GENERAL DISCUSSION Prof. R. N. Zare (Stanford University, USA) said: Can Prof. Kat6 give us any additional information about how the strong magnetic field he uses might affect his conclusions about the photodissociation dynamics of NaK and Rb2? Are angular momentum uncoupling effects important? Prof. H. Kat6 (Kobe University, Japan) said: The effect of nuclear spin on the degree of polarization should be considered in the absence of an external magnetic field or at small magnetic field.' However, if the magnetic field is high enough to uncouple the electronic angular momentum J and the nuclear-spin angular momentum I, the spatial quantization of these vectors takes place independently of each other ( Paschen-Back effect for hyperfine structure2). The magnetic hyperfine structure constant AJ is 1011.9 MHz for "Rb(5 2S1/2), 25.029 MHz for 85Rb(5 2P3/2), 885.82 MHz for 23Na(3 2S1,2) and 18.65 MHz for 23Na(3 2P3/2).3 Hence, the effect of the hyperfine interaction on the polarization can be neglected in magnetic fields as strong as 1.55 T.1 C. H. Greene and R. N. Zare, Annu. Reu. Phys. Chem., 1982, 33, 119. 2 P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961). 3 A. Corney, Atomic and Laser Spectroscopy (Oxford University Press, Oxford, 1977). Prof. K. F. Freed (University of Chicago, USA) said: Prof. Kat6 has presented a series of fascinating experiments studying the external magnetic field dependence of the atomic sublevel populations in photodissociation. The experiments exhibit orienta- tion (difference between up and down components of angular momentum along the magnetic field) in Rb2 but none in NaK.Both are 'L'n transitions. Our previously published papers only consider the high-energy axial recoil limit in which the results are dependent on the nature of the initial and final electronic states only.'.2 Our paper in this meeting3 presents some calculations of orientation for the CH+ photodissociation in the low-energy regime. The near-threshold low-energy orientations and alignments can differ considerably from the high-energy-limited values appropriate to the axial recoil limit.'y2 It would, therefore, be of interest to consider further experiments with wavelength control to study the energy dependence of the orientation phenomena. Our calculations have also included the depolarizing effects of the hyperfine interactions and it is necessary to incorporate these corrections in comparing theory and experiment. 1 S.J. Singer, Y. B. Band and K. F. Freed, J Chem. Phys., 1984, 81, 3064. 2 S. J. Singer, Y. B. Band and K. F. Freed, Adv. Chem. Phys., 1985, 61, 1. 3 C. J. Williams, K. F. Freed, S. J. Slinger and Y. B. Band, Faraday Discuss. Chem. Soc., 1986, 82, 51. Mr C. J. Williams (University of Chicago, USA) said: Prof. Kat6 has measured a polarization ratio of P = 0.10 * 0.02 for the Na (3 2P3/2 --* 3 2S1/2) fluorescence resulting from the direct photodissociation of the NaK molecule after exciting the optically allowed X 'X+ -+ D 'n transition. This is compared to the polarization ratio (P = 21/47) predicted in the high-energy axial recoil limit for this photodissociation by Singer et aZ.' Discrepancies between these two numbers may arise from several sources.First, the magnetic field introduces additional anisotropy and lifts the degeneracy of the magnetic sublevels. Consequently, the frame transformation and recoil limit of Singer et al.' may be inappropriate when these extra anisotropies are not included in the calculations. Secondly, Prof. Kat6 earlier told me that the excess kinetic energy in the X '2+- D 'II dissociation of NaK is currently unknown, and thus it is possible that the recoil limit has not been attained in the experiments. Singer et find that the 3738 General Discussion high-energy axial recoil limit may not be reached until the excess fragment kinetic energy is orders of magnitude larger than the fragment spin-orbit splittings.If this is the case in NaK, full dynamical calculations of the polarization ratio P are required. This feature is already illustrated by our previous calculations, but the additional dynamical effects due to the presence of the magnetic field remain to be studied theoretically. 1 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys. 1983, 79, 6060. 