Oriented Chlorine Atoms As a Probe of the Nonadiabatic Photodissociation Dynamics of Molecular Chlorine Andrew J

JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 20 22 NOVEMBER 2000

Oriented chlorine atoms as a probe of the nonadiabatic photodissociation dynamics of molecular chlorine Andrew J. Alexander,a) Zee Hwan Kim, S. Alex Kandel,b) and Richard N. Zarec) Department of Chemistry, Stanford University, Stanford, California 94305 T. Peter Rakitzis Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, 711 10 Heraklion—Crete, Greece Yukako Asano and Satoshi Yabushita Department of Chemistry, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ͑Received 27 June 2000; accepted 1 September 2000͒ Molecular chlorine was photolyzed using circularly polarized radiation at 310 and 330 nm, and 2 orientation moments of the chlorine-atom Cl( P j) photofragment distributions were measured by resonance enhanced multiphoton ionization using circularly polarized light with Doppler resolution. The product atoms were found to be strongly oriented in the laboratory as a result of both incoherent and coherent dissociation mechanisms, and the orientation moments contributed by each of these mechanisms have been separately measured. The experimental results can be explained by 1⌸ ⍀ϭ nonadiabatic transitions from the C 1u state to higher states of 1u symmetry, induced by radial derivative coupling. Ab initio calculations indicate strong Rosen–Zener–Demkov noncrossing-type radial derivative couplings between states of 1u symmetry. The observed angular ͑␤ ͒ 2 distribution parameter indicates that 88% of Cl*( P1/2) fragments produced at 310 nm originate from a perpendicular transition to the C state. The orientation measurements suggest that 67Ϯ16% 35 2 3⌺ϩ Ϯ 3⌬ of Cl*( P1/2) atoms dissociate via the 1u( 1u) state, and 21 6% dissociate via the 1u( 1u) state. © 2000 American Institute of Physics. ͓S0021-9606͑00͒01444-6͔

3⌸ 3 I. INTRODUCTION tion of involvement of the A 1u state has remained open. Measurements of the chlorine atom photofragment alignment The electronic states of chlorine molecules that are ac- by Rakitzis et al.6 and Bracker et al.7 are consistent with the cessed by ultraviolet radiation in the region around 330 nm dissociation proceeding mainly by adiabatic dissociation via have been of great importance to our understanding of mo- the C state, but have suggested that nonadiabatic transitions lecular bonding and the dynamics that occur when molecules involving the A state do occur. The observation of a coherent 1 dissociate. Indeed, the halogen molecules in general have alignment moment provides further support for the impor- provided a standard for theoretical and experimental studies tance of homogeneous nonadiabatic transitions between the of the electronic states and potential energy curves of di- C and A states.7 2 atomic molecules. The ultraviolet absorption spectrum of To understand the involvement of states that correlate to 2 5 Cl2 is continuous between 250 and 450 nm, with a maximum produce Cl*( P1/2), Samartzis et al. used their measure- at ϳ330 nm. Experimental measurements of the ﬁne- ments of Cl* angular distributions, and Cl/Cl* branching ra- structure branching ratios following dissociation caused by tios to estimate the degree of nonadiabatic transition from the 3 ultraviolet radiation have been made by a number of groups. C state to states that correlate to produce ClϩCl*.Kim 4,5 Samartzis et al. have made detailed ion-imaging and et al.8 have reported measurements of the orientation of Cl* velocity-map imaging studies of Cl2 photodissociation, and atoms as a function of photolysis energy. The coherent ori- have reported angular distributions ͑parametrized by the ͓ (1) ʈ Ќ ͔ entation moment Im a1 ( , ) can be related to the inter- second-order Legendre moment of the distribution, ␤͒,and ference between dissociating pathways originating from par- branching ratios. Present understanding has it that the disso- allel ͑ʈ͒ and perpendicular ͑Ќ͒ transitions whose ﬁnal states ciation around 330 nm is dominated by a perpendicular tran- correlate to the same asymptotic limit, in this case 1⌸ 8–10 sition to the C 1u state, with increasing contributions from ϩ * ϩ Cl Cl . These measurements, along with high-level ab 3⌸ 11,12 the B 0u state at longer wavelengths, although the ques- initio calculations by Yabushita, have challenged us to make a more detailed investigation of the nonadiabatic tran- a͒Present address: Department of Chemistry, University of Edinburgh, West sitions, the states involved, and the dynamics of the dissocia- Mains Road, Edinburgh, EH9 3JJ, UK. tion process. b͒ Present address: Davey Laboratory, Pennsylvania State University, Uni- In 1968, van Brunt and Zare13 predicted that the photo- versity Park, PA 16802. c͒Author to whom correspondence should be addressed; electronic mail: dissociation of a diatomic molecule could produce polarized [email protected] atomic fragments. Experimental observations of polarized

