Richard Zare

Gus Hancock

Graham Richmond

Grant A D Ritchie

Sarah Taylor

Matthew L Costen

Frequency Modulated Circular Dichroism Spectroscopy: Application to ICN Photolysis

Keywords: ICN, photodissociation, orientation, angular momentum, coherent

CN photofragments produced in the 248 nm photolysis of ICN are characterized by frequency-modulated absorption spectroscopy in the red A 2 Π ← X 2 Σ + system. A range of high rotational states in both v = 0 and v = 1 were selected to isolate only those dissociation channels including coincident ground state I( 2 P 3/2 ). Velocity-resolved alignment and orientation parameters are determined from the observed Doppler profiles.

The alignment measurements for both v = 0 and v = 1 levels are very similar, and consistent with dissociation occurring via three distinct pathways, beginning with simultaneous excitation of the 4A'( 3 Π 0+ ), 5A'( 1 Π 1 ) and 5A"( 1 Π 1 ) surfaces. Whilst the incoherent alignment parameters for both v = 0 and v = 1 products are similar, the corresponding coherent orientation parameters are markedly different. CN (v = 0, N) exhibits a large positive orientation, whereas all rotational states probed in v = 1 show a much smaller orientation. This is consistent with the previously observed change in the sign of the coherent orientation parameter between v = 0 and v = 2.

Introduction

The past ten years has seen an explosion of interest in the study of the velocity-resolved angular momentum orientation of photofragments [START_REF] Wouters | Imaging in Chemical Dynamics[END_REF][START_REF] Clark | [END_REF]. This has been driven by the realization that these vector properties contain information not just on the magnitudes of different photofragment pathways, but also on their relative phases [3][4][5]. The vast majority of the experimental studies have investigated the orientation of the electronic angular momenta of the atomic products from the dissociation of diatomics, or in fewer cases, triatomics. In contrast, there have been only a few studies of the relevant rotational angular momentum orientation of the diatomic products from triatomics [6][7][8].

The photodissociation of ICN is a prototype for multi-surface dynamics, displaying coherent and incoherent vector properties in the diatomic fragment, and for which there are a wealth of experimental and theoretical studies. The à continuum, which lies between 210 and 320 nm, has contributions from several optically bright states. Early experimental studies found that the dissociation has two distinct electronic exit channels [9][10][11], ( ) ( )

2 2 3/ 2 ICN hv I P CN X + +  → + ∑ (1)
( ) ( )

2 2 1/ 2 ICN hv I P CN X + +  → + ∑
where I( 2 P 3/2 ) is the ground electronic state and I( 2 P 1/2 ) the excited electronic state, hereafter I and I* respectively. The I*/I branching ratio varies with photolysis wavelength, peaking near the centre of the band at ~260 nm, and falling off towards the wings of the absorption band [12][13][14][15]. The CN product state distributions also exhibit a strong photolysis wavelength dependence. The CN fragments are produced with a nonstatistical rotational distribution; this can be decomposed into markedly different rotational distributions for the two exit channels, with CN fragments produced in conjunction with I rotationally hotter than those produced with I* [9,12,13,[16][17][18][19][20][21] . The CN fragments are vibrationally cold in the centre of this UV band [16,17,22], however, in the low energy tail several percent of the CN are vibrationally excited [19,20,22].

The photodissociation dynamics of ICN can best be interpreted using the work of Amatatsu et al. (AYM) [23,24], whose ab initio calculations showed that the à continuum is comprised of contributions from three potential energy surfaces (PESs), the Condon region, thus lifting the degeneracy of the 1 Ω = states. The 1 Π 1 and 3 Π 1 surfaces therefore split into A' and A" states, while the 3 Π 0+ remains as an A' state. The 3 Π 0+ (4A') surface is populated via a parallel transition from the ground state, and is diabatically correlated to I*. Conversely, the A' and A" components of the 1 Π 1 and 3 Π 1 surfaces both lead diabatically to I, and are populated via perpendicular transitions. The 1 Π 1 (5A') and 3 Π 0+ (4A') states are coupled via a conical intersection after the Franck-Condon region and the bending angle dependence of the surfaces plays an important role in the probability of this curve crossing. These surfaces have been used in classical surface hopping trajectory [23,25], time-independent [26,27] and time-dependent [28,29] quantum scattering calculations.

High resolution Doppler [14][15][16]30] and photofragment translational spectroscopy [10] (PTS) studies have determined vector properties that confirm the mixture of perpendicular and parallel transitions. Velocity resolution of the rotational angular momentum alignment allows the decomposition of the I and I* channels, for individual rovibrational states, into their different contributions from the 4A', 5A' and 5A" surfaces [7,14,15,30]. This provides a signature of where the product amplitude started on the excited PESs, whilst the variation with I/I* channel and CN product state provides information on the conical intersection and the adiabatic and diabatic dynamics. These results confirm the general nature of the AYM PESs. High resolution Doppler studies also indicate the importance of vibrational bend excitation in the non-adiabatic dynamics [15], an effect predicted by AYM and first observed by Kash and Butler, who carried out PTS at 248 nm using two different nozzle temperatures to probe changes in the I*/I branching ratio with parent vibrational temperature [31]. Further investigations into the effect of parent excitation have been carried out by Li et al., using transient frequency modulated (FM) Doppler spectroscopy, for ICN photolysis at 262 nm with parent temperatures of 296 and 550 K, affording greater state selectivity than the previous PTS study [32].