2 S. J. Singer, K. F. Freed and Y. B. Band, J. Chem. Phys., 1984, 81, 3091. Prof. H. Kat6 (Kobe University, Japan) (communicated): The polarization ratio of P = 0.1Ost 0.02 was observed in the absence of the external magnetic field, as in my paper [above eqn (l)]. In our experiment, molecules in thermal equilibrium were irradiated.Hence, molecules populated in many rovibrational levels of the ground electronic state can be excited simultaneously to the dissociative continuum. We need a device to excite molecules from a single level to the dissociative continuum in order to make the analysis clear. Dr G. G. Baht-Kurti (University ofBristo2) and Dr M. Shapiro ( Weizmann Institute, Israel) said: The paper of Hall et al. discusses the measurement of correlations between various fragment attributes in photodissociation processes. One of the primary objectives in studying any photodissociation process is to learn about the underlying molecular features such as the potential-energy surface and the transition dipole moment function. The purpose of measuring the various correlations discussed in the paper of Hall et al.is to gain additional detailed knowledge of the system in order to further our search for these molecular quantities. The experimental observables, including all the correla- tions discussed, are related to the fundamental molecular quantities through the detailed differential photodissociation cross-section. In a previous paper’ we have discussed the relationship of this cross-section to the molecular quantities for a triatomic system, and have derived specific cross-sections for various types of experiments by performing suitable averages over the cross-section for the most detailed possible process. The cross-sections have been expressed in such a way as to isolate the irreducible dynamics of the photofragmentation process from the unavoidable angular and angular momentum algebra.Our analysis of the formal expressions led us in particular to propose that experiments in which the velocity, angular direction and mi states of photofragments were measured would yield much more information on the underlying molecular dynamics than had till then been available. In the language of the paper of Hall et al. this corresponds to the measurement of the correlation between the photofragment velocity and fragment angular momentum vector. Such correlations have also been considered in the work of Dixor2 1 G. G. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. 2 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Dr M. A. O’Halloran (Argonne National Laboratory, USA) said: In experiments performed at Stanford University with Prof.Zare, we also have observed the effects of velocity-angular momentum correlations on the polarization dependence of the laser- induced fluorescence probe of the CN fragment produced in the photodissociation of ICN at 249 nm. In a slightly different formalism from those presented in the papers discussed today, the intensity of the LIF signal may be expressed as’ I = CS d r ’ & ( k d , k,, k, q : a ) o ( k d , k,, k ; Ji, J,, J f ) . kd, ka, k 4 In this equation, dr) are the multipole moments of the angular momentum distribution, E(kd, k,, k, q ; a) are factors dependent on the experimental geometry (a), and o ( k d , k,, k ; Ji , J,, Jf) depend only on the particular probe transition Ji --* J, --* Jf.-0.1 1 -o.4 -0.5 t T 39 Fig.1. Rotational alignment, db2), plotted against rotational quantum number, N", determined from polarizations measured in the two experimental configurations: I( (detector 1) photolysis laser polarization) and I (detector I photolysis laser polarization). 0, PI[; 0, PI. When the angular momentum distribution is created by a cylindrically symmetric dipole process, such as photodissociation, it may possess only moments with k = 0,2 and q = 0, that is to say: dip'.. 1 and If this is the case, then it is sufficient to measure the LIF intensity for only two different geometries in order to determine the alignment, dr). In our experiment, a measurement of the LIF intensity at two different angles of the probe laser polarization is used to determine the alignment of the CN fragment produced in photodissociation of ICN.When we performed our experiment, we measured the polarization response of the LIF probe in two experimental configurations designated 11 or I, according to whether the detector is parallel or perpendicular to the direction of polarization of the photolysis laser. If there were only two moments dp) and dr), we should be able to invert the two sets of polarization data to obtain the same values for the alignment. What we observed, however, as shown in fig. 1, was that there was a small but systematic discrepancy between the alignments determined for the two experimental configurations. We found an explanation for this observation in the correlation between the velocity and the angular momentum of the CN photofragment.Since the probe laser line was narrower than the Doppler width of the transition, we were not observing the entire CN population, but rather those molecules with particular velocity projections on the probe direction. If the direction of the angular momentum vector is correlated with the direction of the velocity, then we do not observe the entire cylindrically symmetric, dipole-created angular momentum distribution, ,but rather a subset with reflection40 General Discussion 1.0 0.5 0.0 fraction Doppler width 0.0 0.5 1.0 0.0 0.5 1.0 1.0 1 0.0 0.5 0 . 