ARTICLES PUBLISHED ONLINE: 12 JUNE 2011 | DOI: 10.1038/NCHEM.1071
Interference structures in the differential cross-sections for inelastic scattering of NO by Ar C. J. Eyles1, M. Brouard1 *, C.-H. Yang2, J. Kłos3, F. J. Aoiz4, A. Gijsbertsen5,6, A. E. Wiskerke5 and S. Stolte5,7,8 Inelastic scattering is a fundamental collisional process that plays an important role in many areas of chemistry, and its detailed study can provide valuable insight into more complex chemical systems. Here, we report the measurement of differential cross-sections for the rotationally inelastic scattering of NO(X2P1/2 , v 5 0, j 5 0.5, f ) by Ar at a collision energy of 530 cm21 in unprecedented detail, with full L-doublet (hence total NO parity) resolution in both the initial and final rotational quantum states. The observed differential cross-sections depend sensitively on the change in total NO parity on collision. Differential cross-sections for total parity-conserving and changing collisions have distinct, novel quantum-mechanical interference structures, reflecting different sensitivities to specific homonuclear and heteronuclear terms in the interaction potential. The experimental data agree remarkably well with rigorous quantum-mechanical scattering calculations, and reveal the role played by total parity in acting as a potential energy landscape filter.
I
nelastic scattering is one of the simplest possible collisional processes, responsible for the transfer of energy from one molecule to another1–3. It plays an important role in areas as diverse as atmospheric, combustion and ultracold chemistry4,5, and can have a profound influence on chemical reactivity. The fully quantum state resolved angular distribution of the scattered products, which describes how the molecules are scattered in space after collision, constitutes one of the most detailed of all dynamical observations6. The measurement of such product angular distributions, which are proportional to the corresponding differential cross-sections (DCSs), can provide valuable insight into more complex chemical systems. Rotational inelastic scattering of the NO molecule is of particular interest, because it is an open shell species with both electronic spin and orbital angular momentum in its ground 2P electronic state. The study of NO(X2P) þ Ar has attracted considerable attention, both experimentally and theoretically (see, for example, refs 4 and 7–14 and references therein), because it provides a model system on which to investigate the breakdown in the Born–Oppenheimer approximation15. The ground state of NO is split into two spin–orbit levels, with the V ¼ 3/2 level lying 123 cm21 above the V ¼ 1/2 level (V is the projection of j onto the internuclear axis, and j is the total angular momentum of NO apart from nuclear spin, with the associated quantum number, j ). Each rotational level is split further into two L-doublet sublevels, consisting of symmetric (labelled e ¼ þ1 or e) and antisymmetric (e ¼ 21 or f ) combinations of þV and 2V wavefunctions. These sublevels differ only in total NO parity, p ¼ e (21)j21/2, determined by the symmetry of the total NO wavefunction with respect to space-fixed inversion, and are nearly degenerate, being separated by 0.01 cm21 for j ¼ 0.5. For a non-colinear approach of Ar, the degeneracy of the P-state is lifted, leading to two
potential energy surfaces (PESs) of A′ and A′′ symmetry15,16. For Hund’s coupling case (a) molecules, in which the electronic orbital and spin angular momenta are both tied to the internuclear axis17, Alexander has shown that spin–orbit conserving (DV ¼ 0) transitions take place on a summed potential, Vsum ¼ (A′ þ A′′ )/2, while spin–orbit changing (DV ¼ 1) collisions are governed by Vdiff ¼ (A′′ 2 A′ )/2 (refs 15,16). In the following, we report for the first time differential cross-sections for the fully L-doublet quantum state selected and resolved scattering of NO(X2P1/2 , v ¼ 0, j ¼ 0.5, f ) by Ar at a collision energy of 530 cm21, focusing exclusively on spin–orbit conserving transitions (differential cross-sections for spin–orbit changing collisions will be considered in a future publication). We show that the differential cross-sections are exquisitely sensitive to the NO L-doublet levels, despite being separated by only a tiny fraction of the experimental collision energy, and in particular sensitive to the change in total NO parity on collision.