With multiple pathways to final product states, ICN photodissociation is an ideal system in which to observe coherence effects. The first observation of coherence was in the relative populations of the spin-rotation manifolds, F 1 and F 2 , which have been found to oscillate with rotational quantum number, N [17,33]. More significantly for this study, ICN was the first system in which molecular fragment rotational orientation arising from circularly polarized 248 nm photolysis was observed [34]. This study, using circularly polarized Laser Induced Fluorescence (LIF) probing, revealed a velocity-averaged orientation of the v = 0 level which varied in sign and magnitude as a function of N. It was suggested that this was a consequence of the I and I* product channels having opposite orientations. Further measurements of the v = 2 level [35], resulted in the remarkable observation that the fragment orientation alternated in sign depending on spin-rotation manifold. These experiments also hinted at the presence of a velocity dependence to the orientation. This velocity dependence was confirmed and characterized for a wide range of N in v = 0, for both 248 and 266 nm photolysis, by Costen and Hall using FM Doppler spectroscopy [7], These experiments demonstrated that single rotational levels of CN produced in the I and I* channels did indeed have opposite orientations, and that both the integral and Doppler-resolved orientations could be described by a single parameter. Fragment orientations of this nature, described by the orientation moment

( ) [ ] ⊥ ||, Re 1 1 a
in the nomenclature introduced by Rakitzis and Zare [4],

are an indication of coherence between parallel and perpendicular photodissociation channels. Molecular fragment orientation of a different symmetry has been reported in the photodissociation of a few other triatomic systems including NO from NO 2 [36][37][38],

and O 2 ( 1 ∆ g ) from O 3 [38][39][40]. The molecular frame orientation in these systems integrates to zero in the laboratory frame, and is undetectable with one-photon Doppler absorption spectroscopy, although it can be observed with REMPI time-of-flight, Doppler-resolved LIF with polarization analyzed emission, or ion-imaging methods. The molecular frame orientation in these systems is described by the orientation moment

( ) [ ] ⊥ ||, Im 1 1 a [4,41], or ) 21 ( 2 0
β in the bipolar moment notation [36]. Despite the ( ) ⊥ ||, notation that suggests multiple surface interference, this type of orientation only requires a simultaneous excitation to continua with different helicity, which can arise on a single directly dissociative surface when the transition moment is neither parallel nor perpendicular to the recoil velocity [36,42]. The only photodissociation systems besides , has been reported, to our knowledge, are the OH products of H 2 O 2 and HOCl [6,8].

This paper concentrates on CN fragment orientation in both the ground and first excited vibrational states. We have employed Doppler resolved, one photon, FM absorption spectroscopy to probe the photoproducts, which affords high velocity resolution due to the very narrow bandwidth of the diode laser probe. In this work we report measurements of velocity-resolved orientation and alignment for CN(X 2 Σ + , v = 0, 1) from the 248 nm photolysis of ICN. The v = 0 measurements span a range of high N states extending from the previously reported states to the limit of the rotational distribution. The v = 1 state measurements reported here are the first for this vibrational state.

Experimental

The CN photofragments were generated from room temperature flowing samples of ICN (Fisher Scientific) at pressures of ≈ 40 mTorr, using 248 nm radiation from a KrF Excimer laser (Lambda Physik COMPex 102). An external cavity diode laser (Sacher Lasertechnik TEC 500) tuneable between 825 and 875 nm was used to probe the CN photofragments on the A 2 Π-X 2 Σ + (2,0) and (3,1) bands. A range of rotational levels from both the F 1 (J = N + ½) and F 2 (J = N -½) manifolds were investigated with sub-Doppler resolution. The near IR radiation was passed through an optical isolator (OFR) before being focused through an electro-optic modulator (EOM) (Quantum Technology Inc., 3500-P) to which a modulation frequency of 406 MHz was applied, and then recollimated prior to passing through the reaction cell. A voltage was applied to the piezo element on the external cavity of the probe laser to step the laser frequency in discrete intervals across the absorption profile of interest. A scanning Fabry-Perot etalon (Melles Griot 13SAE048) was used to monitor the spectral output of the probe laser, allowing the frequency steps to be calibrated.

Four experimental geometries, as illustrated in Figure 1, were used in this work. All four geometries utilise a 1.5 m glass photolysis cell, with the photolysis and probe beams arranged counter-propagating with a crossing angle of 4°. The off-axis angle allowed the photolysis and probe beams to enter the cell through different windows, which avoids window shock heating effects on the probe signal due to passage of the photolysis beam.