0 3 V 0.06 6.0 2.5 - 1.0 fraction Doppler width Fig. 2. Moments of the angular momentum distribution, dy), integrated over various fractions of the Doppler width, for a arallel transition and for u l J The higher moments are normalized to ( a ) df), ( b ) dr), ( c ) dy); ( d ) dc); ( e ) (f> 103dy).symmetry through the plane containing the probe laser and the polarization vector of the photolysis laser. The LIF intensity is then sensitive to moments with k = 0,2, 4 and q = even. Using the expressions of Prof. Dixon,* I calculated the values of these moments, integrated over various fractions of the Doppler width, for the case of a parallel transition with t, I J (fig. 2). When the entire Doppler profile is integrated, dr’ and dr) approach their limiting values and the higher moments go to zero. However, our probe laser is ca. 0.7 of the Doppler width, and there is still some contribution from the higher moments, which may explain our experimental observations.What this calculation also suggests is that if the laser is further narrowed with an intracavity etalon, the polarization response of the probe should be even more sensitive to the velocity-angular momentum correlation. The technique of measuring the polariz- ation response across the Doppler profile would be fundamentally the same as the technique of measuring the shape of the Doppler profile (the LIF intensity across the Doppler profile). The advantage of measuring a polarization, however, is that it is a quantity which can be normalized on a shot-to-shot basis if the polarization of the probe laser is rotated rapidly, and thus it can be less sensitive to changes in sample pressure or laser power. 1 C. H. Greene and R. N. Zare, J. Chem. Phys., 1983, 78, 6741.2 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Dr P. A. Gorry ( University ufManchester) said: A considerable weight is being placed on the p parameter and the dynamical information that can be obtained from it. However, measured p values arise from an amalgamation of several effects, all of which must be allowed for if detailed dynamical information is to be obtained. In general, a measured p value results from a convolution of the initially prepared orientations over rotational velocities, dissociation lifetime and fragment relativeGeneral Discussion 41 velocities.' These effects are particularly important at low dissociation velocities where even the sign of p may be changed.2 In predissociating states the lifetime may be different for each J level requiring a knowledge of each individual lifetime to calculate the correct averaging over rotational velocity.Furthermore, vibrational motions may significantly alter the p value since vibrational motion perpendicular to the dissociation axis appears as a transverse component to the separation ~ e l o c i t y . ~ In addition to such legitimate averaging effects there are several experimental pitfalls to be avoided. First, one must be certain that only one electronic transition is involved, since overlapping transitions with different p values can easily be misinterpreted as dynamical effects. Shapiro has recently shown4 that coherent summation of states of differing p values occurs, rendering the decomposition of the /3 parameter impossible. Finally, great care must be taken to ensure that no saturation is occurring in the photodissociation since this also decreases the measured p value.' 1 S.C. Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4400. 2 R. N. Zare, Mol. Photochem., 1972, 4, 1. 3 G. E. Busch and K. R. Wilsor J. Chem. Phys., 1972, 56, 3638. 4 M. Shapiro, J. Phys. Chem., 1986,90, 3644. 5 J. H. Ling and K. R. Wilson, J. Chem. Phys., 1976, 65, 881. Dr K-H. Gericke (Frankfurt-am-Main, West Germany) said: In the first three papers at this Discussion the vector correlation between the translational and rotational motion of a photofragment has been mentioned and qualitatively established by Doppler spectroscopy. We wish to report on an experiment concerning the photodecomposition of hydrogen peroxide,'.2 where for the first time all vector correlations between p (transition dipole moment in the parent), u (product recoil velocity) and J (product rotation) are determined quantitatively by the use of bipolar moments, recently intro- duced by D i ~ o n .