Results As described in the Methods, the experimental measurements were made using a crossed molecular beam apparatus6, which incorporated a hexapole electric field before the interaction region to enable selection of the initial L-doublet state. By taking advantage of the Stark effect, only those molecules in the ( j ¼ 0.5, f ) L-doublet level of negative total parity are focused into the collision region6. The use of (1 þ 1′ ) resonantly enhanced multiphoton ionization on selected rotational branches, coupled with velocity-mapped ion imaging detection, then allows probing of the scattered NO in a specific final rotational ( j′ ) and L-doublet (e or f ) state. The resulting experimental ion images reflect the centre-of-mass (COM) velocity distribution of the NO(X) molecules after inelastic collision. Figure 1 presents a selection of such images, together with an
1
The Department of Chemistry, University of Oxford, The Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ, UK, 2 Institute for Molecules and Materials, Radboud University Nijmegen, Heijendaalseweg 135, 6525 ED Nijmegen, The Netherlands, 3 Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland, 20742, USA, 4 Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, Universidad Complutense, 28040 Madrid, Spain, 5 Laser Centre and Department of Physical Chemistry, Vrije Universiteit, Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, 6 FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands, 7 Atomic and Molecular Physics Institute, Jilin University, Changchun 130012, China, 8 Laboratoire Francis Perrin, Baˆtiment 522, DRECEM/SPAM/CEA Saclay, 91191 Gif sur Yvette, France. * e-mail:
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Figure 1 | Experimental and fitted ion images. Raw experimental ion images (left) and fits (right) for the scattering process NO(X2P1/2 , v ¼ 0, j ¼ 0.5, f ) þ Ar NO(X2P1/2 , v ¼ 0, j ′ , f ) þ Ar at a collision energy of 530 cm21. The bottom right-hand image depicts an expanded view of the vector (Newton) diagram for the collision producing j ′ ¼ 8.5, f, in which the mean relative velocity (magnitude 860 m s21, labelled ‘REL’) runs from the top left to the bottom right of the image. COM refers to the velocity vector of the centre-of-mass. Data for the other final L-doublet state are shown in the Supplementary Information.
expanded view of the vector (Newton) diagram defining the NO, Ar, COM and relative velocities. The molecular beam expansion conditions used dictate that the Ar and NO beams have similar laboratory (LAB) velocities, and the two sides of the Newton triangle have almost equal lengths. Intensity in the bottom right of the image corresponds to forward scattering, and intensity in the top left to backward scattering of NO with respect to the initial NO velocity in the COM frame. To extract the DCS from the experimental images they were fit using a basis function method (Supplementary section ‘Monte Carlo simulation and fitting of the experimental images’). Figure 1 displays a selection of fits to the raw data performed in this fashion. They can be seen to capture the angular intensities of the ion images for a range of different input data, suggesting that the basis functions provide a good description of the experimental conditions. The experimentally derived DCSs for the f f transitions, images for which are shown in Fig. 1, together with those obtained from similar data for the f e collisions, are presented in Fig. 2, where they are plotted as a function of COM scattering angle, u. The DCSs display a marked dependence on the final rotational state. The maxima in the intensities shift from the forward scattered direction for j ′ ¼ 6.5 to progressively more sideways scattered directions at j ′ ¼ 11.5. Transfer of translational to rotational energy is most efficient for collisions with small impact parameters, which probe the repulsive part of the potential, and give rise to sideways and backward scattering. Conversely, ‘glancing’ collisions, which 2
DOI: 10.1038/NCHEM.1071