Geometries 1 and 2 are described in terms of the angles θ a and χ a , as defined by Dixon [43], describing the propagation and polarization vectors of the probe relative to the photolysis electric vector [15,44]. In geometries 3 and 4 the counter-propagating beams of opposite helicities co-rotate in the space-fixed frame, labelled CP = 0, whilst those of the same helicity counter-rotate and are labelled CP = 1 [7].

The photolysis beam was passed through a Rochon prism polariser (MgF 2 , B. Halle GmbH) to linearly polarise the radiation. For geometries 3 and 4 where circularly polarised photolysis radiation is required, the beam was passed through a Fresnel Rhomb (B. Halle GmbH) immediately prior to the cell. The polarisation of the probe radiation was controlled using a photoelastic modulator (PEM) (Hinds Instruments PEM 90 F55 Optical Head). The PEM contains a birefringent material which has a stress dependent retardation. Modulating the stress on this material using a piezoelectric driver produces a sinusoidal variation of the retardation, and hence polarisation of the beam. The 248 nm photolysis beam was triggered to coincide with the point in the stress cycle with the desired probe polarisation. The timing of the photolysis pulse was controlled by the data acquisition computer, enabling geometries 1 and 2, and similarly 3 and 4, to be acquired over the same experimental run, alternating a preset number of averages for each probe polarisation for each successive step across the absorption profile. Regular checks of the purity of the circular polarisation used in geometries 3 and 4 were carried out as in the work of Costen et al [7].

After passing through the reaction cell the near IR radiation was focused onto a fast InGaAs photodiode (1 GHz, New Focus), suitably attenuated by a neutral density filter to ensure that the power of the probe was within the linearity limits of the detector. The detected signals were amplified using either one, or two, 500 MHz amplifiers (Minicircuits ZFL-500LN) as required, and then demodulated with reference to the rf signal applied to the EOM in an rf demodulator circuit (Pulsar Microwave). The resulting The nascent pure FM absorption profiles were extracted by the method used in our previous work [45]. First, a numerical integration over a series of time intervals with

Analysis

The nascent Doppler profiles have characteristic lineshapes that depend on experimental geometry, spectroscopic branch and the correlations between velocity and angular momentum that we seek to determine. There are several ways in which those correlations can be parameterised [START_REF] Wouters | Imaging in Chemical Dynamics[END_REF]3,5,46]. We choose to use the bipolar moment formalism introduced by Dixon [43]. In Dixon's original description, these moments characterise the correlations between the transition dipole moment, µ, the fragment velocity, v, and the rotational angular momentum, J. This is valid for linearly polarized photolysis at high-J, and dissociation via a single PES. When multiple surfaces, circularly polarized light and coherent effects are introduced, it is more practical to reference the bipolar moments to the laboratory frame quantization axis, and to recognise that there may be correlations between bipolar moments, as they parameterize more fundamental orientation and alignment moments [7]. However, it is convenient to express the alignment bipolar moments, ( )

2 1 2 0 k k β
, in the more familiar µ-fixed frame form, to facilitate their comparison to literature. This can be achieved by multiplying them by a factor of 5/2, and is the form in which they are presented here.

The method of analysis employed in this work is that of Costen et al., as described in detail in the literature [7,15]. In summary, for either linearly or circularly polarized photolysis, the one-photon absorption Doppler profiles with a single speed, v 0 , in the centre-of-mass frame are given by,

0 2 2 4 4 0 0 0 1 ( ) 2 w w D w g g P g P v v v       = + +             (2)
where w ≤ v 0 is the component of the laboratory velocity along the probe direction, P 2 (x) and P 4 (x) are Legendre polynomials, and the coefficients g i contain the five lowest order alignment and two lowest order orientation bipolar moments, wherein they are multiplied by b n coefficients. The b n coefficients in turn depend upon the angles defining the relationship between the photolysis polarisation axis and the probe propagation direction and polarisation, and on the spectroscopic branch type.

Specifically, in geometries 3 and 4 where the probe and pump beams are counterpropagating and circularly polarised the lineshapes are described by the following expression [7].

2 (1) 1 1 0 2 0 0 2 0 0 (2) 0 2 2 2 0 2 0 0 2 0 4 0 0 0 3 ( ) 1 5 (20) ( 1) (01) 5 (21) 2 1 1 5 9 ( ) (22) (02) (22) (42) 2 2 7 7 β β β β β β β       = + + - +                     - + - +                 CP w w D w P h P v v w w w h V J P P P v v v (3)
Here, CP = 0 for co-rotating polarisations whilst CP = 1 for the counter-rotating geometry. The bipolar moments, ( )

2 1 0 k k k β
are here referenced to the laboratory frame. together with a translational anisotropy, were used to generate laboratory frame bipolar moments [7]. In the results reported here, four alignment parameters;

( ) The error analysis employed Monte Carlo estimates of the error bounds [15]. For a given experimental data set one thousand noisy FM spectra for each profile were generated.

|| 2 0 a , ( ) ⊥ 2 0 a , ( ) ⊥ 2 2 a , ( ) [ ]
This was achieved by taking the best fit for each profile and applying pseudorandom

Gaussian noise. The level of noise applied was determined from twice the standard deviation of the residuals of the best fit. Differences in the ratios of the integrated areas of profiles taken in an interleaved fashion over several experiments were accounted for by application of a pseudorandom intensity variation to one of the profiles in each pair.