Downloaded 24 Feb 2012 to 171.64.124.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions J. Chem. Phys., Vol. 113, No. 20, 22 November 2000 Oriented chlorine atoms 9023 atomic fragments were first made in the early 1980s by photon ionization͒ at around 235 nm. The transitions used ؠ 2 52 ؠ 2 4 2 15,17 16 14,15 Vasyutinskii and by Rothe et al., Vasyutinskii, were 3s 3p 4p P1/2–3s 3p P3/2 at 236.518 nm and ؠ 2 52 ؠ 2 4 2 18 9 Siebbeles et al., and Mo et al. have presented quantum 3s 3p 4p P3/2–3s 3p P1/2 at 234.620 nm. These transi- mechanical treatments of atomic photofragment polarization. tions were specifically chosen to be sensitive to the orienta- Recently, measurements of the polarization of the electronic tion moments of the electron angular momentum distribu- angular momentum of photofragments have shown consider- tion. The atoms were probed using alternately left and right able promise for revealing details of the unbound states of circularly polarized light on a shot-to-shot basis. Thin-film molecules.19–21 Although these studies cannot match the polarizers ͑CVI Laser͒ were used to improve the quality of depth of information revealed by conventional spectroscopy, the linearly polarized ultraviolet radiation. The circular po- it is clear that they allow us to probe dynamics that were larization of the probe laser radiation was introduced by us- hitherto inaccessible. ing a 241 nm zero-order quarter waveplate ͑CVI Laser͒ and Photofragment orientation can occur by coherent disso- the handedness was changed on a shot-to-shot basis using a ciation mechanisms, but can also be induced by using circu- photoelastic modulator ͑Hinds PEM-80͒. The high quality larly polarized photolysis radiation; in this case, the direc- ͑Ͼ100:1͒ of probe laser circular polarization was confirmed ؠ 2 52 ؠ 2 4 2 tional nature of the photon angular momentum must be by REMPI using the Cl*(3s 3p 4p; P1/2–3s 3p P1/2) conserved in the laboratory frame. Zare and co-workers22,23 transition at 237.074 nm. have studied the orientation of CN fragments produced by The probe laser was arranged in a collinear counter- dissociation of ICN using circularly polarized radiation. propagating geometry with respect to the photolysis laser. Vasyutinskii and co-workers24–27 have made important theo- The dissociation and detection was carried out at the extrac- retical and experimental studies using the optical magnetic tion region of a time-of-flight mass spectrometer. Unlike pre- birefringence ͑Faraday͒ technique. Recently, Korovin et al.28 vious studies, however, the total Clϩ ion signal was col- reported the first observation of spin-oriented Rb-atom pho- lected, and the sensitivity to product velocity was achieved tofragments, produced by photolysis of RbI at 266 nm using by scanning over the Doppler-broadened line shape of the circularly polarized light. Their results indicated the presence REMPI transition. Because the chlorine atoms are traveling of both coherent and incoherent dissociation mechanisms, relatively fast ͑ϳ2kmsϪ1͒ with a well-definedspeed,no although these mechanisms could not be quantified sepa- efforts were made to further narrow the linewidth of the rately. probe dye laser ͑Spectra-Physics PDL-3; nominal fundamen- In this paper, we report the observation of electronically tal linewidth ϳ0.07 cmϪ1͒. oriented Cl-atom photofragments from the dissociation of The definition of the handedness of circular polarization Cl2 at 310 and 330 nm using circularly polarized photolysis that we use is the conventional one, i.e., left circular polar- and probe radiation. Our measurements support the presence ization ͑LCP͒ has positive handedness or helicity, and obeys of both coherent and incoherent dissociation mechanisms. the right-hand rule with the thumb pointing in the direction From our measurements we estimate the extent of nonadia- of the propagation vector.30 For LCP the electromagnetic batic radial derivative coupling that leads to production of field rotates counterclockwise in a fixed plane as viewed Cl*, and we are able to identify the states that are involved in looking into the oncoming wave, and each photon has a pro- the nonadiabatic dynamics. In what follows we present a jection of one unit of angular momentum ͑ϩប͒ with respect brief introduction to the experimental and theoretical meth- to its propagation vector.31 The absolute handedness of the ods employed ͑Sec. II͒. Results are presented in Sec. III and circularly polarized light was determined using a single a discussion in Sec. IV. A brief summary and conclusions fused-silica Fresnel rhomb ͑CVI Laser͒. The absolute phase appear in Sec. V. of the output of the rhomb can be calculated using Fresnel’s equations.30 The Fresnel rhomb was oriented in the beam path after the unknown circularly polarizing element; the ␲/4 II. METHOD phase of the two circularly polarizing elements either cancel A. Experiment or add to give linearly polarized light with 0 or ␲/2 phase. Full descriptions of the experimental apparatus and tech- For example, if the light is initially horizontally polarized ͑ ͒ niques used have been given elsewhere,6,29 and only details HP , and after the two circular elements the light is also HP, pertinent to the present study will be given here. A dilute we know that the two circular elements have the same hand- solution ͑ϳ8%͒ of molecular chlorine ͑Matheson, 99.999%͒ edness. Further, if we know that the Fresnel rhomb is physi- in high-purity helium ͑Liquid Carbonic, 99.995%͒ was pre- cally oriented to give LCP, then the other circular element mixed and expanded into high vacuum through a pulsed must also be set to give LCP. nozzle ͑General Valve, Series 9, 0.6 mm orifice͒. The stag- nation pressure of the sample used was typically 450 Torr. B. Data analysis Chlorine was dissociated using circularly polarized light at 310 and 330 nm. A zero-order 308 nm quarter waveplate For these experiments, the laboratory axis with highest ͑CVI Laser͒ was used to control the circular polarization at symmetry ͑Z axis͒ is defined by the propagation vector of the 310 nm, and a Soleil-Babinet compensator ͑Special Optics circularly polarized ͑CP͒ photolysis radiation. We refer to ͒ Inc. was used at 330 nm. Product chlorine atoms in the Doppler profiles taken with CP probe radiation as DL and DR 2 2 ground Cl( P3/2) and excited Cl*( P1/2) states were detected for the counterpropagating probe laser light being LCP or selectively using 2ϩ1 REMPI ͑resonance enhanced multi- RCP, respectively. Isotropic profiles that do not depend on