mainly sample the long-range attractive part of the potential, tend to be more forward scattered, and are less efficient at inducing rotational excitation. Figure 2 also compares the experimental results with DCSs obtained from exact open-shell close-coupled quantum-mechanical (CC QM) scattering calculations (see Methods). These were made with the HIBRIDON suite of codes (see http://www.chm.unipg.it/ chimgen/mb/hibridon/index.html) using the ab initio PESs of Alexander10. Given the very detailed nature of the experimental data, the level of agreement between theory and experiment is extremely good. The positions and amplitudes of the maxima and minima in the experimental DCSs are particularly well reproduced by theory, suggesting that the PESs and the dynamical calculations are remarkably accurate. The more rapid oscillations in the quantum-mechanical data seen in the region of small scattering angles (known as ‘diffraction oscillations’2) arise from interfering ‘trajectories’ at impact parameters leading to forward scattering. This structure is not observable in the present experiments, because the velocity distributions in the two molecular beams produce a series of overlapping Newton spheres of scattered molecules that smear out the oscillations. The fully quantum-state resolved DCSs of the scattered NO(X) are strikingly sensitive to the change in total parity on collision (compare the red and green lines in Fig. 2). Total parity-conserving transitions (Dj ¼ even, f f or e e, and Dj ¼ odd, f e or e f, for which Dp/2 ¼ 0) generally show multiple peak structure in their DCSs, while the parity-changing collisions (Dj ¼ even, f e or e f and Dj ¼ odd, f f or e e, for which Dp/2 ¼+1) invariably display just a single maximum. Previous measurements of the DCSs for NO(X)þ Ar (refs 9, 11, 13) have not resolved the initial L-doublet state, and the consequence of the resulting initial state averaging is to significantly blur the oscillatory structure observed in the fully parity resolved DCSs. To reinforce this point, Fig. 3 compares the theoretical DCSs for the transitions NO(X2P1/2 , j ¼ 0.5, e/f ) þ Ar NO(X2P1/2 , j ′ , f ) þ Ar, that is, for different initial L-doublet levels and specific final states. When both the initial and final L-doublet states are resolved (black dashed and blue dotted lines in Fig. 3), the total parity-conserving transitions exhibit DCSs with an oscillatory structure, which is almost absent for the total parity-changing transitions. Clearly, experimental resolution of the initial NO(X) L-doublet level allows for a much more refined assessment of the accuracy of the quantummechanical calculations than has hitherto been possible, and is also essential to reveal the role played by the total parity of the NO(X) wavefunction.
Discussion Quasi-classical trajectory simulations using the Vsum PES do not show clear evidence of multiple peaks in the DCSs, suggesting that the structure in the experimental DCSs must have a quantum-mechanical origin. NO parity must also play an important role. Although the total parity of the NO þ Ar scattering wavefunction must be conserved throughout the course of the collision, the parity of the NO molecular wavefunction (and hence also the triatomic parity) may be changed, and this will also have a profound impact on the outcome of the collision. Model hard shell calculations indicate that the main features of the DCSs can be understood qualitatively in terms of contributions to inelastic scattering from four interfering pathways18,19. These correspond to the different angles of approach g, which lead to products flying into the same scattering angle, u. In the following simple treatment, which is adapted from the hard shell ellipse models of McCurdy and Miller18 and Korsch and Schinke19,20, these pathways are approximated as occurring at the limiting Jacobi angles reflecting ‘side-on’ (g ¼ 908) and ‘head-on’ (g ¼ 08 or 1808) trajectories associated with N-end and O-end collisions,
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DOI: 10.1038/NCHEM.1071
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Figure 2 | Experimental versus quantum-mechanically calculated DCSs. Comparison of the DCSs for NO(X2P1/2 , v ¼ 0, j ¼ 0.5, f ) þ Ar from experiment (red continuous lines, total parity-conserving; green dashed lines, parity-changing transitions) and CC QM theory (black dashed lines, parityconserving; blue dotted lines, parity-changing transitions) at a collision energy of 530 cm21. The initial state has negative total parity, p ¼ 21, and ′ the final states have parity p ¼ e (21)j 21/2, such that total parity-conserving transitions (in red) are those with Dj ¼ j ′ 2 j ¼ even, f levels, and with Dj ¼ odd, e levels. The experimental data, resulting from the averaging over multiple ion images, have been scaled to the theoretical cross-sections. Vertical error bars indicate combined estimates of both statistical and systematic errors (2s).