Finally, error in the frequency scale was determined by finding the deviation in the width of late time profiles from the calculated thermalized width, which was in turn applied to the 1000 generated noisy sets of spectra. These 1000 sets were then fitted using the same analysis as applied to the data and the 95% confidence limits of the returned parameters are quoted as the error bounds.

Results

The five lowest order alignment bipolar moments, and the coherent orientation moment,

( ) [ ] ⊥ ||, Re 1 1 a
, have been determined for a range of rotational states for both v = 0 and 1 vibrational states of the CN photofragment. Although the fitting parameter space used was that defined by the coherent and incoherent orientation and alignment moments, we have chosen to report the alignment results in the µ-fixed bipolar moment parameterisation, as this provides the best comparison to the previous literature. We note here that, in contrast to earlier work which probed both high and low N states, here we probe only high N states, which are formed purely in coincidence with ground state I atoms. The A 2 Π-X 2 Σ + transition used has higher sensitivity to angular momentum correlations than the B 2 Σ + -X 2 Σ + transition usually used in LIF experiments, owing to the presence of Q branches, which have an opposite sensitivity to alignment compared to P and R branch lines. The P or R branch line for each rotational state was probed in all four geometries shown in Figure 1. Doppler profiles were also recorded in geometries 1 and 2 for the Q branch for each rotational state whenever possible. The six lines obtained for each rotational state are simultaneously fitted as described in the previous section. In the case of the quantum states where measurements on the corresponding Q branch were not possible, the 4 remaining profiles were fitted with v fixed perpendicular to J (in practice fixing ( )

|| 2 0 a = ( ) ⊥ 2 0 a =-1)
to avoid floating a poorly determined parameter [44,47,48]. 3), where as noted previously the difference between profiles with CP = 0 and 1 is only the h (1) term, dependent on the two orientation moments.

Rigorous comparisons with previous alignment and orientation measurements have been made in order to confirm the experimental and analysis methods employed in this work.

Previous measurements were made over a wide range of rotational levels in CN v = 0 using the same technique [7]. The rotational states probed here extend from the higher end of the literature, through to previously unmeasured N states that lie at the upper limit of the rotational population distribution.

Two parameterizations of the velocity-alignment correlations of the CN fragments are reported. First, as the five low order linear bipolar moments, normalized to the Dixon µfixed frame limits. Second, by the amplitudes of the incoherent linear combinations of the five limiting cases of the relative directions of µ, v and J [43,44]. This representation is useful as the amplitudes, labelled A-E in this description, can be assigned to transitions to However, through comparison with theory [23] and previous experimental work [15],

these cases can be assigned to the A' and A" components of 1 Π 1 . Cases A and D correspond to parallel and perpendicular transitions respectively, leading to J v || through a depolarisation mechanism beyond the axial recoil approximation.

First we present a comparison of the measured alignment parameters to those found previously. The A-E amplitudes for the rotational states studied in this work, together with those from the work of Costen et al. [15] that lie within that same range of N, are presented in Figure 3. The amplitudes found in this work are in good agreement with those found previously. Case B is seen to dominate for all rotational states, with the majority of the remaining amplitude partitioned between Cases C and E. The Case B amplitude can be seen to increase with N as the fraction in C and E falls. There is also a much smaller but non-zero fraction in Cases A and D. The resulting bipolar moments from the alternative parameterization are given in Table 1, alongside those from literature [15].

The orientation moments for the CN v = 0 fragments for the range of rotational states probed are given in Table 2. Previous experiments have shown that the orientation of high-J fragments is defined by a single parameter, defined by Rakitzis and Zare as Finally, Table 1 also includes the parent ICN internal energy required to fit the profiles.

Whilst the uncertainties associated with these values are fairly large, the general trend, is for higher rotational states to be formed from parent molecules with enhanced internal energy.. Similar behaviour has been observed at this and other photodissociation wavelengths, indicating that the higher N rotational states for v = 0 consistently arise from the photodissociation of the internally excited ICN parent molecules [15]. shown in Figure 5.

The A-E amplitudes are shown in figure 6, and the bipolar moments, coherent orientation parameter and ICN parent energy are presented in Table 3. The alignment parameters suggest similar behaviour to that observed for the ground vibrational state fragments. The

A-E amplitudes in Figure 6 again show that Case B dominates. The remaining amplitude is found in Cases C and E, which by analogy with v = 0 can be attributed to the A' and A" components of the 1 Π 1 surface. There is also evidence of the same trends observed in the vibrational ground state, with the Case B amplitude increasing with N as the fraction in C and E falls, as well as small but significant contributions from cases A and D. The observed internal energies of the parent ICN are also given in Table 3 indicating that vibrationally excited CN products are formed from parent molecules whose average internal energies are comparable to those that lead to formation of CN (v = 0). , in marked contrast to those measured for v = 0, are found to be close to zero. This clear reduction in the degree of orientation is evident when directly comparing the FM absorption profiles recorded in geometries 3 and 4 for v = 0 and v = 1. Figure 7(a) shows the co-and counter-rotating Doppler profiles for the (2,0) P 1 (48) line, in which a clear difference can be seen in both the magnitude and curvature of the lineshapes. shows the (3,1) P 1 (44) line for the same geometries, where there is no clear difference between the two profiles within experimental error. As described earlier, the difference in magnitude and shape between the signals obtained with co-and counter-rotating polarisations is due purely to the orientation moment. The similarity of the signals for v = 1 supports the very small orientation moments returned for these profiles.