~ H202 has been photodissociated at a wavelength of 266nm and the OH fragments completely characterized by Doppler and polarisation spectroscopy using the laser- induced fluorescence technique at six different excitation-detection geometries. The entire internal state distribution (vibration, rotation, spin and A components), trans- lational energy, angular distribution and vector correlations between p( H202), u( OH) and J(OH) are measured. The OH fragments are formed exclusively in the X 2113j2,1/2 ground state with 90% of the available energy, E,, = 248 kJ mol-' being released as OH recoil translation.The internal motion of OH is vibrationally cold ( fr < 0.002), while the rotational excitation (fr = 0.1) can be described by a Boltzmann distribution with a temperature parameter of Trot = 1530 f 150 K for higher J. The two spin states are found to be populated nearly statistically. The n- component of the A doublet shows a higher population than the I'I' component and this inversion increases with increasing OH rotation. The various vector correlations are analysed and evaluated in terms of the four bipolar moments pi(02), pi(20), p:(22) and pi(22) by observation of more than 200 Doppler lineshapes. The observed profiles of recoil Doppler-broadened spectral lines are strongly dependent on the nature of the transition (see fig. 3), the excitation-detection geometry and the relative polarisations of the photolysing and analysing laser light.However, the line intensities show only a minor dependence on geometry and polarisa- tion. Therefore, the OH fragments are only weakly aligned [ &j2) = $:(02) G 0.11 for all rotational states N(0H) [fig. 4(d)]. The bipolar moment pi( 20) corresponds to the conventiordly defined spatial anisotropy parameter p = 2p;(20) and is found to be negative, pi(20) = -0.36 [fig. 4(a)]. Thus the angular distribution peaks in the direction perpendicular to the electric vector of the dissociating laser light (nearly a sin2 8 distribution). Since the transition moment is perpendicular to the product recoil direction, 2.e.the 0-0 axis, the excited electronic42 1.0 0.8 Genera I Discussion 0.2 0.0 309.85 309.86 309.87 309.88 309.89 wavelength/ nm Fig. 3. Doppler profile of the Ql(lO) main line ( a ) and the accompanying 4P21(10) satellite line ( b ) . The origin of both lines is the same quantum state. The different shape is mainly caused by a strong and positive v(OH), J ( 0 H ) correlation, indicating a more parallel orientation of J ( 0 H ) to v(0H). state at 266 nm in H202 is of ' A symmetry. Deviation from the limiting value of #3 = -1 is caused, for an ' A -+ ' A transition, by internal motion of H202. The lifetime T of the excited The moment /3:(22), which describes the correlation between the translational and rotational moment of the fragment, is positive and increases with increasing J ( 0 H ) [fig.4(b)], showing a bias towards v ( 0 H ) and J ( 0 H ) being parallel to one another. The influence on the observed Doppler profiles associated with pg(22) depends only on the branch of the excitation transition and is completely independent of beam geometries and polarisation. Thus p:(22) may be a measure of the dynamics of predissociating states where all other vector correlations are smeared out in the frame of observation. We observe a low positive value of pG(22) [fig. 4(c)] which describes the mutual correlation of the photoproduct translational and rotational vectors [ u( OH), J ( OH)] and of the transition dipole vector [p(H202)] in the parent molecule. The determination of the vector correlations in the photodissociation of H,02 at 266 nm allows an analysis of the expectation values of the J ( 0 H ) components.When we define a coordinate system with p(H202) being parallel to the z-axis and u(OH)(x- axis) perpendicular to p(H202) then the expectation value of ( J : ) should be very small. The OH product rotation is generated by the bending vibration and by the torsional mode in hydrogen peroxide, where the origin of the expectation value ( J : ) =: 450 cm-' are the bending modes of roughly planar H202 with the H atoms in trans position, while the expectation value of ( J i ) == 600 cm-' generated by the internal torsional rotation of H202, either directly from