Figure 3 | An illustration of the blurring effect of averaging over the initial NO L-doublet states. Calculated DCSs for NO(X2P1/2 , v ¼ 0, j ¼ 0.5) þ Ar NO(X2P1/2 , v ¼ 0, j′ ) þ Ar at a collision energy of 530 cm21. The dashed black and dotted blue lines correspond to parity-conserving and paritychanging collisions, respectively (as in Fig. 2). The solid red line represents the average over initial L-doublet states, that is, an average of the ( f f ) and (e f ) transitions, which would not be separable in the absence of hexapole selection. Note that structure which is clearly visible in the parityresolved data would be significantly washed out by this averaging.
as illustrated in Fig. 4 and discussed further below. Within this model the DCSs for the parity-conserving transitions at a given scattering angle are given by the equation (Supplementary section ‘Model calculations and interpretation’)
dstot / 2 − 2 cos(DfN − DfO ) dvf i
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ds / 6 + 4(cos DfN + cos DfO ) + 2 cos(DfN − DfO ) dvf i
(1)
where DfN and DfO are the relative phase shifts associated with scattering off either of the two ends and the side of the NO molecule. These relative phase shifts are illustrated in Fig. 4. The dominant contribution to the DCS for the parity-conserving transitions can be seen to arise from the interference between the trajectories impacting on the pointed ends and flatter middle of the NO molecule, as embodied in the cosDfN and cosDfO terms. These parity-conserving DCSs depend mainly, but not exclusively, on the homonuclear terms in the interaction potential, with heteronuclear features of the potential appearing through the cos(DfN 2 DfO) term. Owing to the near homonuclear nature of the NO molecule, the phase shifts DfN and DfO will take quite similar values. Therefore, the heteronuclear cos(DfN 2 DfO) term will not be as important as the homonuclear-like terms, cosDfN and cosDfO , in determining the oscillatory structure in the parity-conserving DCSs, because (DfN 2 DfO) varies more slowly with scattering angle than either DfN or DfO.
For the parity-changing collisions, the corresponding DCSs are given by the expression (2)
The parity-changing DCSs can thus be seen to depend solely on the interference between trajectories scattered from opposite ends of the NO molecule. This interference will depend on the heteronuclear terms in the interaction potential, and it is readily apparent that the parity-changing transitions will disappear in the absence of these terms, as required. The phase shifts needed to evaluate the above expressions can be estimated in the classically allowed region, within the infinite-ordersudden (IOS) approximation21 of Korsch and Schinke19,20, as the WKB phase difference between the paths hitting the molecule ‘head on’ and ‘side on’. As shown in Supplementary section ‘A simple hard shell model’, these are dependent on the de Broglie wavelength of the scattering particles, the scattering angle and the differences between the major and minor semi-axes at the two ends of the molecule, (AO 2 B) and (AN 2 B) (ref. 19). Once the phase shifts are known, the relative DCSs can be evaluated (Fig. 5). Note that the model calculations have been scaled appropriately to the CC QM DCSs. The model is able to reproduce qualitatively the structure in the observed DCSs, and in particular accounts for the different number of peaks observed in the parity-conserving and parity-changing collisions, as well as their approximate locations.
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Figure 4 | Illustration of the four limiting paths used in the hard shell calculations. The four paths that contribute to the total scattering amplitude in the simple hard shell model, and the relative phase shifts that exist between them. The four paths lead to scattering into the same scattering angle u, and correspond to four different orientations of the NO molecule with respect to the incoming Ar atom (identified as orange circles). Note that Dp/2 ¼ 0 for parity-conserving collisions and Dp/2 ¼+1 for paritychanging collisions, where Dp is the change in the total NO parity on collision. See text and Supplementary Information for further discussion about the relative phase shifts.
