprisingly strong. The experimental results are in excellent agreement with the predictions from quantum scattering calculations which are based on an ab initio ND₃-D₂ potential energy surface.

How reactant polarization can be used to change the effect of interference on reactive collisions

It is common knowledge that integral and differential cross sections (DCSs) are strongly dependent on the spatial distribution of the molecular axis of the reactants. Hence, by controlling the axis distribution, it is possible to either promote or hinder the yield of products into specific final states or scattering angles. This idea has been successfully implemented in experiments by polarizing the internuclear axis before the reaction takes place, either by manipulating the rotational angular distribution or by the Stark effect in the presence of an orienting field. When there is a dominant reaction mechanism, characterized by a set of impact parameters and angles of attack, it is expected that a preparation that helps the system to reach the transition state associated with that mechanism will promote the reaction, whilst a different preparation would generally impair the reaction. However, when two or more competing mechanisms via interference contribute to the reaction into specific scattering angles and final states, it is not evident which would be the effect of changing the axis preparation. To address this problem, throughout this article we have simulated the effect that different experimental preparations have on the DCSs for the H + D2 reaction at relatively high energies, for which it has been shown that several competing mechanisms give rise to interference that shapes the DCS. To this aim, we have extended the formulation of the polarization dependent DCS to calculate polarization dependent generalized deflection functions of ranks greater than zero. Our results show that interference is very sensitive to changes in the internuclear axis preparation, and that the shape of the DCS can be controlled exquisitely.

Imaging inelastic scattering of CO with argon: polarization dependent differential cross sections

Rotationally inelastic scattering of carbon monoxide (CO) with argon at a collision energy of 700 cm⁻¹ has been investigated by measuring polarization dependent differential scattering cross sections (PDDCSs) for rotationally excited CO molecules using a crossed molecular beam apparatus coupled with velocity-map ion imaging.

Correlated energy transfer in rotationally and spin-orbit inelastic collisions of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-)

We present a combined experimental and theoretical study of state-to-state inelastic scattering of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-) molecules at a collision energy of 480 cm-1, focusing in particular on the observation and interpretation of correlated excitations in both NO and O2. Various final states of the NO radical, in both spin-orbit manifolds, were measured with high resolution using a crossed molecular beam apparatus which employs a combination of Stark deceleration and velocity map imaging. Velocity map imaging directly measures both the angular distribution and the radial velocity distribution of the scattered NO molecules, which probes the kinetic energy uptake or release and hence correlated excitations of NO-O2 pairs. Simultaneous excitations of NO and O2 were resolved for all studied final states of NO. In all cases, the experimental results excellently agree with the results of simulations based on quantum scattering calculations. Trends are discussed by analyzing the scattering wave functions from the calculations.

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.

State-to-State Differential Cross Sections for Inelastic Collisions of NO Radicals with para-H2 and ortho-D2

We present state-to-state differential cross sections for collisions of NO molecules (X²Π_1/2, j = 1/2f) with para-H₂ and ortho-D₂ molecules, at a collision energy of 510 and 450 cm^–1, respectively. The angular scattering distributions for various final states of the NO radical are measured with high resolution using a crossed molecular beam apparatus that employs the combination of Stark deceleration and velocity map imaging. Rotational rainbows as well as diffraction oscillations are fully resolved in the scattering images. The observed angular scattering distributions are in excellent agreement with the cross sections obtained from quantum close-coupling scattering calculations based on recently computed NO–H₂ potential energy surfaces, except for excitation of NO into the j = 7/2f channel. For this particular inelastic channel, a significant discrepancy with theory is observed, despite various additional measurements and calculations, at present, not understood.

