Differential and integral cross sections for the inelastic scattering of NO (X 2Π) by Ar based on a new ab initio potential energy surface

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.

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.

Time-independent quantum theory on vibrational inelastic scattering between atoms and open-shell diatomic molecules: Applications to NO + Ar and NO + H scattering

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(²Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin-orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(²Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Three-dimensional potential energy surfaces of ArNO (X̃ 2Π)

Until now, the potential energy surfaces (PESs) of the ArNO complex found in the literature were two-dimensional, with the NO interatomic distance being fixed. In this work, we present the first accurate three-dimensional ground state X̃ ²Π PESs (both A' and A″) of ArNO computed at the CCSD(T)/CBS level of theory. The equilibrium geometries and the well depths (D_e) are compared to several other electronic structure methods. We found that using the multireference method, MRCI-F12 makes the surfaces much shallower (by 25%) and the depth of the surfaces does not agree with experimental data. The explicitly correlated coupled-cluster method underestimates the well depth as well. Analytic representations for both A' and A″ surfaces were fit to 4380 ab initio points to within 2.71 cm^-1. A three-dimensional Numerov propagator method in Delves coordinates is used to compute the bound state spectrum up to J_tot = 6.5. The recommended dissociation energies are D₀ = 97.2 cm^-1 for the adiabatic ground state and D_e = 133.7 (128.1) cm^-1 for A' (A″).

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°).

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.

Quantum-state-resolved studies of aqueous evaporation dynamics: NO ejection from a liquid water microjet

This work presents the first fully quantum-state-resolved measurements of a solute molecule evaporating from the gas-liquid interface in vacuum. Specifically, laser-induced fluorescence detection of NO(²Π_{1/2, 3/2}, v = 0, J) evaporating from an ∼5 mM NO-water solution provides a detailed characterization of the rotational and spin-orbit distributions emerging from a ⌀4-5 μm liquid microjet into vacuum. The internal-quantum-state populations are found to be well described by Boltzmann distributions, but corresponding to temperatures substantially colder (up to 50 K for rotational and 30 K for spin-orbit) than the water surface. The results therefore raise the intriguing possibility of non-equilibrium dynamics in the evaporation of dissolved gases at the vacuum-liquid-water interface. In order to best interpret these data, we use a model for evaporative cooling of the liquid microjet and develop a model for collisional cooling of the nascent NO evaporant in the expanding water vapor. In particular, the collisional-cooling model illustrates that, despite the 1/r drop-off in density near the microjet greatly reducing the probability of collisions in the expanding water vapor, even small inelastic cross sections (≲ 20 Ų) could account for the experimentally observed temperature differences. The current results do not rule out the possibility of non-equilibrium evaporation dynamics, but certainly suggest that correct interpretation of liquid-microjet studies, even under conditions previously considered as "collision-free," may require more careful consideration of residual collisional dynamics.

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.

Integral steric asymmetry in the inelastic scattering of NO(X2Π)

The integral steric asymmetry for the inelastic scattering of NO(X) by a variety of collision partners was recorded using a crossed molecular beam apparatus. The initial state of the NO(X, v = 0, j = 1/2, Ω=1/2, ϵ=-1,f) molecule was selected using a hexapole electric field, before the NO bond axis was oriented in a static electric field, allowing probing of the scattering of the collision partner at either the N- or O-end of the molecule. Scattered NO molecules were state selectively probed using (1 + 1') resonantly enhanced multiphoton ionisation, coupled with velocity-map ion imaging. Experimental integral steric asymmetries are presented for NO(X) + Ar, for both spin-orbit manifolds, and Kr, for the spin-orbit conserving manifold. The integral steric asymmetry for spin-orbit conserving and changing transitions of the NO(X) + O₂ system is also presented. Close-coupled quantum mechanical scattering calculations employing well-tested ab initio potential energy surfaces were able to reproduce the steric asymmetry observed for the NO-rare gas systems. Quantum mechanical scattering and quasi-classical trajectory calculations were further used to help interpret the integral steric asymmetry for NO + O₂. Whilst the main features of the integral steric asymmetry of NO with the rare gases are also observed for the O₂ collision partner, some subtle differences provide insight into the form of the underlying potentials for the more complex system.

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.

A new perspective: imaging the stereochemistry of molecular collisions

The concept of the steric effect plays a central role in chemistry. This Perspective describes how the polarization of reactant molecules in space can be used to probe directly the steric effect, and highlights some of the new measurements that are made possible by coupling reactant orientation and alignment with ion imaging techniques.

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.

Symmetry-adapted perturbation theory based on unrestricted Kohn-Sham orbitals for high-spin open-shell van der Waals complexes

Two open-shell formulations of the symmetry-adapted perturbation theory are presented. They are based on the spin-unrestricted Kohn-Sham (SAPT(UKS)) and unrestricted Hartree-Fock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory (DFT) compared to the previous formulation of open-shell SAPT based on spin-restricted Kohn-Sham method of Żuchowski et al. [J. Chem. Phys. 129, 084101 (2008)]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following open-shell van der Waals complexes: He···NH, H(2)O···HO(2), He···OH, Ar···OH, Ar···NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Π-state radicals (He···OH, Ar···OH, Ar···NO). In the interactions of transition metal dimers ((3)Σ(u)(+))Au(2) and ((13)Σ(g)(+))Cr(2) we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.