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The qualitative success of the model suggests that the dynamics of the collisions are mainly determined by the repulsive part of the potential for all but the most forward scattering angles (which are classically forbidden in the hard shell model) and the lowest rotational states. Furthermore, the multiple peaks in the total NO parity-conserving DCSs are seen to be due principally to quantum interferences associated with the path differences arising from scattering at the side and either of the two ends of the NO(X) molecule18,19. In the homonuclear case, when the two ends of the molecule are identical, the structures in the DCS, commonly referred to as ‘rainbow oscillations’2, collapse to a single oscillatory feature. As mentioned above, for the slightly heteronuclear NO þ Ar system, the location and frequency of the two sets of rainbow structures are critically sensitive to the de Broglie wavelength of the scattering particles, and to the differences between the major and minor semi-axes at the two ends of the molecule. The multiple peak structure in the DCSs for total parity-conserving transitions then appears as a coherent superposition of contributions from these two rainbows, and these DCSs are therefore sensitive to both homonuclear and heteronuclear terms in the interaction potential. In contrast, for the parity-changing collisions the structure in the DCSs reflects the interference between the two paths striking either end of the molecule. The form of these DCSs reflects directly the difference between the O and N ends of the molecule, characterized by heteronuclear terms in the potential. The fact that NO is a near-homonuclear molecule ((AO 2 AN) ≪ (AO þ AN)) means that for these parity-changing collisions the phase difference arising from scattering from the two ends of the molecule is relatively small, and only a single strong peak in the DCS is observed (see top row of Fig. 5b).
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Figure 5 | Comparison of DCSs from the hard shell model with those from CC QM and QQT theory. The top row of the figure shows the results of the simple hard shell model resolved into contributions from scattering from the N-end of the molecule (blue dotted line) and the O-end of the molecule (green dotted line). In the model, the total hard shell DCS is the coherent sum of these contributions (red solid lines). The remaining rows present a comparison of the CC QM DCSs (black dashed lines) with the hard shell model DCSs (red solid lines), and with the results of hard shell QQT calculations22 (blue dotted lines). The left and right panels are for the V ¼ 0.5, j ¼ 0.5 V ¼ 0.5, j ′ ¼ 6.5 and 10.5, transitions, respectively. The top three rows (a) represent parity-conserving transitions (for the hard shell model calculated using equation (1)) and the bottom two rows (b) correspond to parity-changing transitions (for the hard shell model calculated using equation (2)). The vertical blue bars illustrate positions of destructive (DfN 2 DfO ¼ p ) and constructive (DfN 2 DfO ¼ 0, 2p ) interference in the parity-conserving and -changing DCSs, respectively, as indicated by the hard shell calculations. The hard shell model and QQT DCSs have been scaled to the QM results.