Angular distributions for the inelastic scattering of NO(X2Π) with O2(X3Σg-)

The inelastic scattering of NO(X²Π) by O₂(X³Σ_g^-) was studied at a mean collision energy of 550 cm^-1 using velocity-map ion imaging. The initial quantum state of the NO(X²Π, v = 0, j = 0.5, Ω=0.5, 𝜖 = -1, f) molecule was selected using a hexapole electric field, and specific Λ-doublet levels of scattered NO were probed using (1+1^') resonantly enhanced multiphoton ionization. A modified "onion-peeling" algorithm was employed to extract angular scattering information from the series of "pancaked," nested Newton spheres arising as a consequence of the rotational excitation of the molecular oxygen collision partner. The extracted differential cross sections for NO(X) f→f and f→e Λ-doublet resolved, spin-orbit conserving transitions, partially resolved in the oxygen co-product rotational quantum state, are reported, along with O₂ fragment pair-correlated rotational state population. The inelastic scattering of NO with O₂ is shown to share many similarities with the scattering of NO(X) with the rare gases. However, subtle differences in the angular distributions between the two collision partners are observed.

Experimental testing of ab initio potential energy surfaces: Stereodynamics of NO(A2Σ+) + Ne inelastic scattering at multiple collision energies

We present a crossed molecular beam velocity-map ion imaging study of state-to-state rotational energy transfer of NO(A²Σ⁺, v = 0, N = 0, j = 0.5) in collisions with Ne atoms. From these measurements, we report differential cross sections and angle-resolved rotational angular momentum alignment moments for product states N' = 3 and 5-10 for collisions at an average energy of 523 cm^-1, and N' = 3 and 5-14 for collisions at an average energy of 1309 cm^-1, respectively. The experimental results are compared to the results of close-coupled quantum scattering calculations on two literature ab initio potential energy surfaces (PESs) [Pajón-Suárez et al., Chem. Phys. Lett. 429, 389 (2006) and Cybulski and Fernández, J. Phys. Chem. A 116, 7319 (2012)]. The differential cross sections from both experiment and theory show clear rotational rainbow structures at both collision energies, and comparison of the angles observed for the rainbow peaks leads to the conclusion that Cybulski and Fernández PES better represents the NO(A²Σ⁺)-Ne interaction at the collision energies used here. Sharp, forward scattered (<10°), peaks are observed in the experimental differential cross sections for a wide range of N' at both collision energies, which are not reproduced by theory on either PES. We identify these as L-type rainbows, characteristic of attractive interactions, and consistent with a shallow well in the collinear Ne-N-O geometry, similar to that calculated for the NO(A²Σ⁺)-Ar surface [Kłos et al., J. Chem. Phys. 129, 244303 (2008)], but absent from both of the NO(A²Σ⁺)-Ne surfaces tested here. The angle-resolved alignment moments calculated by quantum scattering theory are generally in good agreement with the experimental results, but both experiment and quantum scattering theories are dramatically different to the predictions of a classical rigid-shell, kinematic-apse conservation model. Strong oscillations are resolved in the experimental alignment moments as a function of scattering angle, confirming and extending the preliminary report of this behavior [Steill et al., J. Phys. Chem. A 117, 8163 (2013)]. These oscillations are correlated with structure in the differential cross section, suggesting an interference effect is responsible for their appearance.

Comparative stereodynamics in molecule-atom and molecule-molecule rotational energy transfer: NO(A(2)Σ(+)) + He and D2

We present a crossed molecular beam scattering study, using velocity-map ion-imaging detection, of state-to-state rotational energy transfer for NO(A(2)Σ(+)) in collisions with the kinematically identical colliders He and D2. We report differential cross sections and angle-resolved rotational angular momentum polarization moments for transfer of NO(A, v = 0, N = 0, j = 0.5) to NO(A, v = 0, N' = 3, 5-12) in collisions with He and D2 at respective average collision energies of 670 cm(-1) and 663 cm(-1). Quantum scattering calculations on a literature ab initio potential energy surface for NO(A)-He [J. Kłos et al., J. Chem. Phys. 129, 244303 (2008)] yield near-quantitative agreement with the experimental differential scattering cross sections and good agreement with the rotational polarization moments. This confirms that the Kłos et al. potential is accurate within the experimental collisional energy range. Comparison of the experimental results for NO(A) + D2 and He collisions provides information on the hitherto unknown NO(A)-D2 potential energy surface. The similarities in the measured scattering dynamics of NO(A) imply that the general form of the NO(A)-D2 potential must be similar to that calculated for NO(A)-He. A consistent trend for the rotational rainbow maximum in the differential cross sections for NO(A) + D2 to peak at more forward angles than those for NO(A) + He is consistent with the NO(A)-D2 potential being more anisotropic with respect to NO(A) orientation. No evidence is found in the experimental measurements for coincident rotational excitation of the D2, consistent with the potential having low anisotropy with respect to D2. The NO(A) + He polarization moments deviate systematically from the predictions of a hard-shell, kinematic-apse scattering model, with larger deviations as N' increases, which we attribute to the shallow gradient of the anisotropic repulsive NO(A)-He potential energy surface.