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the orientation of the product atom can be defined as Diso ϭ ϩ DL DR . The corresponding anisotropic difference profiles that contain odd moment orientation information are ϭ Ϫ defined as Daniso DL DR . The laboratory frame detection probability in the present experiment can be conveniently written in terms of the (k) aq (p) moments of Rakitzis and Zare, where p is used to denote parallel ͑ʈ͒ or perpendicular ͑Ќ͒ or mixed ͑ʈ,Ќ͒ transitions:10 ϭ ϩ␤ ⌫͒ ␥͒ϩ 1 ⌫ Dlab 1 P2͑cos P2͑cos G s1 cos 1 ϫͫ ͑ ϩ␤͒ ͑1͒͑Ќ͒ 2 ␥Ϫ ͓ ͑1͒͑ʈ Ќ͔͒ 2 ␥ͬ 1 a0 cos Re a1 , sin ͱ2 ϩ 3 ⌫͓͑ ϩ␤͒ ͑3͒͑Ќ͒ ␥ ͑ ␥͒ G s3 cos 1 a0 cos P3 cos FIG. 1. Typical anisotropic Doppler profile basis functions for the moments a(1)(Ќ) ͑solid line͒ showing a double velocity peak, Re͓a(1)(ʈ,Ќ)͔ ͑dashed Ϫ ͓ ͑3͒͑ʈ Ќ͔͒ 2 ␥͑ Ϫ 2 ␥͔͒ ͑ ͒ 0 1 Re a1 , sin 1 5cos . 1 ͒ (3) Ќ ͑ ͒ line showing a single velocity peak, and a0 ( ) dot-dashed line showing In Eq. ͑1͒⌫is the angle of the CP probe propagation vector oscillations. All profiles have been broadened with an arbitrary Gaussian ͑ function to simulate the finite linewidth of the transition. The abscissa is with respect to the CP photolysis propagation vector the lab scaled in arbitrary units of Doppler-shifted frequency and the moments have Z axis͒: In the present experiments ⌫ϭ180°. ␥ is the angle been scaled to show the most detail. between the direction of recoil of the fragments and the lab Z axis, and Pk denotes a Legendre polynomial of order k.For Cl* atoms, jϭ1/2, and there are no moments with kϾ1, i.e., dance with the Cl atoms being produced almost entirely by the a(3) ͑p͒ terms cannot exist. The sensitivity parameters for q dissociation via a pure perpendicular transition to the C the REMPI process (s ) can be easily calculated using the k state.5 In previous work, we have reported that the Cl* atoms method of Mo and Suzuki:32 In the notation of Rakitzis ͓ (1) ʈ Ќ ͔ 33 ϭϪ displayanIma1 ( , ) at 310 nm, resulting from coherent et al. we find for ground-state Cl, s1 2.323, s3 8 ϭϪ1.936, and for excited-state Cl* we find s ϭϪ1.732. dissociation via the B and C states. However, at this 1 ͓ (1) ʈ Ќ ͔ We must also account for hyperfine depolarization of the wavelength we see no evidence of a Re a1 ( , ) :The ͓ (1) ʈ Ќ ͔ product atoms,34 for which we take the long-time limit of Im a1 ( , ) is dependent on the sine of the phase differ- the nuclear hyperfine depolarization ratio: G1ϭ0.5, G3 ence of radial wave functions created on the two curves, ͑⌬␾͒ ͓ (1) ʈ Ќ ͔ ͑⌬␾͒ ϭ 1ϭ * sin , whereas the Re a1 ( , ) has a cos 0.2 (Cl) and G 0.375 (Cl ). 9 As in previous works,6,35 isotropic and anisotropic Dop- dependence. Our previous measurements indicate that ͓ (1) ʈ Ќ ͔ pler profiles were fitted with basis functions generated by a Im a1 ( , ) is large at 310 nm, and so we may expect the ͓ (1) ʈ Ќ ͔ Monte Carlo simulation using Eq. ͑1͒. The translational an- Re a1 ( , ) to be small, in agreement with the present ͑ ͒ isotropy ␤ parameter was taken from the work of Samartzis results see Sec. IV . et al.,5 and multiplied by Ϫ0.5 to account for the use of CP Figure 3 shows Doppler profiles with fits for Cl and Cl* photolysis light.36 The basis functions were convoluted with atoms produced from chlorine molecules photolyzed at 330 an empirical blurring function ͑Gaussian͒ to account for the nm. The Cl atom results do not show the two peaks of the (1) Ќ laser linewidth. Figure 1 presents typical anisotropic basis a0 ( ) so clearly, due to the slow speed of the Cl atoms and (1) Ќ ͓ (1) ʈ Ќ ͔ (3) Ќ the frequency bandwidth of the laser. As was found at 310 functions for the a0 ( ), Re a1 ( , ) ,anda0 ( ). The (1) Ќ ͓ (1) ʈ Ќ ͔ nm, the Cl atoms are formed mainly via the C state, and we Doppler forms of the a0 ( ) and Re a1 ( , ) are clearly (1) Ќ do not expect to see any Re͓a(1)(ʈ,Ќ)͔. The Cl* results at different, with the a0 ( ) peaking for those fragments trav- 1 eling toward and away from the probe laser light, and the 330 nm, however, clearly show contributions from both (1) (1) ͓ (1) ʈ Ќ ͔ a (Ќ) and Re͓a (ʈ,Ќ)͔, indicating the presence of both Re a1 ( , ) showing a single peak for products at the line 0 1 (3) Ќ parallel and perpendicular transitions. We found that it was center. The a0 ( ), on the other hand, shows oscillations, resulting from the third-order Legendre function in Eq. ͑1͒. not possible to fit the Cl* data properly by assuming only an (1) Ќ ͓ (1) ʈ Ќ ͔ a0 ( ) or only a Re a1 ( , ) . ͑ ͒ ␥ III. RESULTS By integrating Eq. 1 with respect to cos ,wecanwrite Ϫ Figure 2 shows isotropic and anisotropic Doppler pro- IL IR ϭ 1 1 ͓͑ ϩ␤͒ ͑1͒͑Ќ͒Ϫͱ ͑1͒͑ʈ Ќ͔͒ ͑ ͒ files for Cl and Cl* atoms from chlorine molecules photo- ϩ 3 G s1 1 a0 2a1 , , 2 IL IR lyzed at 310 nm. Also shown are the fits obtained using the basis function method described previously. Both the Cl and where IL/R is the ionization signal integrated over the Dop- (3) Ќ Cl* data can be fitted using only the first-order orientation pler line shape. Note that the a0 ( ) term vanishes in the (1) Ќ (1) Ќ moment a0 ( ): For the Cl atoms, we did not fit for contri- integration. Assuming that only a0 ( ) needs to be consid- (3) Ќ butions from a0 ( ) because its presence cannot be detected ered, it is possible to obtain an estimate for this moment by within the limits of the experimental noise. Further, there taking the ratio of integrated difference to the integrated sum ͓ (1) ʈ Ќ ͔ ͓ (3) ʈ Ќ ͔ appears to be no Re a1 ( , ) or Re a1 ( , ) in accor- of the experimental data, which avoids the need to use the

FIG. 3. As in Fig. 2 but showing data obtained at the photolysis wavelength of 330 nm. FIG. 2. Isotropic ͑upper trace͒ and anisotropic ͑lower trace͒ Doppler profiles ͑ ͒ 35 2 ͑ ͒ 35 2 for a Cl( P3/2) atoms and b Cl*( P1/2) atoms at 310 nm. The isotropic Doppler profiles are not dependent on product orientation. The anisotropic profiles can be related to orientation moments of the electronic angu- feel that they do not represent true uncertainties for the mea- lar momentum distribution, as detailed in the text. Thin solid lines represent the experimental data, and thick solid lines are the fits obtained as detailed surement. The Monte Carlo method, however, does allow us (1) Ќ in the text. to estimate the relative uncertainties in the a0 ( )and ͓ (1) ʈ Ќ ͔ ͑ ͒ Re a1 ( , ) that contribute to the Cl* 330 nm data: the covariance between these fitted moments is also reflected in basis fitting method. The results of this method, and of the the Monte Carlo uncertainties. basis function fitting are shown in Table I. For completeness, Possible sources of systematic error in our measure- the integrated result for Cl* produced at 330 nm is also ments include background signal from the probe laser, which (1) Ќ shown in Table I, although we cannot separate the a0 ( ) would contribute to the isotropic but not to the anisotropic ͓ (1) ʈ Ќ ͔ 35 37 (1) Ќ and Re a1 ( , ) moments. The results for Cl and Cl are signal and tend to decrease the observed a0 ( ): We esti- in excellent agreement, serving as independent measure- mate this effect to be less than 2% for the results in Table I. (3) Ќ 3,5 ments of the orientation. Contributions from an a0 ( ) We used the ␤ parameter taken from previous studies to (1) Ќ would modify the fitted a0 ( ) value compared to the inte- analyze our data, although we did not take account of uncer- grated value; however, the good agreement between the two tainties in those values. We estimate a possible additional (3) Ќ ␤ analysis methods suggests that the a0 ( ) contribution is 5% uncertainty resulting from uncertainties in the param- small. The error bars for the integrated results were obtained eter. Indeed, in a previous work37 we have proposed the use from standard deviations across a set ͑typically 10͒ of mea- of polarization moments as a more sensitive measurement of sured profiles. The uncertainties listed for the fitting method the ␤ parameter. that uses basis functions were obtained by a Monte Carlo A high quality of the CP light in these experiments was sampling method that was applied to the averaged data; found to be crucial: We have observed that refractive ele- sampled fits that lay visibly beyond the random noise were ments ͑lenses, windows, etc.͒ can decrease the quality of discarded. The uncertainties obtained in this way appear polarization. The Soleil–Babinet compensator is calibrated smaller than the profile-to-profile variance, and we therefore for the wavelength being used, and we have found that it is

Downloaded 24 Feb 2012 to 171.64.124.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions 9026 J. Chem. Phys., Vol. 113, No. 20, 22 November 2000 Alexander et al.