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To illustrate that the structure in the DCSs arises from a coherent quantum-mechanical interference effect, it is helpful to consider the separate contributions to the DCSs from the scattering off the N and O ends of the molecule. These contributions are shown in Fig. 5a for the two parity-conserving transitions leading to j ′ ¼ 6.5 and 10.5, as derived from the hard shell model. As can be seen, the interference pattern in the parity-conserving DCSs arises as the coherent sum of the scattering from the N and O ends of the molecule. The coherent nature of the scattering is particularly evident in the model DCSs for the parity-conserving transitions at angles around the peaks in the parity-changing DCSs, the locations of which are highlighted by vertical blue lines in Fig. 5. Near these angles, the cross-sections for the parity-conserving transitions are significantly less than those obtained from the incoherent sum of the contributions from the two ends of the molecule. Note, furthermore, that both the dips in intensity in the parity-conserving DCSs, as well as the corresponding peaks in the parity-changing DCSs, arise from the slightly heteronuclear nature of the NO molecule. We believe that these interference features will be general to inelastic scattering of near-heteronuclear molecules at the appropriate de Broglie wavelength. The structure in the DCSs for NO total parity-conserving and parity-changing collisions is somewhat better accounted for by the hard shell quasi-quantum treatment (QQT) of Stolte et al.22 (see Fig. 5 and Supplementary section ‘Quasi-quantum treatment calculations’). This model includes a more rigorous determination of the phase differences discussed above, and uses a hard shell potential determined from the contour of Vsum at an energy corresponding to the collision energy of the present experiments. Note that the QQT data (as well as those from the simple hard shell model) have been scaled to match best the CC QM DCSs. Although these model calculations are unable to generate reliable integral cross-sections, and therefore cannot take the place of exact QM scattering theory, they do help to provide some insight into the origin of the observed angular distributions. The QQT calculations confirm that the change in the total parity of the NO(X) on collision dictates which homonuclear and heteronuclear terms in the potential are important, and hence determines the chemical shape of the NO molecule experienced by the scattered Ar atom. Strikingly, the model calculations also reveal that the dips in intensity in the parity-conserving DCSs and the peaks in the parity-changing DCSs (located at points illustrated by the blue vertical lines in the panels of Fig. 5) both arise from a novel quantum interference effect reflecting the slightly heteronuclear nature of the NO molecule. A more quantitative link between the dynamics of the NO total parity-conserving and parity-changing transitions and the homonuclear and heteronuclear terms in the interaction potential23,24 is provided by considering the potential matrix elements that control the scattering behaviour15,16. By performing CC QM scattering calculations on a modified Vsum potential, as described in Supplementary section ‘Parity dependent potential matrix elements’, it is possible to establish the relative sensitivities of parity-conserving and parity-changing collisions to heteronuclear and homonuclear terms in the potential, and to confirm the qualitative picture provided by the hard shell and QQT models described above. One advantage of the potential matrix element approach is that, unlike the simple hard shell and QQT models, it should be possible to use it to rationalize spin–orbit changing collisions, as well as the spin–orbit conserving transitions considered here. To conclude, we have demonstrated that full quantum-state resolution of the initial and final L-doublet state is essential to gain a complete picture of the inelastic scattering dynamics of NO(X) þ Ar. Although structured DCSs have been observed previously in L-doublet averaged experiments on this system9,11,13, it is only when both the initial and final NO parities are resolved that the
origin of the oscillations is revealed as being a novel parity-dependent quantum-mechanical interference effect. Such phenomena provide for a test of theory at an unprecedented level of detail, and could be important in the inelastic scattering of both closed- and open-shell species by isolated atoms and molecules in the gas phase, as well as with surfaces.