State-to-State Inelastic Scattering of O2 with Helium

Molecular oxygen (O2) is extremely important for a wide variety of processes on and outside Earth. Indeed, O2–He collisions are crucial to model O2 abundance in space or to create ultracold O2 molecules. A crossed molecular beam experiment to probe rotational excitation of O2 due to helium collisions at energies of 660 cm–1 is reported. Velocity map imaging was combined with state-selective detection of O2(X3Σg–) by (2+1) resonance-enhanced multiphoton ionization. The obtained raw O2+ images were corrected from density to flux and the differential cross sections (DCS) were then extracted for six O2 final states. Exact quantum mechanical calculations were also performed. A very good agreement between experimental and theoretical DCSs was found by using an initial O2 beam population ratio of 80% for the first rotational state and 20% for the first excited state. The agreement demonstrates our ability to model inelastic processes between O2 molecules and rare gas both theoretically and experimentally.

Rotational Orientation Effects in NO(X) + Ar Inelastic Collisions

Rotational angular momentum orientation effects in the rotationally inelastic collisions of NO(X) with Ar have been investigated both experimentally and theoretically at a collision energy of 530 cm(-1). The collision-induced orientation has been determined experimentally using a hexapole electric field to select the ϵ = -1 Λ-doublet level of the NO(X) j = 1/2 initial state. Fully quantum state resolved polarization-dependent differential cross sections were recorded experimentally using a crossed molecular beam apparatus coupled with a (1 + 1') resonance-enhanced multiphoton ionization detection scheme and subsequent velocity-map imaging. To determine the NO sense of rotation, the probe radiation was circularly polarized. Experimental orientation polarization-dependent differential cross sections are compared with those obtained from quantum mechanical scattering calculations and are found to be in good agreement. The origin of the collision-induced orientation has been investigated by means of close-coupled quantum mechanical, quantum mechanical hard shell, quasi-classical trajectory (QCT), and classical hard shell calculations at the same collision energy. Although there is evidence for the operation of limiting classical mechanisms, the rotational orientation cannot be accounted for by QCT calculations and is found to be strongly influenced by quantum mechanical effects.

Inelastic Scattering of CO with He: Polarization Dependent Differential State-to-State Cross Sections

A joint theoretical and experimental study of state-to-state rotationally inelastic polarization dependent differential cross sections (PDDCSs) for CO (v = 0, j = 0, 1, 2) molecules colliding with helium is reported for collision energies of 513 and 840 cm(-1). In a crossed molecular beam experiment, velocity map imaging (VMI) with state-selective detection by (2 + 1) and (1 + 1') resonance enhanced multiphoton ionization (REMPI) is used to probe rotational excitation of CO due to scattering. By taking account of the known fractions of the j = 0, 1, and 2 states of CO in the rotationally cold molecular beam (Trot ≈ 3 K), close-coupling theory based on high-quality ab initio potential energy surfaces for the CO-He interaction is used to simulate the differential cross sections for the mixed initial states. With polarization-sensitive 1 + 1' REMPI detection and a direct analysis procedure described by Suits et al. ( J. Phys, Chem. A 2015 , 119 , 5925 ), alignment moments are extracted from the images and the latter are compared with images simulated by theory using the calculated DCS and alignment moments. In general, good agreement of theory with the experimental results is found, indicating the reliability of the experiment in reproducing state-to-state differential and polarization-dependent differential cross sections.

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.