TABLE I. Photofragment orientation moments obtained by fitting of Dop- in the discussion that follows, we consider the effects of ͑ ͒ pler profiles, and by integration see the text for details measured from the nonadiabatic transitions semiquantitatively in the adiabatic photolysis of Cl2 at 310 and 330 nm. The integrated result for Cl* at 330 nm 7 has been included for completeness. The translation anisotropies ͑␤͒ used dissociation framework. for the data analysis were taken from Samartzis et al. ͑Ref. 5͒, and have If we consider a photofragmentation process producing been multiplied by Ϫ1/2 to account for the use of circularly polarized pho- two atomic fragments A and B, the dynamical functions can tolysis light. be related to the electronic dipole transition of the molecule 7 Photolysis Integrated AB, and are defined by ␤ (1) Ќ (1) Ќ wavelength/nm Product atom Fitted a0 ( ) a0 ( ) ϩ ͑ Ј͒ϭ ͑Ϫ ͒ jA mA 310 35Cl 0.5 0.13Ϯ0.02 0.14Ϯ0.04 f K q,q ͚ 1 37 Ј Cl 0.5 0.18Ϯ0.02 0.20Ϯ0.04 mA ,mA 35Cl* 0.32 Ϫ0.24Ϯ0.01 Ϫ0.27Ϯ0.06 37Cl* 0.32 Ϫ0.23Ϯ0.02 Ϫ0.30Ϯ0.07 jA jA K 35 ϫͩ ͪ ͑ ͒ Ϯ Ϯ M j ⍀ m M j ⍀ mЈ *, 330 Cl 0.5 0.23 0.01 0.23 0.04 Ϫm mЈ qϪqЈ A i A A i A 35 (1) Ќ Ϫ Ϫ Ϯ A A Cl* a0 ( ) 0.12 0.26 0.17 ͓ (1) ʈ Ќ ͔ Ϯ Ϯ ͑ ͒ Re a1 ( , ) 0.43 0.10 0.69 0.17 5

where jA is the atomic A fragment angular momentum. The projection mA along the recoil axis is quantized, and is di- ϩ rectly equivalent to the familiar (2 jA 1) magnetic substates 34 much more reliable than commercial nominal zero-order of angular momentum jA . The components of the initial ͑ ͒ waveplates. The results at 310 and 330 nm differ in the (Ji)andfinal J electronic molecular angular momentum ⍀ ⍀ quarter-wave polarizing element used. A small percentage of along the recoil axis are denoted i and , respectively. The linear polarization in our circularly polarized photolysis light transition dipole matrix elements M ⍀ can be calculated jA imA would contribute to the isotropic (Diso) signal, but not to the following the methods of Vasyutinskii and co-workers,17 and ⍀ anisotropic (Daniso) profile, effectively reducing the observed require a knowledge of the matrix elements T that jAmAjBmB orientation moments. Frequent systematic checks were used ⍀ ͑ ͒ correlate the excited molecular states with the angular mo- to avoid errors caused by poor polarization see Sec. II . ͉ mentum states j,m j͘ of the atomic photofragments. Vasyutinskii and co-workers have evaluated T matrix elements using a first-order perturbation calculation in an ͉ IV. DISCUSSION atomic j,m j͘ basis by taking into account the long-range 38 (k) 10 multipolar charge interaction of the atomic fragments. For The aq (p) polarization moments of Rakitzis and Zare the two channels under consideration, the chlorine atoms carry information concerning the spatial distribution of an- have the same electronic parity and therefore the long-range gular momentum vectors. The polarization moments are interactions to be considered are quadrupole–quadrupole and equivalent to the spherical tensor moments that have been dispersion ͑induced-dipole–induced-dipole͒ interactions.39 commonly used to describe the angular momentum 34 The long-range effects of these interactions have been con- distribution. From the polarization moments, we obtain de- sidered quantitatively for the molecular chlorine system by tailed information about the electronic dynamics that occur 40 (k) Saute et al. As will be discussed later, by comparing the during the photodissociation process. The aq (p) can be (k) theoretically expected values of aq (p) with the experimen- written in terms of the quantum dynamical functions tally measured values, we can gain a detailed answer as to Ј 9 f K(q,q ) of Siebbeles et al., which states are involved in the photodissociation process. ͑ ͒ Such details provide the first step toward understanding ͑ ͒ f 1 1,1 a 1 ͑Ќ͒ϭ , ͑3͒ which states may take part in the dissociation, and the 0 f ͑1,1͒ 0 mechanism for their interaction. Ϫ ͱ ͒ 3 2 f 1͑1,0 „2 … a͑1͒͑ʈ,Ќ͒ϭ . ͑4͒ A. Cl P3Õ2 atoms 1 f ͑0,0͒ϩ2 f ͑1,1͒ 0 0 According to the experimentally observed ␤ parameter, Equation ͑3͒ is written in the limit of a pure perpendicular ground-state Cl atoms at photolysis wavelengths of 310 and transition, and would vanish for a pure parallel transition. 330 nm are produced mostly via perpendicular transitions. The dynamical functions contain information on the dynam- Following Bracker et al.7 we find that the two lowest states ͉ ͉ ics of the photofragmentation process; in particular they de- of 1u symmetry correlate to atomic jA ,mA͘ jB ,mB͘ states pend on the molecular transition dipole ͑for a detailed dis- as cussion, we refer the reader elsewhere9͒. The dynamical R→ϱ 1 treatment of Siebbeles et al. was formulated assuming adia- ͉ ͑1͒͘ → ͉͑ 3 3͉͘ 3Ϫ 1͘ϩ͉ 3Ϫ 1͉͘ 3 3͘ ͑ ͒ 1u A —— 2 2 2 2 2 2 2 2 ), 6 batic dissociation within the axial recoil approximation. A ͱ2 fully quantum treatment of photodissociation that relies only R→ϱ ͑ ͒ on the assumption of an electronic dipole transition in the ͉1 2 ͘ ——→ ͉ 3 1͉͘ 3 1͘, ͑7͒ molecule has recently been given by Mo et al.18 However, u C 2 2 2 2 following previous work on the photodissociation of Cl2 ,we where R denotes the Cl2 internuclear separation. To conve- will assume that the axial recoil approximation is valid, and niently distinguish between the five states of 1u symmetry,