Discussion

The measurements made in this work fall into two categories. First, velocity-alignment correlations that describe the incoherent photodissociation dynamics, and second, orientation correlations resulting from coherent effects. In each case measurements have been made on a range of rotational states for both the ground and first vibrational state of CN(X 2 Σ + ). Whilst CN fragments in both vibrational states exhibit similar alignment they differ markedly in their orientation.

v = 0 photoproducts

We first note the excellent, quantitative, agreement, for both orientation and alignment, between our results for CN(X 2 Σ + , v = 0, F 1 , N = 47, 48) and the literature [7,15,34]. This gives us confidence in the following discussion that our experimental method is sound, and that the observed effects are real and reproducible. We have extended the earlier measurements of v = 0 up to the limit of product rotation, and the resulting incoherent alignment correlations are in agreement with previous models of ICN photodissociation.

These CN states, formed in coincidence with I, can be accessed via three different pathways. First, excitation to the 4A'( 3 Π 0+ ) surface, followed by an adiabatic path to surface, followed by a diabatic path to the exit channel. These three pathways correspond to cases B, E and C respectively. The coupling of the 4A'( 3 Π 0+ ) and 5A'( 1 Π 1 ) surfaces is dependent upon the ICN bending angle, with the probability of curve crossing increasing as the bending angle becomes larger [23]. The bending angle is in turn related to the final rotational excitation of the CN; the greater the bending of the ICN the greater the rotational excitation of the CN fragment. A major contribution to the higher rotational states of the CN fragments is therefore from the more highly bent ICN molecules that follow an adiabatic path between the A' surfaces. This explains the increase in the case B amplitude with N that is observed. The decrease in the case E amplitude is explained by the same principle and leads to an opposite trend with respect to N. Strongly bent pathways originating on the 5A'( 1 Π 1 ) surface have a greater probability of undergoing an adiabatic coupling to the 4A'( 3 Π 0+ ), and as such the case E amplitude falls with increasing N. The above description suggests that all amplitude should arise in the B, C and E channels. In practice, small amounts of cases A and D are also observed. As previously described, this can be assigned to non-axial recoil through Coriolis-coupling of parent rotation into product J [15].

These high-N product states are also observed to arise preferentially from excited parent ICN. This is not surprising, as the degree of parent excitation has a direct effect upon the curve crossing probabilities and the product rotational excitation. At room temperature there is significant excitation of the ICN low frequency bending vibration at 321 cm -1 , and in the I-C stretch (470 cm -1 ). Trajectory calculations by Amatatsu et al. [23] found that initial bending vibration resulted in trajectories sampling larger bending angles at the conical intersection. The coupling between the A' surfaces is stronger for larger bending angles, and as such the transition probability between the A' surfaces increases for bent excited ICN. As the majority of the product flux starts on the 4A'( 3 Π 0+ ) surface, increasing the non-adiabatic transition probability increases the fraction of this flux that transfers to the 5A'( 1 Π 1 ) surface correlating to I, and thus the total I fraction. Thus increasing the parent temperature increases the I/I* branching ratio. This was observed experimentally by Kash and Butler [31]. In a study closely related to this one, Li et al. phase shift can only be developed before the conical intersection, this implies that there is little or no correlation between final N for the results presented here, and the ICN bend angle at the conical intersection for the trajectories that lead to those final states. The distribution into different high-N states is then purely the result of the strong torques on the 5A'( 1 Π 1 ) surface.

v = 1 photoproducts

The first observation on the velocity-alignment correlations, and hence the incoherent dynamics that lead to v = 1 CN, is their remarkable similarity to those for v = 0. Within our experimental precision, there is essentially no difference between these parameters.

This immediately implies that the paths to the final product states in v = 1 are essentially identical to those to v = 0, including the adiabatic/diabatic branching ratio. The Doppler profiles for v = 1 also require very similar parent ICN internal energies to successfully fit their observed width, leading to the conclusion that parent molecules with similar average internal energies are contributing to the formation of both v = 0 and v = 1 CN products.

The low yield of vibrationally excited products (~4 %) and the similarity of the incoherent dynamics with v = 0 suggests that the CN vibration acts largely as a spectator in the dissociation process, and is consistent with a number of theoretical studies of ICN photodissociation [26-29] which treat the CN bond length as fixed.

The coherent orientation moment is, however, very different for v = 1 compared to v = 0.