Analysis of velocity-mapped ion images from high-resolution crossed-beam scattering experiments: a tutorial review

A Stark decelerator produces beams of molecules with high quantum state purity, and small spatial, temporal and velocity spreads. These tamed molecular beams are ideally suited for high-resolution crossed beam scattering experiments. When velocity map imaging is used, the Stark decelerator allows the measurement of scattering images with unprecedented radial sharpness and angular resolution. Differential cross sections must be extracted from these high-resolution images with extreme care, however. Common image analysis techniques that are used throughout in crossed beam experiments can result in systematic errors, in particular in the determination of collision energy, and the allocation of scattering angles to observed peaks in the angular scattering distribution. Using a high-resolution data set on inelastic collisions of velocity-controlled NO radicals with Ne atoms, we describe the challenges met by the high resolution, and present methods to mitigate or overcome them. PACS Codes: 34.50.-s; 37.10.Mn.

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.

Direct Extraction of Alignment Moments from Inelastic Scattering Images

We present a novel means of analyzing velocity-map images of angular momentum polarization in inelastic scattering. In this approach, linear combinations of angular distributions obtained by integrating select regions of images for two probe laser polarizations directly yield the alignment-free differential cross sections and the differential alignment moments. No fitting is needed in the analysis. The method relies on the fact that the angular distribution for out-of-plane scattering is encoded in the distribution along the relative velocity vector, and this may be recovered quantitatively owing to the redundancy of the in-plane and out-of-plane scattering for the horizontal polarization case.

The modified quasi-quantum treatment of rotationally inelastic NO(X)-He scattering

A modified quasi-quantum treatment (MQQT) of molecular scattering has been developed to account for the softness of the repulsive part of the anisotropic atom-molecule PES. A contour of the PES is chosen such that the barrier height is just large enough to reflect the incoming kinetic energy, directed anti-parallel to the hard shell normal at the site of impact. The resulting rotationally inelastic quantum state resolved DCSs and ICSs of He + NO(X) at Ecol = 508 cm(-1) are compared to those obtained from regular QQT and from quantum mechanically exact calculations performed on the full highest quality ab initio Vsum PES. The MQQT parity changing DCSs for Δj ≤ 4 exhibit much better agreement with the QM DCSs than is obtained using regular QQT, particularly in the forward scattered direction. The improvements upon the remaining MQQT DCSs with respect to the regular QQT were minor, due to the near incompressible hard shell character of the n ≠ 1 or 3 anisotropic Legendre polynomial terms of the PES.

Steric effects and quantum interference in the inelastic scattering of NO(X) + Ar

New measurements of the differential steric effect for NO + Ar inelastic scattering highlight the importance of quantum interference.

Rotationally inelastic collisions of NO(X) with Ar are investigated in unprecedented detail using state-to-state, crossed molecular beam experiments. The NO(X) molecules are selected in the Ω = 0.5, j = 0.5, f state and then oriented such that either the ‘N’ or ‘O’ end of the molecule is directed towards the incoming Ar atom. Velocity map ion imaging is then used to probe the scattered NO molecules in well-defined quantum states. We show that the fully quantum state-resolved differential steric asymmetry, which quantifies how the relative efficiency for scattering off the ‘O’ and the ‘N’ ends of the molecule varies with scattering angle, is strongly affected by quantum interference. Significant changes in both integral and differential cross sections are found depending on whether collisions occur with the N or O ends of the molecule. The results are well accounted for by rigorous quantum mechanical calculations, in contrast to both classical trajectory calculations and more simplistic models that provide, at best, an incomplete picture of the dynamics.

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.

Inelastic Scattering of NO by Kr: Rotational Polarization over a Rainbow

We use molecular beams and ion imaging to determine quantum state resolved angular distributions of NO radicals after inelastic collision with Kr. We also determine both the sense and the plane of rotation (the rotational orientation and alignment, respectively) of the scattered NO. By full selection and then detection of the quantum parity of the NO molecule, our experiment is uniquely sensitive to quantum interference. For forward-scattered NO, we report hitherto unseen changes in the plane and sense of rotation with scattering angle and show, remarkably, that the rotation of the NO molecule after collision can be near-maximally oriented for certain transitions and scattering angles. These effects are enhanced by the full parity selection in the experiment and result from the interplay between attractive and repulsive forces.

Molecular collisions coming into focus

Control over molecules in a Stark decelerator enables the measurement of diffraction oscillations in NO-atom scattering.

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.