(2) Ќ From the results of Bracker et al. we obtain a0 ( ) ϭϪ Ϯ (2) Ќ ϭϪ Ϯ 0.35 0.04 and a2 ( ) 0.15 0.04. Following the method of calculating polarization moments from the transition diplole matrix elements as outlined previously, theory predicts that adiabatic dissociation via the C state produces a ϭ (2) Ќ ϭϪ maximal m j 1/2 alignment a0 ( ) 0.8, and that the A (2) Ќ ϭ state produces zero alignment a0 ( ) 0. Such results led Bracker et al. to the conclusion that homogeneous nonadiabatic transitions occur from the C to the A states, effectively (2) Ќ 7 reducing the observed a0 ( ). ͑ ͒ (1) Ќ From the theory, using Eq. 3 , we calculate a0 ( ) ϭ0.258 for dissociation via either the A or the C state, and the result is in excellent agreement with the measured (1) Ќ a0 ( ) value at 330 nm. The agreement between theory and experiment is not as good at 310 nm, although we have no a priori reason to believe that the measured results at 310 nm should differ significantly from the result obtained at 330 nm. In fact the theoretical result can be obtained by a simple calculation of the orientation of a jϭ3/2 atom in a magnetic ϭ (1)ϭ ͱ ϩ 34 substate m j 1/2: a0 m j / j( j 1). Physically, we see that the single unit of angular momentum carried by the CP photon is shared equally between the two atoms: either two FIG. 4. Correlation diagram showing all of the electronic states of Cl2 , ͑ ͒ 2 atoms both with m ϭϩ1/2, or both in a linear superposition Refs. 2 and 3 . On the right-hand side ground-state Cl( P3/2) and excited- j 2 ϭϩ Ϫ state Cl*( P1/2) are denoted as Cl and Cl*, respectively, as in the text. The of m j 3/2 and 1/2. In this case, measurement of the left-hand side shows the electronic configuration of the molecular orbitals a(1)(Ќ) moment cannot distinguish between the 1 states A ␴ ␲ ␲ ␴ 0 u 5 g2 u2 g*5 u* . The electronic terms are shown along with the projection ⍀ ⍀ϭ or C. Calculating the third-order orientation moment of total electronic angular momentum, .Thefive states of 1u symme- (3) Ќ try that are important for the present discussion are labeled in energetic a0 ( ) for the above-mentioned states we find that when (1) ͑ ϭϩ (3) Ќ ϭϪ order from 1 to 5, as they are in the text, e.g., 1u is the lowest state A m j 1/2, a0 ( ) 0.31, and a linear superposition of state͒. States X, A, B,andC are also highlighted for convenience. ϭϩ Ϫ (3) Ќ ϭ m j 3/2 and 1/2 yields a0 ( ) 0.21. To further under- (3) Ќ stand the involvement of the a0 ( ) moment in our data, we (1) Ќ (3) Ќ simulated profiles using values of a0 ( )anda0 ( ) cal- (n) (1) Ќ we have labeled the ordering of the molecular ⍀ states as culated previously, but fitting them with an a0 ( ) only. It u (3) Ќ (1) Ќ a superscript ͑n͒, see Fig. 4. The transition dipole ͑T͒ matrix was found that the a0 ( ) modified the fitted a0 ( )byup ϭϩ (1) Ќ elements show that the C state correlates to produce two to 20%. For the case of m j 1/2, the fitted a0 ( )maybe 2 ϭϩ ͓ ͑ ͔͒ Cl( P3/2) atoms both with m j 1/2 see Eq. 7 and that underestimated by up to 20%, which may account for the the A state correlates to produce Cl atoms in a symmetric difference in the fitted and integrated values shown in Table ϭϩ ϭϪ ͓ (1) Ќ linear superposition of m j 3/2 and m j 1/2 see I. However, the a0 ( ) orientation moment cannot distin- Eq. ͑6͔͒. guish between the A and the C states. Combined with the (2) Ќ Previous measurements of the electronic alignment of results for a0 ( ), we conclude that the dominant channel the Cl atoms suggest that the C state is mostly responsible for producing ClϩCl is adiabatic dissociation via the C state for the production of Cl atoms around 310 to 330 nm. Ra- with contributions from nonadiabatic transitions between the 6 (2) Ќ Ϫ Ϯ kitzis et al. measured an a0 ( ) value of 0.50 0.10, and C state and the A state. (2) Ќ Ϫ Ϯ an a2 ( ) value of 0.32 0.06, at a photolysis wavelength 2 B. Cl*„ P Õ … atoms of 320 nm. We can convert the alignment parameters 1 2 ␣ ␥ ␩ 7 (s2 , 2 , 2 , 2) measured by Bracker et al. at a photolysis Previous studies of the ultraviolet photodissociation of wavelength of 355 nm, using molecular chlorine indicate that excited-state Cl* atoms are produced by dissociation via mixed ͑parallel and perpendicu- 1͑ ϩ␤͒ 2͑ʈ͒ϭ Ϫ ␣ ͑ ͒ 3 5 1 a0 s2 2 2 , 8 lar͒ transitions in the region of 270–400 nm. Evidence for the mixed transitions include the nonlimiting ␤ parameter,5 1 ␤ and the measurement of the Im͓a(1)(ʈ,Ќ)͔ orientation mo- ͩ 1Ϫ ͪ a2͑Ќ͒ϭs ϩ␣ , ͑9͒ 1 5 2 0 2 2 ment that depends on the coherence between the dissociation via parallel and perpendicular transitions.8 In previous work, ͓ (1) ʈ Ќ ͔ 15 we observed an oscillation in the Im a1 ( , ) as a function 2͑ʈ Ќ͒ϭϪ ␥ ͑ ͒ a1 , 2 , 10 of photolysis wavelength. This oscillation results from the ͱ6 photolysis energy dependence of the coherence between parallel and perpendicular transitions. At the photolysis wave- 2 ␤ 5 ͩ Ϫ ͪ 2͑Ќ͒ϭϪ ␩ ͑ ͒ length 330 nm, the number of Cl* atoms produced via par- 1 a2 2 . 11 3 2 ͱ6 allel and perpendicular transitions is approximately equal.

Downloaded 24 Feb 2012 to 171.64.124.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions 9028 J. Chem. Phys., Vol. 113, No. 20, 22 November 2000 Alexander et al.