The moment,

( ) [ ] ⊥ ||, Re 1 1 a
, listed in Table 3, is small or close to zero for all of the observed product states in v = 1. The success in reproducing the literature v = 0 orientation measurements, together with the internally consistent incoherent alignment measurements for these v = 1 states, gives us confidence that this is not an experimental artefact.

As discussed previously, it is generally assumed that the coherent orientation moment is sensitive to the phase differences between the amplitudes evolving on the multiple PESs that correlate to these final product states. amplitudes (the BCE fractions) and the adiabatic/diabatic branching are essentially identical for v = 0 and v = 1. This in turn implies a very similar evolution of the wavepackets evolving to these final states. If the product fluxes for the two vibrational states come from the same initial conditions, and evolve in very similar fashions, how can they have different phase shifts? One possible explanation for this central observation of this paper lies in the kinetic energy available to the recoiling fragments. We will assume that only interference between the B and E pathways gives rise to the coherent orientation. We will also assume that the vibrational energy is partitioned early in the dissociation pathway. The v = 0 and v = 1 products start from similar positions and evolve towards the conical intersection in a very similar fashion, arriving at the seam with similar bending angles. However, the v = 1 flux arrives later than the v = 0 flux, as a result of the lower kinetic energy available for v = 1. Thus a different phase angle exists between the B and E fluxes for the two vibrational channels. After the intersection seam, the product flux evolves solely on the 5A'( 1 Π 1 ) surface, from basically the same starting point independent of vibrational state, and the strong exit channel torque generates the high rotation observed for both channels. A mechanism such as this would generate the observed similar incoherent alignment correlations but disparate coherent orientation moments.

Although this is a speculative mechanism, support for a strong vibrational product state dependence of the coherent orientation parameter can be drawn from the observations of Zare and co-workers [35] on the integrated orientation of v = 2 CN fragments from 248nm photolysis. They report the quantity C(N), defined as,

(1) 1 0 (2) 2 0 3 (01) ( ) 2
( ) (02)

I I h C N I I h V J β β ↑↑ ↑↓ ↑↑ ↑↓ - = = + - (4)
where I ↑↑ and I ↑↓ are the areas of LIF Doppler profiles, or the areas of FM Doppler profiles that have been transformed to 'normal' absorption profiles [49,50], in the corotating and counter-rotating geometries respectively. The parameter V(J), approaches a value of 2 for the high rotational quantum states probed in this work. In the definition used here, the relationship [7] between ( ) with previous experimental and theoretical work [15,23,24]. Three distinct pathways are observed. Excitation to the 4A'( 3 Π 0+ ) surface followed by an adiabatic path to the 5A'( 1 Π 1 ) surface, alternatively, dissociation can occur following a diabatic path along the 5A'( 1 Π 1 ) surface. Finally, excitation can occur to the uncoupled 5A"( 1 Π 1 ) surface followed by a diabatic path to the I asymptote. The first of these pathways is seen to dominate for all the rotational states, with its contribution increasing with N, resulting from the bending angle dependence of the curve crossing between the A' surfaces.

Significantly, the velocity-resolved alignment measurements for v = 1 products of similar

2 1 0 k k K β , for CN(X 2 Σ + , v = 0, F 1 /F 2 ,
[ ] ⊥ ||, Re 1 1 a for CN (X 2 Σ + , v = 1, F 1 , N).

limits separated by 50

 50 ns of the recorded I and Q signals was performed. The laser frequency detuning was calibrated from the monitor etalon signals where the separation of the sideband from the carrier frequency is equal to the modulation frequency. The frequency scale is then combined with the result from the integration to give I and Q signals at given times post photolysis. The late time I and Q signals, when thermalization is sufficient to model the absorption profile with a Gaussian lineshape, are simultaneously fitted to determine the FM phase angle, θ, enabling the pure FM absorption signal to be isolated. The nascent signals are then taken as those occurring from 0 to 50 ns post photolysis.

  photodissociation, defined as the coherent orientation moment

a

  were used. Doppler profiles for the various experimental geometries and branches were then simulated as given by equation 3, and the related expressions for the linear geometries[7]. Previous experiments have shown that the speed of the CN products may be affected by product channel specific ICN internal energy distributions, particularly in minor product channels such as those probed in these experiments[15]. These were included by generating the Doppler profiles assuming a Gaussian ICN internal energy distribution with a variable width and centre. The resulting Doppler profiles were then convolved with the parent ICN thermal Maxwell-Boltzmann speed distribution to give laboratory frame Doppler profiles. The simulated Doppler profiles were transformed to FM Doppler profiles via a finite difference method, and fitted to the experimental data simultaneously for all acquired geometries. Integral alignment and orientation effects were included by a common normalization for profiles acquired in an interleaved fashion. The assumed orientation and alignment parameters were then iteratively varied to minimize the least-squares deviation between experiment and the simulations.