Methods Computational procedures. The CC QM dynamical calculations were performed with the HIBRIDON suite of codes (http://www.chm.unipg.it/chimgen/mb/ hibridon/index.html), which uses a hybrid propagator comprising the log-derivative propagator by Manolopoulos25,26 and the Airy propagator for the long-range region. A propagation from 4.5 bohr to 60 bohr was used, and included a rotational basis with all NO(X) states up to j ¼ 20.5 and all partial waves up to total angular momentum quantum number, J ¼ 160. These calculations used both the Vsum ¼ (A′ þ A′′ )/2 and Vdiff ¼ (A′′ 2 A′ )/2 potential energy surfaces (PESs) of Alexander10 (which assume a fixed bond length for the NO(X) molecule). Calculations were run over a grid of collision energies from 500 cm21 to 560 cm21 with a spacing of 15 cm21, and the theoretical CC QM DCSs were averaged over the appropriate experimental collision energy distribution (see below). Although this has the effect of somewhat blurring the oscillations in the forward scattered direction at low values of j′ (that is, of blurring the ‘diffraction oscillations’21), the DCSs remain otherwise unchanged over this range of energies. Experimental procedures. The experiments made use of a crossed molecular beam apparatus, coupled with hexapole initial quantum state selection and (1 þ 1′ ) resonantly enhanced multiphoton ionization (REMPI) velocity-mapped ion imaging final-state detection6. A backing pressure of 3 bar was used for each of the two molecular beams, with that for NO being seeded at 15% in Ar to increase the degree of adiabatic cooling. The NO beam passed through a hexapole state selector before being intersected in the scattering chamber by the Ar atomic beam. Simulations, described in Supplementary section ‘Experimental and data analysis procedures’, suggest that the beam conditions applied yielded an approximately Gaussian collision energy distribution with a mean of 530 cm21, and a full-width at half maximum (FWHM) of 50 cm21. Adiabatic expansion of the molecular beam forces the majority of NO(X) molecules into their ground rotational state. However, given that the splitting between the lower e and upper f components is only 0.01180 cm21, both L-doublet levels will be near-equally populated in the molecular beam. Application of a hexapole electric field allows the selection of the L-doublet level by focusing those molecules in the upper e ¼ 21, f L-doublet component of the j ¼ 1/2 state into the interaction region, while defocusing molecules in the lower j ¼ 1/2, e ¼ þ1, e L-doublet component27. The e and f L-doublet components for higher j states are only slightly focused or defocused due to their much weaker Stark effect, as described in detail previously6. Scattered NO(X2P1/2 , v′ ¼ 0, j′ ) was detected using (1 þ 1′ ) REMPI using the 0–0 band of the A2Sþ X2P transition around 226 nm, followed by ionization at 308 nm. The probe laser was tuned to individual rotational lines to allow observation of the quantum state resolved DCS, with the identity of the rotational branch determining the final L-doublet level probed. f f collisions were obtained by probing NO(X) on the satellite R21 transition, while f e collisions were probed from an analysis of data recorded on the R11 and overlapping Q21 satellite branches. Velocity-mapped28 ion imaging29 optics were used to accelerate the ionized NOþ molecules out of the scattering centre onto a microchannel plate (MCP). The extraction field used to velocity-map the NO ions was insufficient to mix the NO(X) L-doublet levels and orient the NO. The flashes on the MCPs caused by ion impact were recorded using a charge-coupled device camera and transferred to a PC for subsequent averaging and data analysis. The data analysis and data fitting of the ion images is described further in Supplementary section ‘Monte Carlo simulation and fitting of the experimental images’.
Received 12 January 2011; accepted 17 May 2011; published online 12 June 2011
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Acknowledgements Support was provided by the UK EPSRC (to M.B. via programme grant no. EP/G00224X/1), the EU (to M.B. via FP7 EU People ITN project 238671), Consolider Ingenio 2010 (grant CSD2009-00038) and the Spanish Ministry of Science and Innovation (grant CTQ2008-02578/BQU). J.K. acknowledges financial support from the US National Science Foundation (grant no. CHE-0848110 to M.H. Alexander (Department of Chemistry and Biochemistry, University of Maryland, USA)) and the University Complutense de Madrid/Grupo Santander (under the ‘Movilidad de Investigadores Extranjeros’ programme). The support of the LASERLAB EUROPE is also gratefully acknowledged. Finally, the authors thank D.H. Parker and G. McBane for valuable discussions, and A. Ballast for help with collecting some of the data reported here.
Author contributions The research project was conceived by M.B., F.J.A. and S.S., and the experiments were performed by C.J.E., C.-H.Y., A.G., A.E.W. and S.S. Calculations were performed by C.J.E., A.G., J.K., F.J.A. and S.S., and the paper was written by M.B. and C.J.E. All authors contributed to discussions about the content of the paper.
Additional information The authors declare no competing financial interests. Supplementary information accompanies this paper at www.nature.com/naturechemistry. Reprints and permission information is available online at http://www.nature.com/reprints/. Correspondence and requests for materials should be addressed to M.B.
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