(1) ʈ Ќ The magnitude of the coherent a1 ( , ) moment can be largest when there are equal contributions from parallel and perpendicular states, assuming that the transitions are per- fectly in phase with each other. Taking the imaginary and (1) ʈ Ќ real parts of the a1 ( , ), as mentioned in Sec. III, the ͓ (1) ʈ Ќ ͔ ͓ (1) ʈ Ќ ͔ Im a1 ( , ) and Re a1 ( , ) are 90° out of phase and ͓ (1) ʈ Ќ ͔ ͑ the measured Im a1 ( , ) at 330 nm is small 0.032 Ϯ0.005͒, despite the fact that the contributions from parallel and perpendicular transitions are almost equal at this photolysis wavelength. Consequently, we might expect the ͓ (1) ʈ Ќ ͔ Re a1 ( , ) to be large. This supposition is supported by ͓ (1) ʈ Ќ ͔ the oscillation in Im a1 ( , ) as a function of photolysis wavelength that was observed by Kim et al.: The oscillation appears to change sign at around 330 nm.8 The maximum ͓ (1) ʈ Ќ ͔ allowed value of the Re a1 ( , ) can be calculated by ro- (1) Ќ tating a maximal a0 ( ) distribution using Wigner rotation matrices.34 FIG. 5. Ab initio potential energy curves as a function of the internuclear ͑ ͒ ͑ ͒ ͑ ͒ ͓ 1 ͔ϭ 1͑ 1 Ϫ 1 ͒ separation R, showing the excited states of Cl2 relevant to the present dis- Re a1 2 aϩ1 aϪ1 cussion. Solid curves are the states of 1u symmetry, labeled as in Fig. 4, the ϭ 1 ͑1͓͒ ͑1͒ ͑␪͒Ϫ ͑1͒ ͑␪͔͒ dashed curve is the B state. The axes have been scaled to highlight the 2a0 dϩ10 dϪ10 potential energy curves shown, and the ground electronic state of Cl2 has been omitted for convenience. The peak positions of ab initio calculated j)͘ ) ץ ץ ͉(ϭ͗ (i 1 ϭ ͑1͒ ␪ ͑ ͒ radial derivative coupling matrix elements gij 1u ( / R)1u are shown a0 sin . 12 ͱ as solid vertical bars between the 1u states. The magnitudes of these cou- 2 Ϫ pling terms are also shown in units of bohr 1. k ␪ ␪ϭ The dqЈq( ) are the real rotation matrices, and 90°. For jϭ1/2 the maximum a(1)(Ќ) is 0.577, and the maximum 0 R→ϱ 1 ͓ (1) ʈ Ќ ͔ ͉ ͑4͒͘ → ͉͑ 3 1͉͘ 1 1͘ϩ͉ 1 1͉͘ 3 1͘ ͑ ͒ calculated Re a1 ( , ) is 0.408, which agrees with the 1u ⌬ —— 2 2 2 2 2 2 2 2 ). 15 value that we have measured ͑0.43Ϯ0.10͒. ͱ2 From the present study the most striking effect that we Using these correlations and Eqs. ͑3͒–͑5͒ as before, we find observe is a negative orientation for the Cl* atom, i.e., the (1) Ќ that the B state would produce zero orientation a0 ( ) for Cl* fragments are oriented with the opposite sense compared either the Cl or the Cl* photofragments: the initial ⍀ϭ0 to the photolysis laser CP light. We may calculate the ex- leaves no projection for the final atomic fragments. The 1(3) (1) Ќ u pected a0 ( ) from the electronic correlation diagram using (4) and the 1u states would produce maximal Cl* orientations the T matrix in the same manner as described previously. In but of opposite sign, a(1)(Ќ)ϭϪ0.577 for the 1(3) state and * 0 u previous work, we suggested that the production of Cl at- a(1)(Ќ)ϭϩ0.577 for the 1(4) state. We immediately assign oms occurs by direct absorption via a parallel transition to 0 u ϩ the major portion of the observed Cl* fragments to dissocia- the B 0u state, and also by absorption via a perpendicular (3) (2) tion via the 1u state because of the observed negative ori- transition to the C 1u state followed by some nonadiabatic entation in the lab frame. At a photolysis wavelength of 310 transition. The nonadiabatic transition may involve either an nm, the spatial distribution of the fragments ␤͑Cl*͒ϭ0.32,5 inhomogeneous Coriolis mechanism coupling from the C to which implies that 88% of the Cl* fragments originate from the B state, or a homogeneous radial derivative coupling a perpendicular transition. If all of these fragments dissoci- ͑RDC͒ to a higher state of 1 symmetry;39 seeFig.5.We u ated via RDC to the 1(3) state, we might expect to see an exclude direct dissociation via one of the higher 1 states by u u a(1)(Ќ) value of 0.88ϫ͑Ϫ0.577͒ϭϪ0.51. The 12% that the Franck–Condon principle, noting the large cross section 0 originate from the parallel ͑B state͒ transition have zero ori- for production of Cl atoms from the C state. The states that entation and reduce the observed orientation from the maxi- correlate to produce Cl* fragments that we will consider are (1) Ќ 35 ͑3⌬ 3⌺ϩ͒ mal value. The observed a0 ( ) for Cl* at these energies two states of 1u symmetry u and u and one state of ͑Ϫ Ϯ ͒ ϩ ͑ 3⌸ ͒ 0.27 0.06 is much smaller than maximal, but suggests 0u symmetry the B u state . For these states the correla- 35 40 that at least 47Ϯ10% of the Cl* dissociate via RDC to the tions in terms of atomic fragments are (3) 1u state with the remaining percentage having a net zero R→ϱ orientation: We shall discuss possible mechanisms in the fol- ͉ ϩ͘ → 1͉͑ 3 1͉͘ 1Ϫ 1͘Ϫ͉ 1Ϫ 1͉͘ 3 1͘Ϫ͉ 3Ϫ 1͉͘ 1 1͘ 37 0u B —— 2 2 2 2 2 2 2 2 2 2 2 2 2 lowing. For Cl*, the estimate of percentage dissociation (3) Ϯ via RDC to the 1u state is 52 12%: We have no reason to ϩ͉ 1 1 ͉ 3Ϫ 1 ͑ ͒ believe that the different isotopes of Cl would produce sig- 2 2͘ 2 2͘), 13 nificantly different results. At 330 nm ␤͑Cl*͒ϭϪ0.12,5 im- plying 59% of the Cl* atoms originate from a perpendicular R→ϱ 1 ͑3͒ 3 3 1 1 1 1 3 3 transition. If all of the fragments originating from a perpen- ͉1 ͘⌺ ——→ ͉͑ ͉͘ Ϫ ͘ϩ͉ Ϫ ͉͘ ͘), ͑14͒ u ͱ 2 2 2 2 2 2 2 2 (3) 2 dicular transition were to dissociate via the 1u state we