excitation into the-initial level, or from the torque provided by the strong angular dependence of the AIA[ (4a)*( 5 ~ ) ~ ( 4 b ) ' ( 5b)'I state potential surface.' A state should be of the order of T S 60 fs. The overall rotational distribution function P( J ) is then given byGeneral Discussion 43 0 / - / / & I I I I I I I I , - 0.8 0.4 0.3 0.2 0.1 0 I 1 I I 1 1 1 I I 1 0.2 1 fdJ r I-- -I--- 3 5 7 9 NOH Fig. 4. Bipolar moments ( a ) pi(02), ( b ) p;(22), ( c ) pi(20), ( d ) pi(22) as a function of NOH. The anisotropy parameter pi(02) corresponds to the alignment parameter AL2), pi(O2) =i The conventionally defined anisotropy parameter p is proportional to the bipolar moment &20), pg(20) = ip. Its large negative value indicates that the OH fragments are ejected essentially perpendicular to the transition dipole moment p( H202). The increasing positive value of &22) with increasing rotation of the fragment indicates a more parallel orientation of J ( 0 H ) to tr(0H).The bipolar moment pi( 22) describes the correlation of the translational and rotational motion of OH and of the transition dipole moment p(H202). The short-dashed curve stems from calculations on the basis of a semiclassical dynamical model.' The observed scalar and vectorial properties can be qualitatively described by a semi- classical dynamical model. 1 K-H. Gericke, S. Klee, F. J. Comes and R. N. Dixon, J. Chem. Phys., 1986,85, 4463. 2 S. Nee, K-H. Gericke and F. J. Comes, J. Chem. Phys., 1986, 85, 40. 3 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. Prof. F. J. Comes ( Frankfurt-am-Main, West Germany) said: The photodissociation of H202 at the wavelengths 266 and 248 nm obviously shows that there is only one upper state, A 'A, which is excited.This situation may change if an exciting radiation of shorter wavelength, e.g., 193 nm is used. There exists already a measurement at that wavelength' from which it follows that the population of the rotational levels, P ( J ) , in the vibrationless state of OH is non- Boltzmann, but with P( J ) / (2J + 1 ) decreasing monotonically. No vibrational excitation was found. Recently we have repeated the photofragmentation of H202 at 193 nm with the important result that the earlier measurements are strongly influenced by rotational relaxation.' Under the experimental conditions of Ondrey et al.' the same distribution44 Genera 1 Discussion 0 0 0 0 o o 0 0 0 0 - 0% .0 0 O 0 0 0 0 0 0 0 B Fig. 5. Rotational state distribution of OH fragments from the photolysis of H202 at 193 nm. Contributions from the two spin states are given by squares from the 2113/2 and by circles for the 2 h / 2 . was found again but at much lower pressures (5 mTorr) and shorter delay times between pump and probe laser (50 ns) the rotational state distribution changed, showing that now at low J the population was strongly reduced (fig. 5). The rotational state distribution is strongly inverted with P( J ) / (2J + 1 ) now increas- ing for J I 12. Also lineshapes were measured, from which Peff parameters could be extracted. As an example the lineshape of Ql(lO) transition is shown (fig. 6). So far no alignment has been considered, for it is estimated to be small under the experimental conditions.The asymmetry parameter Peff = +0.35 (obtained from a fitting procedure) is slightly more positive than the one found when using 266 nm as the excitation wavelength. The positive value may indicate that besides the 'A-state the 'B-state is also excited at 193 nm. The Doppler shift shows that the OH fragments carry a translational energy of 185 kJ mol-' each, which is ca. 84% of the available energy. As no vibrational excitation is involved in the photofragmentation process, Doppler measurements of the OH in a specific rotational state may allow to determine the rotational energy of the other fragment which is coincidently formed in the photofragmentation. 1 G. Ondrey, N. van Veen and R. Bersohn, J. Chem. Phys., 1983, 78, 3732.2 A. U. Grunewald, K-H. Gericke and F. J. Comes, Chem. Phys. Lett., 1986, 132, 121. Prof. R. N. Dixon (University of Bristol) said: The papers by Hall et aZ. and by Docker et al. both describe experiments which demonstrate the existence of a vector correlation between the angular momentum and the angular distribution of translational momentum of a photoproduct. In the interpretation of such experiments it is important to separate those aspects of the observables which derive from the chosen geometrical arrangement of the experiment from those which are associated with the anisotropy of the intramolecular forces which operate during the dissociation, and which are of prime interest.General Discussion 45 1.0 0.8 x U 3 0.4 E Y .