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

Rotational angular momentum alignment effects in the rotationally inelastic collisions of NO(X) with Ar have been investigated at a collision energy of 66 meV by means of hexapole electric field initial state selection coupled with velocity-map ion imaging final state detection. The fully quantum state resolved second rank renormalized polarization dependent differential cross sections determined experimentally are reported for a selection of spin-orbit conserving and changing transitions for the first time. The results are compared with the findings of previous theoretical investigations, and in particular with the results of exact quantum mechanical scattering calculations. The agreement between experiment and theory is generally found to be good throughout the entire scattering angle range. The results reveal that the hard shell nature of the interaction potential is predominantly responsible for the rotational alignment of the NO(X) upon collision with Ar.

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.

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.

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

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

Experimental and theoretical study of rotationally inelastic collisions of CN(A2pi) with N2

Optical-optical double resonance was employed to study rotational energy transfer in collisions of selected rotational/fine-structure levels of CN(A2pi, v = 3) with N2. The CN radical was generated by 193 nm photolysis of BrCN in a slow flow of N2 at total pressures of 0.2-1.4 Torr. Specific fine-structure lambda-doublet levels of CN(A2pi, v = 3) were prepared by pulsed dye laser excitation on isolated lines in the CN A-X (3,0) band, while the initially excited and collisionally populated levels were observed after a short delay by laser-induced fluorescence in the B-A (3,3) band. Total removal rate constants for specified rotational/fine-structure levels involving total angular momentum J from 4.5 to 12.5 were determined. These rate constants decrease with increasing J, with no obvious dependence on the fine-structure/lambda-doublet label. State-to-state relative rate constants were determined for several initial levels and show a strikingly strong collisional propensity to conserve the fine-structure/lambda-doublet label. Comparison is made with the results of quantum scattering calculations based on potential energy surfaces averaged over the orientation of the N2 molecule. Reasonable agreement is found with experimentally determined total removal rate constants. However, the computed state-to-state rate constants show a stronger propensity for fine-structure and lambda-doublet changing transitions. These differences between experiment and theory could be due to the neglect of the N2 orientation and the correlation of the CN and N2 angular motions.

Molecular beam scattering of NO+Ne: A joint theoretical and experimental study

The collision dynamics of the NO+Ne system is investigated in a molecular beam scattering experiment at a collision energy of 1055 cm(-1). Employing resonance enhanced multiphoton ionization of NO, we measured state-resolved integral and differential cross sections for the excitation to various levels of both spin-orbit manifolds. The dependence of the scattered intensity on the laser polarization is used to extract differential quadrupole moments for the collision induced angular momentum alignment. The set of cross section data is compared with results of a full quantum mechanical close coupling calculation using the set of ab initio potential energy surfaces of Alexander et al. [J. Chem. Phys. 114, 5588 (2001)]. In previous work, it was found that the positions and rotational substructures for the lowest bend-stretch vibrational states derived from these surfaces agree very well with the observed spectrum of the NO-Ne complex. For the same potential, we find that the calculated cross sections show a less satisfactory agreement with the experimental data. While the overall Jf dependence and magnitude of the integral and differential cross sections are in good agreement, noticeable discrepancies exist for the angle dependence of the differential cross sections. In general, the calculated rotational rainbow structures are shifted towards larger scattering angles indicating that the anisotropy of the potential is overestimated in the fit to the ab initio points or in the ab initio calculation itself. For most states, we find the measured alignment moments to be in excellent agreement with the results of the calculation as well as with predictions of sudden models. Significant deviations from the sudden models are observed only for those fine-structure changing collisions which are dominated by forward scattering. Results of the full quantum calculation confirm the deviations for these states.

Fully state-resolved differential cross sections for the inelastic scattering of the open-shell NO molecule by Ar

State-resolved differential cross sections (DCSs) for the inelastic scattering of NO(j" = 0.5, Omega" = 1/2) + Ar --> NO(j', Omega' = 1/2, 3/2) + Ar were obtained at a collision energy of 516 cm(-1), both experimentally and theoretically. A crossed molecular beam ion-imaging apparatus was used to measure DCSs for 20 final (j', Omega') states, including spin-orbit conserving (DeltaOmega = 0) and changing (DeltaOmega = 1) transitions. Quantum close-coupling scattering calculations on ab initio coupled-cluster CCSD(T) and CEPA (correlated electron pair approximation) potential energy surfaces were also performed. Although small discrepancies were found for the DeltaOmega = 1 transitions, we find marked agreement between theory and experiment for the collision dynamics of this system, which is the paradigm for the collisional relaxation of a molecular radical.

Chemistry. Close encounters

No chemical reaction can take place without a collision between atoms or molecules. State-of-the-art experimental and theoretical techniques are providing ever more detailed insights into how such collisions proceed. In his Perspective, Crim highlights the report by Lorenz et al., who have succeeded in determining not only the amount but also the sense of rotation of NO molecules after collision with argon atoms. The results can only be explained when subtle quantum mechanical effects are considered.

Direct measurement of the preferred sense of NO rotation after collision with argon

The preferred sense of product molecule rotation (clockwise or counterclockwise) in a bimolecular collision system has been measured. Rotationally inelastic collisions of nitric oxide (NO) molecules with Ar atoms were studied by combining crossed molecular beams, circularly polarized resonant multiphoton ionization probing, and velocity-mapped ion imaging detection. The observed sense of NO product rotation varies with deflection angle and is a strong function of the NO final rotational state. The largest preferences for sense of rotation are observed at the highest kinematically allowed product rotational states; for lower rotational states, the variation with deflection angle becomes oscillatory. Quantum calculations on the most recently reported NO-Ar potential give good agreement with the observed oscillation patterns in the sense of rotation.