TABLE II. Ab initio relative absorption coefficients from the ground ͑X͒ to tions are usually small. This simplification is partly justified the first three excited states of Cl2 are shown at wavelengths of 310 and 330 (3) because the molecular orbitals do not change very much at nm. The nonadiabatic transition probability from the C to the 1u state, PRZD, was calculated using the semiclassical expression of Rosen–Zener– the longer bond distances of interest. Demkov ͑Refs. 39 and 42͒, where the parameters were fitted only from the As typical models of the RDC mechanism, curve cross- adiabatic energies. The calculations yield an estimated ␤ parameter for Cl* ing Landau–Zener and noncrossing Rosen–Zener–Demkov photofragments that is in very good agreement with experimental results of ͑RZD͒ models are well known.39,42 In the latter model, the Samartzis et al. ͑Ref. 5͒. ⌬ϭ energy difference between the two diabatic states Hii Ϫ 310 nm 330 nm H jj is constant and the diabatic coupling element Hij depends on the internuclear distance R as H ϭA exp(Ϫ␣R). A – X absorption 3.160ϫ10Ϫ5 1.261ϫ10Ϫ4 ij B – X absorption 3.277ϫ10Ϫ4 1.392ϫ10Ϫ3 Inspecting the potential curves and the corresponding adia- C – X absorption 0.2908 0.4461 batic CI wave functions, the nonadiabatic behavior of the 1u RZD (3) ϫ Ϫ3 ϫ Ϫ3 P C –1u 5.42 10 3.52 10 states was found to follow the RZD model approximately. ␤͑Cl*͒ ab initio 0.25 Ϫ0.21 For each pair of coupled adiabatic states ⌿(i) and ⌿( j),the ␤͑Cl*͒a 0.32 Ϫ0.12 matrix element gij behaves as aReference 5. ␣ 1 ϭ ͑ ͒ gij ␣ Ϫ ͒ , 16 4 cosh͕ ͑R Rmax ͖ would expect a(1)(Ќ)ϭϪ0.34. From our measured value of ␣ ϭ 0 with a peak value of /4 at R Rmax , where A (1) Ќ Ϫ Ϯ Ϯ ϫ Ϫ␣ ϭ⌬ a0 ( )( 0.26 0.17) we estimate that at least 52 44% of exp( Rmax) /2 is satisfied. We have fitted the param- 35 (3) ␣ ⌬ ⌬ all Cl* fragments dissociate via the 1u state. eters , A, , Rmax from the ab initio results. The values As mentioned previously, some remaining percentage of were determined from the adiabatic energy difference at & the Cl* fragments that originate from a perpendicular transi- Rmax, divided by : This relation must be satisfied for the tion must have net zero orientation, and this may occur by noncrossing-type RZD model. Rmax and the peak values absorption to the C state followed by: of some of the coupling elements are indicated schematically ϭ ͑ ͑ ͒ in Fig. 5, e.g., g23 peaks at Rmax 5.7 bohr 1 bohr a transition by Coriolis mechanism to the B state, with Ϫ11 ⍀ϭ ϭ5.29ϫ10 m). The fitted parameters were used to com- 0, 39,42 ͑ ͒ (3) pute RZD nonadiabatic transition probabilities, b transition by RDC mechanism equally to the 1u and 1(4) states producing fragments with opposite orienta- u 1 tion that cancel to give net zero orientation. RZDϭ ͑ ͒ P ␲⌬ , 17 1ϩexpͩ ͪ Coriolis coupling will be dependent on the rotational ប␣v temperature of the chlorine gas, and this temperature has not been fully characterized for our pulsed expansion. It may be where v is the relative velocity of the fragment atoms at ͑ ͒ ⌬ possible to investigate the Coriolis mechanism by selective Rmax . It follows from Eq. 17 that as v becomes large, or RZD excitation of Cl2 molecular rotational states, or by altering becomes small, P approaches the diabatic limiting value RZD RZD the temperature or collision conditions of the expansion in a of 1/2. We therefore expect that P2→1 and P3→4 can be quite controlled manner. However, for the present experiments, we large since the coupling states correlate to common dissocia- believe that these effects are small.3 Ab initio calculations tion limits, as Fig. 5 shows, and ⌬ is very small for both RZD RZD predict a negligibly small Coriolis transition probability couplings. On the other hand, P2→3 and P2→4 are expected Ϫ ͑on the order of 10 6͒ for rotational temperatures of 100 to to be rather small since the magnitude of ⌬ corresponds to 300 K.12 the spin–orbit splitting of the Cl atom. From the above-mentioned arguments, we discount From their alignment experiments at a photolysis wave- mechanism ͑a͒. Taking stock of the approximations implied length of 355 nm ͑see Sec. IV B͒ Bracker et al.7 estimated a ϭ by the theoretical treatment, it can be seen that our estimates strong nonadiabatic transition probability of P2→1 0.60 (3) Ϯ of the RDC transition to the 1u state are conservative. Re- 0.04 from the C to A state. From our alignment 6 ϭ Ϯ call that some of the fragments have orientation of opposite measurements at 320 nm we estimate P2→1 0.38 0.13. sense, as in condition ͑b͒ noted previously. Estimates of rela- The A and C states converge adiabatically to the same atomic ␤ tive absorption coefficients, parameters, and nonadiabatic limit, and the RDC matrix element g21 has a peak at a longer (3) ϭ transition probabilities from the C to the 1u state calculated distance (Rmax 7.7 bohr), making the transition nearly reso- in our previous ab initio study11 are shown in Table II. For nant, thus, it is no surprise that the transition probability is the present study, the ab initio spin–orbit configuration- large. At the photolysis wavelength 355 nm, Eq. ͑17͒ gives ͑ ͒ RZD ϭ interaction CI calculations of the potential energy curves of P2→1 0.41, in reasonable agreement with the large transi- RZD Cl2 have been extended to include calculation of the RDC tion probability observed, and at 320 nm we estimate P2→1 ⌿( j) ϭ ץ ץ ͉(ϭ ⌿(i matrix elements, gij ͗ ( / R) ͘, between the dif- 0.42, which is in excellent agreement with our experi- ferent adiabatic states of 1u symmetry. The theoretical meth- ments. ods are similar to those previously applied to ICl molecule.41 For the present calculations, we obtained fairly large RZD In the calculations of RDC elements, we have neglected the near-resonant nonadiabatic transition probabilities of P3→4 so-called molecular orbital derivative terms, whose contribu- ϭ0.273(0.256), and small noncrossing-type nonadiabatic

Downloaded 24 Feb 2012 to 171.64.124.19. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions 9030 J. Chem. Phys., Vol. 113, No. 20, 22 November 2000 Alexander et al.