v = 0

 0 CN photofragmentsFM Doppler profiles were acquired in geometries 1 to 4 for a selection of rotational states between N = 35 and N = 60, for both F 1 and F 2 manifolds in the v = 0 vibrational level.The acquired profiles and the corresponding best fit for the (2,0) P 1 (N = 48) line, and the corresponding Q branch line, are shown in Figure2. The difference in the line profiles for the P and Q branch lines taken in the same geometry illustrates the differing alignment sensitivity for these branches. The difference between the co-and counter-rotating profiles, acquired in geometries 3 and 4, is solely due to orientation of the CN fragments, the preference for one sense of rotation over the other. This is clear from the lineshape given in equation (

  states in the following manner. Excitation to the 3 Π 0+ state occurs via a parallel transition, and assuming rapid dissociation with axial recoil generates a limiting ⊥ v J correlation, and results in velocity-alignment correlations described by Case B.Case C describes the J µ v ⊥ correlation which is expected for the A" component of a perpendicular transition, whilst Case E, with ⊥ ⊥ v J µ µ µ µ can be associated with the A' component of a perpendicular transition. Through experiment it is not possible to determine whether Cases C and E correspond to transitions to the 1 Π 1 or 3 Π 1 surfaces.

  7]. The experimental data across all rotational states and both spin-rotation manifolds were again found to fit successfully with this assumption, resulting in the fixed ratio between the moments, against N in Figure4, together with those found previously by Costen and Hall for the range 40 ≤ N ≤ 60 (all of which are formed in coincidence with I)[7]. The values found in these experiments are in keeping with the general trend observed in this prior work.

v = 1

 1 CN photofragmentsFM Doppler profiles were also acquired in geometries 1 to 4 for CN (X 2 Σ + , v = 1) fragments in F 1 rotational states between N = 38 and N = 53. The acquired profiles and the resulting best fit for the (3,1) P 1(44) line, and the corresponding Q branch line, are

Deleted:

  As previously observed, thisDeleted: Deleted: ly Deleted: increases with increasing N, from ≈ 300 cm -1 for N = 47 to ≈ 800 cm -1 for N

Figure 7

 7

5A'( 1 Π

 1 1 ). Second, dissociation can occur following excitation to, and a purely diabatic the 5A'( 1 Π 1 ) surface. Finally, excitation can occur to the uncoupled 5A"( 1 Π 1 )

a

  spectroscopy to study the temperature dependence of the dynamics for 262 nm photodissociation at 296 and 550K[32]. They reported the BCE branching fractions and I/I* ratio for a range of rotational states. No measurable differences were found in the BCE fractions for any of the (v = 0) rotational states observed, although Ndependent changes to the I/I* branching ratio were found that were consistent with the non-adiabatic transition argument presented above. The high rotational excitation of the CN fragments formed in coincidence with I results from the torque exerted on the strongly bent 5A'( 1 Π 1 ) after the conical intersection. Bent initial states sample stronger torques on this surface, with the result that the highest rotationally excited product states are expected to arise preferentially from the vibrationally bent excited parent ICN, consistent with our observations. The coherent orientation moment, figure4is also in excellent agreement with previous measurements in the same range of N[7]. As N increases to its dynamical maximum[14], N ≈ 65, displays little or no decrease, and stays approximately constant at around +0.25. In the description developed for atomic fragments of diatomic photodissociation, the coherent orientation can be directly related to the phase shift between wavepackets evolving on the parallel and perpendicular surfaces. For the case of ICN photolysis we must be cautious in making the same assignment. There are three different surfaces converging on the same asymptotic state for the I channel of ICN. We therefore have 3 amplitudes, B, C and E and two phase differences. This more complex, three channel interference could plausibly produce more complicated Doppler lineshapes, including terms in  search for asymmetry in the circular dichroism Doppler profiles could not confirm any signals of this type. The agreement in sign and general behaviour of the measured orientation with the wavepacket calculations by Wei and Carrington[29] on the AYM surfaces seems to confirm that the only observable interference effect generating orientation is between the two A' paths (B and E). Within this picture, the approximately constant coherent orientation for the high N states from 248 nm photolysis suggests that the phase shift between B and E components is independent of product state N. Since the

  anisotropy, β, and the rotational alignment bipolar moment, measurements, and are found to be similar for high-N v = 0, 1 and 2, we can compare the C(N) measurements of Zare and co-workers to the orientation moments reported here. Whilst orientation is observed, for v = 2 it is both smaller in magnitude and exhibits markedly different behaviour to that of the v = 0 fragments. In the range N = 31 -41 the sign of C(N) is found to depend on the spin-rotation state, with F 1 taking positive values and F 2 negative values, whilst the magnitude is about half that observed for the equivalent N for v = 0. This range of N is close to the energetic threshold for production of CN in coincidence with I*, and Black et al. speculated that the observed behaviour might be associated with interferences arising from that channel.The highest rotational states studied, N = 48 and 53, are directly comparable to the range of N studied here for v = 0 and 1, and showed no variation with spin-rotation state.

Figure 8 1 h

 81 Figure 8 shows C(N) plotted for rotational states N = 48 and 53 as a function of vibrational quantum number. For P branch transitions, as studied in this work and that of Black et al., ( ) 1 h is negative, and hence a negative orientation parameter, C(N), corresponds to a negative coherent orientation moment,

FiguresFigure 1 .