- 0.2 0 309.845 309.8 55 309 865 wavelength/nm 309.875 Fig. 6.Doppler lineshape of Q1( 10) transition of the (0,O) band of OH (X 'n). &= +0.35 is obtained by deconvolution with a 300 K thermal motion of H202 (A v = 0.069 cm-') and a Gaussian laser profile (Av, = 0.1 cm-'). Laser beams are counter-propagated and linearly polarized parallel to each other with the E vector parallel to the direction of observation. One approach to this separation has been described in a recent publication,' in which the vector correlation is described by a set of bipolar moments. For a single product J value and translational wavevector k a fundamental description of the pair angular distribution function will be by a density matrix p ( k J ) . The observables are related to one or more moments of this distribution defined by where the bipolar tensor operator is given by2 and n( k, k2K) is a renormalisation constant chosen to obtain simple numerical ranges for the dimensionless moment^.^ One manifestation of this vector coupling concerns the profiles of photofragment spectral lines which are broadened by the Doppler shift of fast recoil, as in both the papers under discussion.These profiles are sensitive to both the propagation directions and polarisations of all photons that are involved in detecting a fragment spectrum. In the case of laser-induced fluorescence detection following photofragmentation with linearly polarised light the most general line profile involves bipolar moments with 0 = 0, K = 0 and 2, k, = 0, 2, 4 and 6, and k2 = 0, 2 and 4, and can be represented by46 General Discussion where P,, is a Legendre polynomial, xD is the fractional Doppler shift from line centre (8v/AvD) and the g,, are linear combinations of the bipolar moments with geometry- dependent coefficients.Eqn (3) provides a method of analysis of line profiles, from which one or more non-zero moments can be determined,’ thereby providing a method of interpreting experimental data to deduce the form of the pair density matrix and the underlying photofragmentation dynamics. This approach has been used in connection with the 266 nm photolysis of hydrogen per~xide.~ A possible disadvantage of an analysis through moments is that (in principle) nine non-zero moments contribute to the line profiles with LIF detection. Limited resolution and signal-to-noise ratios, and a finite velocity spread, may militate against determining all of these.The most fruitful approach to interpretation will, therefore, probably be a combination of moment analysis and forward calculation from a dynamical model. A One important aspect of this analysis is that the bipolar moment p,0(22) = ( P2( 6 J ) ) is overall isotropic and is, therefore, independent of the frame of reference. Con- sequently, there may still be detectable u/J correlation between product motions even for weakly predissociated parent states, for which the memory of the initial excitation will be lost through extensive rotation before dissociation. This will particularly be the case when the weak predissociation involves a slow radiationless transition to a final state with an initially well defined geometry, from which rapid dissociation occurs on a repulsive surface.The angular distribution of u is probed by the propagation direction of the analysing light, and J by its electric vector, and these two are fixed at right-angles by the transverse nature of light. Thus the influence of p:(22) on a line profile is independent of the experimental geometry, but is in general of opposite sign for Q-branch transitions compared with P or R transitions. A comparison between different branches therefore provides a method of testing for u / J correlation. 1 R. N. Dixon, J. Chem. Phys., 1986, 85, 1866. 2 D. M. Brink and G. R. Satchler, Angular Mommenturn (Clarendon Press, Oxford, 2nd edn, 1968). 3 See C. H. Greene and R.N. Zare, Annu. Rev. Phys. Chem., 1982, 33, 119 for a discussion of tensor 4 K-H. Gericke, S. Klee, F. J. Comes and R. N. Dixon, J. Chem. Phys., 1986, 85, 4463. operators and multipole moments. Prof. J. C . Polanyi (University of Toronto) said: Surprise has been expressed that correlation between product velocity, u’, and rotation, J’, can be-as we heard it expressed-‘maintained’ despite lingering of the dissociating molecule in an electroni- cally excited state that ultimately predissociates. The correlation is likely, however, to be due to the fact that u’ and J‘ have a common origin, namely the repulsion along the direction of what was previously a bond and has, as a consequence of predissociation, become an anti-bond. The source of the bulk of u‘ and J’, according to this view, lies in an event that occurs as the photoproducts separate, consequently the prior lifetime of the photo-excited species has no bearing on the extent of the correlation.This type of correlation has been extensively explored for product excitation in what are termed ‘repulsive’ chemical reactions, for which a major portion of the energy release occurs as the reaction products separate.’ Photolysis, since it resembles the second half of a chemical reaction, is pre-eminently (though not exclusively) a repulsive event. In the simple case A*BC (the dot represents the repulsion) the apportionment of recoil energy between u’ and J’ can be calculated from the distance by which the point of a plication of the force is removed from the centre-of-mass of the molecular fragment BC!3 The u’J‘ correlation arises from the fact that there is a limited range of ‘transition- state geometries’ for the labile AOBC, and a correspondingly restricted range of values for the torque.The correlation is interesting to the extent that it sheds light on the range of ‘transition-state geometries’. The reaction-dynamicist must contend not only with aGeneral Discussion 47 substantial range of intermediate geometries, but also with the presence in the transition state of angular momentum that derives from energetic reagents. In photodissociation, averaging over these quantities is less severe since the energy of the transition state is that of a stable molecule at normal temperatures. The averaging can be further sup- pressed if the range of energies and geometries that lead to dissociation is reduced by the existence of a localised inter-system crossing.This suggests that the most advantageous case for v’J’ correlation is the one that occasioned this comment, namely the case of photo-excitation to an excited state which, following a delay for exploration of the available phase space, passes through a narrow ‘gateway’ onto a repulsive potential that leads (from a restricted region of phase-space) to the explosion into photofragments. 1 N. H. Hijazi and J. C. Polanyi, J. Chem. Phys., 1975, 63, 2249. 2 P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 50, 4623. 3 M. G. Prisant, C. T. Rettner and R. N. Zare, J. Chem. Phys., 1984, 81, 2699. Prof. P. L. Houston (Cornell University) said: An alternative theory for relating the degree of correlation between angular momentum and velocity vectors has been presented by Hall et al.’ Consider the case when the Doppler profile is measured with light propagating along a Z-axis which makes an angle 8’ with respect to the electric vector of the linearly polarized dissociating light.The Doppler profile of molecules moving in a direction specified by the polar angle x and the azimuthal angle 4 with respect to the propagation direction will depend (1) on the number of fragments recoiling into this angle and (2) on their M, distribution on the Z-axis, taken here to be the direction of propagation. Molecules recoiling at polar and azimuthal angles x and 4 with respect to the direction of propagation will make a specified polar angle, 8, with respect to the electric vector of the dissociating light. The angle 8 is related to the angles 8’, x and 4 by the condition cos 8 = cos 8‘ cos x +sin 8‘ sin x sin 4 ( 1 ) where 4 is measured from the plane containing the probe direction and the polarization vector of the dissociation laser. In order to calculate the Doppler profile, we need to ascertain the M, distribution on the Z-axis of propagation, but the correlation between o and J is most conveniently described in the molecular frame using v as the axis of quantization. We define the probabilities for projections M, of J onto v to be the diagonal elements of a density matrix p ( 8 ) .The density matrices corresponding to the two basis sets M,, and M, are related by a unitary transformation:2 (2) P ’ ( X , 8’, 4) = rm-4, x, 4)1-1P(wm-4, x, +)I where p( 8) describes the distribution of projections of J onto v, and p’( x, 6’, 4) contains diagonal elements, describing the probabilities for projections of J onto 2, and off- diagonal elements, describing the coherences.The intensity of laser-induced fluorescence for molecules described by the matrix p’ is given by3,4 I(x, 8‘) - I d4W(x, 8’, 4) Tr A F (3 1 where W( x, 8‘, 4) = [ 1 + pP2(cos 8)] gives the probability of recoil into a given direction, and the matrices A and F describe the