RZD ϭ ϫ Ϫ3 ϫ Ϫ3 the electronic angular momentum of product ground-state transition probabilities of P2→3 1.67 10 (0.952 10 ) RZD ϭ ϫ Ϫ20 ϫ Ϫ22 ␭ϭ ͑ ͒ Cl(2P ) and excited-state Cl*(2P ) chlorine atoms were and P2→4 4.5 10 (7.9 10 ) for 310 330 nm re- 3/2 1/2 RZD measured, and the contributions from both coherent and in- spectively. The P2→3 are a little smaller than our previous theoretical estimates ͑shown in Table II͒, which were calcu- coherent dissociation mechanisms were resolved. The ex- lated using only the adiabatic energy differences without the perimental results for Cl* can be explained by nonadiabatic 11 1⌸ RDC elements. Part of the underestimation comes from our transitions from the C 1u state to higher states of 1u sym- approximate evaluation of the RDC elements, especially for metry, induced by noncrossing-type radial derivative cou- those with peaks at shorter bond distances, where the varia- pling. Ab initio calculations indicate signiﬁcant Rosen– tion of the molecular orbitals cannot be neglected. In spite of Zener–Demkov type radial derivative couplings between (2) 1⌸ (3) 3⌺ϩ this uncertainty, we believe that the one-step nonadiabatic the 1u (C 1u) and 1u ( 1u) states, and between the ϩ (4) 1(3)(3⌺ ) and 1(4)(3⌬ ) states. At the photolysis wave- transition from the C state to the 1u state is negligible. u 1u u 1u (4) length of 310 nm, 88% of the observed Cl* fragments origi- Furthermore, Cl* dissociation on the 1u state should origi- (3) nate from a perpendicular transition. The orientation mea- nate from the C state via the intermediate 1u state by two- RZD RZD RZD Ϯ 35 * step transition, since P → ӶP → ϫP → . surements suggest that 67 16% of Cl atoms dissociate 2 4 2 3 3 4 (3) 3⌺ϩ Ϯ Reviewing the data available, we make the following via the 1u ( 1u) state, and 21 6% dissociate via the (4) 3⌬ hypotheses. After initial absorption to the C state, less than 1u ( u) state. We conclude that nonadiabatic transitions 1% of chlorine molecules make a nonadiabatic transition to induced by noncrossing-type radial derivative coupling play (3) a dominant role in controlling the orientation of the resulting the 1u state. The majority of the fragments go on to produce two ground state Cl atoms adiabatically via the C state, Cl* atom photofragments. or by nonadiabatic crossing to the A state. By measuring the The results demonstrate that measurements of the elec- Cl* fragments, however, we are really selecting a special tronic orientation not only provide a detailed picture of the subset of molecules that absorb the ultraviolet light: There- electronic states accessed but also of the nonadiabatic tran- fore, the absolute transition probability from the C state to sitions that occur far from the Franck–Condon region. Taken (3) together, the present measurements of photofragment orien- the 1u state need not be large. In order to produce the observed mixed ␤ parameter, the number of molecules that tation caused by photolysis with circularly polarized light, 8 experience a nonadiabatic transition should be of the same the previous measurements of photofragment orientation 6,7 order as the number that are directly absorbed to the B state: and alignment caused by photolysis with linearly polarized (3) light, provide new information on how simple molecules see Table II. However, after transition to the 1u state, molecules may experience a strong nonadiabatic transition to the separate into their constituent atoms under the action of ra- (4) diation. 1u state, as a result of the fairly large near-resonant non- RZD ͑ adiabatic transition probability P3→4 cf., the strong transi- 7 tion between the C and A states estimated by Bracker et al. ͒. ACKNOWLEDGMENTS This behavior would explain the reduced from maximal values of the orientation parameter that we have measured for We are grateful to Oleg Vasyutinskii and David van Cl* atoms. Baak for useful discussions. S.Y. thanks Hiroki Nakamura at Consider the particular case of 35Cl* at 310 nm ͑see IMS, Okazaki, for useful discussions. Z.H.K. gratefully ac- prior text͒. We return to the question of the partitioning of knowledges receipt of a Dr. Franklin Veatch Memorial Fel- lowship. This work was funded by the National Science the fragment atoms between the different states of 1u symmetry. Recall that we attributed the observed negative Foundation under Grant No. CHE-99-00305. S.Y. was sup- (1) Ќ ported by a Grants-in-Aid for Scientiﬁc Research from the a0 ( ) to 12% dissociating via parallel transition to the B state, with zero orientation, and 47Ϯ10% dissociating via the Ministry of Education, Science, Culture, and Sports of Japan, (3) (1) Ќ ϭϪ and by Research and Development Applying Advanced 1u state with maximal orientation a0 ( ) 0.577. The remaining percentage of fragments originates from a perpen- Computational Science and Technology, Japan Science and dicular transition ͑41Ϯ10%͒. We split this percentage Technology Corporation. (3) (4) equally between the 1u and 1u states, with equal and opposite orientations that cancel to give a net zero orientation, 1 G. Herzberg, Molecular Spectra and Molecular Structure. I. Spectra of From this data we estimate a transition probability from the Diatomic Molecules ͑van Nostrand Reinhold, New York, 1950͒. (3) (4) 2 R. S. Mulliken, Phys. Rev. 36, 1440 ͑1930͒. 1 to the 1 state of P → ϭ0.23Ϯ0.06. This estimate is u u 3 4 3 Y. Matsumi, K. Tonokura, and M. Kawasaki, J. Chem. Phys. 97, 1065 in excellent agreement with the theoretically calculated RZD ͑1992͒. RZD ϭ 4 nonadiabatic transition probability P3→4 0.27. In total, the P. C. Samartzis, I. Sakellariou, T. Gougousi, and T. N. Kitsopoulos, J. a(1)(Ќ) measurements suggest that 67Ϯ16% of 35Cl* atoms Chem. Phys. 107,43͑1997͒. 0 5 (3) 3⌺ϩ Ϯ P. C. Samartzis, B. L. Bakker, T. P. Rakitzis, D. H. Parker, and T. N. dissociate via the 1u ( 1u) state, and 21 6% dissociate via ͑ ͒ (4) Kitsopoulos, J. Chem. Phys. 110, 5201 1999 . 3⌬ 6 the 1u ( 1u) state. Thus, we conclude that dissociation via T. P. Rakitzis, S. A. Kandel, A. J. Alexander, Z. H. Kim, and R. N. Zare, ϩ the 1(3)(3⌺ ) state plays the major role in the production of J. Chem. Phys. 110, 3351 ͑1999͒. u 1u 7 Cl* atoms. A. S. Bracker, E. R. Wouters, A. G. Suits, and O. S. Vasyutinskii, J. Chem. Phys. 110,6749͑1999͒. V. CONCLUSIONS 8 Z. H. Kim, A. J. Alexander, S. A. Kandel, T. P. Rakitzis, and R. N. Zare, Faraday Discuss. 113,27͑1999͒. Molecular chlorine was photodissociated at 310 and 330 9 L. Siebbeles, M. Glass-Maujean, O. S. Vasyutinskii, J. A. Beswick, and O. nm using circularly polarized light. Orientation moments of Roncero, J. Chem. Phys. 100, 3610 ͑1994͒.

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