 1 Figures Figure 1.Pump and probe geometries denoted 1 to 4, all with the laser beams counterpropagating.

Figure 2 . 25 Figure 3 .Figure 4 .Figure 5 .Figure 6 . 29 Figure 7 .

 2253456297 Figure 1. Pump and probe geometries denoted 1 to 4, all with the laser beams counterpropagating.

30 Figure 8 .

 308 Figure 8. The degree of orientation, C(N), plotted against vibrational quantum number for N = 48 (solid squares) and N = 53 (open circles). The v = 2 values are estimated from figure 5 in reference [35].

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  The incoherent measurements tell us that the

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Table 1 .

 1 Remarkably, the orientation for the high-N products of v = 1 is found to be dramatically smaller, despite the close similarity of all other aspects of the dissociation dynamics. We suggest that this is an indication of the different accumulated phase shifts arising from the kinetic energy release available to the fragments in different vibrational states prior to the conical intersection. It is clear that such detailed measurements of velocity-resolved orientation and alignment continue to challenge our current theoretical understanding of the dynamics of multiple surface dissociations. Bipolar moments, ( )

	N are essentially identical to those of the ground state, indicating that the incoherent
	photodissociation dynamics that lead to high-N products are independent of CN
	vibrational state. A large coherent orientation moment,	[ Re 1 1 a	( ) ] ⊥ ||,	is found for v = 0,
	independent of N.

Table 2 .

 2 N) together with those previously reported by Costen et al.[15], for comparison, marked with *. Where no error is quoted for the Orientation bipolar moments, ( ) Σ + , v = 0, F 1 /F 2 , N).

				β	( ) 0 22 0	moment, v was fixed perpendicular to J in the fit.
	N	β	2 0 (02)		β	2 0 (20)	β	0 0 (22)	β	2 0 (22)	β	2 0 (42)	E int / cm -1
	*46 (F 1 )	-0.05	+0.03 -0.01	0.43	+0.02 -0.02	-0.45	+0.02 -0.01	0.28	+0.01 -0.01	-0.15	+0.02 -0.01	200 ± 150
	47 (F 1 )	-0.02 ± 0.11	0.35 ± 0.04	-0.50	0.26 ± 0.05	-0.19 ± 0.04	300 ± 400
	48 (F 1 )	-0.18 ± 0.12	0.47 ± 0.03	-0.34 ± 0.03	0.33 ± 0.04	-0.21 ± 0.01	400 ± 400
	*50 (F 1 )	-0.15	+0.06 -0.05		0.46	+0.01 -0.02	-0.42	+0.02 -0.03	0.28	+0.02 -0.02	-0.21	+0.03 -0.02	300 ± 200
	52 (F 2 )	-0.21 ± 0.05	0.59 ± 0.05	-0.45 ± 0.01	0.32 ± 0.02	-0.22 ± 0.04	400 ± 400
	53 (F 2 )	-0.20 ± 0.06	0.50 ± 0.02	-0.49 ± 0.02	0.36 ± 0.02	-0.19 ± 0.03	800 ± 350
	54 (F 2 )	-0.18 ± 0.10	0.59 ± 0.03	-0.46 ± 0.03	0.37 ± 0.02	-0.22 ± 0.08	900 ± 350
	55 (F 2 )	-0.31 ± 0.10	0.62 ± 0.05	-0.50	0.44 ± 0.06	-0.24 ± 0.05	600 ± 400
	56 (F 2 )	-0.30 ± 0.10	0.58 ± 0.04	-0.50	0.38 ± 0.06	-0.23 ± 0.05	400 ± 300
	57 (F 2 )	-0.16 ± 0.15	0.58 ± 0.08	-0.50	0.30 ± 0.09	-0.34 ± 0.07	400 ± 450
	59 (F 2 )	-0.24 ± 0.03	0.67 ± 0.05	-0.43 ± 0.02	0.36 ± 0.02	-0.30 ± 0.03 1100 ± 400
	59 (F 1 )	-0.22 ± 0.11	0.57 ± 0.03	-0.40 ± 0.04	0.43 ± 0.03	-0.25 ± 0.05	800 ± 300
	60 (F 2 )	-0.28 ± 0.04	0.70 ± 0.04	-0.50 ± 0.02	0.43 ± 0.02	-0.33 ± 0.03	800 ± 350

Table 3 .

 3 Bipolar moments, ( )

	β	0 K	1 k k	2	, and coherent orientation moment,	( )

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Acknowledgements

This work was supported by the EPSRC (Portfolio partnership scheme LASER) and by the Leverhulme Trust (GR). GADR is grateful to the Royal Society for a University Research Fellowship and ST is grateful to NERC for the award of a studentship. Work by GEH at Brookhaven National Laboratory was supported by the Division of Chemical Sciences, Geosciences, & Biosciences of the U.S. Department of Energy. MLC thanks the Research Councils UK for an Academic Fellowship. We would also like to acknowledge the help of Alex Wilbur with aspects of the error analysis programming.