absorption and fluorescence steps, respectively. The matrices AFg and FFg are given by A zM = C (J’ K ’ M I Q, I JKM, ‘) p ’( MJ ‘ M, ) (JKMJ I Q,I J‘ K ’ M ’) (4)48 General Discussion where the summation is over MJr, MJ from -J to J, and IJKM) are the symmetric-top wavefunctions.For linear polarization the @ matrices occurring in the absorption or fluorescence steps can each be described as a sum: where F = X , Y, 2 are the laboratory coordinates, g = x, y, z are the molecular co- ordinates, and the coefficients A F are the projections of the electric vector onto the laboratory coordinates, while the coefficients A, are the projections of the dipole moment onto the molecular coordinates. The elements aFg are the direction cosine matrices, listed el~ewhere.~ I ( x , O r ) in eqn (3) gives the intensity of laser-induced fluorescence as a function of Doppler detuning, x, for any particular relative angle 8’ between the polarization vector of the dissociation laser and the probing direction. In response to a question by Professor J.P. Simons as to why we looked for any correlations in glyoxal, I would like to comment as follows. The vibrational-rotational distribution of the CO product from glyoxal was particularly uninformative as to which dissociation channels might be responsible for the observed product. The CO was produced entirely in u = 1 and with a rotational distribution stretching from J < 10 to J > 60. The distribution showed no structure which might have been interpreted as being due to the three possible channels: H2C0 + CO, HCOH + CO and H,+ 2CO. We measured the Doppler profiles of individual rotational lines in order to see which channels contributed at each product J level.At first, before our spectral resolution was improved to 0.16 cm-’, we noticed the curious effect that all of the Q-lines appeared to be broader than the corresponding P- or R-lines. With improved resolution, we discovered that the Q lines all had ‘dips’ in the centre, whereas the P- and R-lines did not. That this effect is due to the correlation between u and J is demonstrated in the paper; a more complete account will be published shortly.‘ The widths of the rotational lines provided evidence that most of the population in the highest rotational levels was produced by the H2C0 + CO channel. 1 G. E. Hall, I. Burak, N. Sivakumar and P. L. Houston, Phys. Rev. Lett., 1986, 56, 1671. 2 A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, 1957), p.61. 3 The procedure used here follows the notes for the 1980 Baker Lectures, Cornell University, R. N. Zare, 4 G. Breit and I. S. Lowen, Phys. Rev., 1934, 46, 590. 5 P. C . Cross, R. M. Hainer and G. W. King, J. Chem. Phys., 1944, 12, 210. 6 I. Burak, J. W. Hepburn, N. Sivakumar, G. E. Hall, G. Chawla and P. L. Houston, State-to-State personal communication; see also R. N. Zare, J. Chem. Phys., 1966, 45, 4510. Photodissociation Dynamics of trans-Glyoxal, J. Chem. Phys., accepted for publication. Dr G. E. Hall (Cornell Uniuersity) said: As a summary of our paper, I make the following comments. Photofragmentation of molecules with more than three atoms can lead to photo- fragment Doppler lineshapes that are substantially harder to analyse than from triatomic parent molecules. The Doppler lineshapes can be considered to be determined by three photofragment properties. First is the distribution of kinetic energies of the spectro- scopically selected photofragment. Second is the angular distribution of the fragments relative to the polarization axis of the dissociating light. The added complication of angular distributions that are different for different kinetic energies, corresponding to different internal states of the unmeasured fragment, cannot be ruled out in general. Finally, the Doppler lineshapes will be affected by the anisotropy of J, described by the correlations between J, v and J, p. Without some special simplification, this is too much information to extract uniquely from measured lineshapes.General Discussion 49 In the case of OCS, we know the kinetic energy distribution is sharp and we know the correlation between J and u. We can extract p and test the analysis procedure. In the case of glyoxal, the slow predissociation and rotationally unresolved excitation ensures isotropic fragmentation velocities. Here, qualitative features of the J, u correla- tion can be deduced, even with a broad velocity distribution. In the case of H202, the small degree of internal excitation of the OH fragments makes the kinetic energy distribution sharp enough to extract detailed vector correlations.