Photodissociation of O2 Via the Herzberg Continuum: Measurements of O-Atom Alignment and Orientation Andrew J

JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 23 15 JUNE 2003

Photodissociation of O2 via the Herzberg continuum: Measurements of O-atom alignment and orientation Andrew J. Alexander,a) Zee Hwan Kim,b) and Richard N. Zarec) Department of Chemistry, Stanford University, Stanford, California 94305-5080 ͑Received 29 January 2003; accepted 24 March 2003͒

Irradiation of molecular oxygen O2 in the region of the Herzberg continuum between 218 nm and 3 ϩ 3 3 239 nm results in the production of open-shell photofragments O( P) O( P). Product O( P j ; jϭ0,1,2) atoms were ionized using resonantly enhanced multiphoton ionization ͑2ϩ1 REMPI͒ near 225 nm and the ions collected in a velocity-sensitive time-of-ﬂight mass spectrometer. By controlling the polarization of the photolysis and ionization radiation, we have measured alignment and orientation parameters of O-atom electronic angular momentum (j) in the molecule frame. The results show alignment from both parallel and perpendicular transitions that are cylindrically symmetric about the velocity (v) of the recoiling O atom. We also observe electronic alignment that is noncylindrically symmetric about v, resulting from coherence between multiply excited dissociative states. Photodissociation with linearly polarized light is shown to produce O atoms that are oriented in the molecule frame, resulting from interference between parallel and perpendicular dissociative states of O2 . Semiclassical calculations that include spin–orbit coupling between six excited states reproduce closely the observed polarization. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1574511͔

I. INTRODUCTION ties of the product O atoms with respect to the electric field vector ⑀ of the linearly polarized photolysis radiation. The Oxygen plays a key role in the chemistry of the Earth’s angular distribution can be written using the expression4 atmosphere. The splitting of the oxygen bond by ultraviolet ͑UV͒ solar radiation is the primary step in the formation of 1 I͑␪⑀͒ϭ ͓1ϩ␤P ͑cos ␪⑀͔͒, ͑1͒ ozone (O3), and is responsible for the existence of the ozone ␲ 2 1 4 layer. The UV photodissociation of O2 can be loosely ••• ␪ classed in three different wavelength regions: the Herzberg where P2( ) is the second order Legendre polynomial, ⑀ continuum ͑242–200 nm͒, the Schumann–Runge bands is the polar angle between v and ⑀, and the spatial distribu- ͑200–176 nm͒, and the Schumann–Runge continuum ͑176– tion of velocities is parameterized by ␤. The ␤ parameter 100 nm͒. takes the limits ϩ2 for a parallel (ʈ) transition and Ϫ1 for a The Herzberg continuum is the region of near-threshold perpendicular (Ќ) transition. At 226 nm, ␤ϭ0.61 for 3 ϩ 3 3 ʈ Ќ dissociation of O2 to give O( P) O( P). The electronic O( P2), indicating a mixture of 54% ( ) with 46% ( ). configuration of the O atoms (1s22s22p4) leads to a consid- Buijsse et al. have developed a detailed photoabsorption erable number of electronic states of the O2 molecule, and a model to directly compare with the experimental results. The 3⌺Ϫ Herzberg I transition was found to be the most significant, ground state X g that is unusual in that it has two un- paired electrons. In the Herzberg continuum, absorption oc- accounting for 86% of the total cross section at 242 nm, and 3⌺ϩ Ј 3⌬ 1⌺Ϫ rising to 94% at 198 nm. The resulting electric dipole tran- curs from the X state to the A u , A u , and c u states: these are called the Herzberg I, II, and III transitions sition includes both parallel and perpendicular components respectively. These Herzberg transitions are electric dipole ʈ SO forbidden, and the absorption cross sections (␴) are weak: 3 Ϫ 3 Ϫ 3 ϩ X ⌺ Ϯ →B ⌺ Ϯ ↔A ⌺ Ϯ , ͑2͒ for example, ␴Ϸ10Ϫ24 cm2 at 240 nm.2 Oscillator strength g, 1 u, 1 u, 1 for the Herzberg transitions is borrowed from electric dipole SO Ќ ͑ ͒ 3⌺Ϫ ↔ 3⌸ → 3⌺ϩ ͑ ͒ allowed transitions, mainly through spin–orbit SO interac- X g,0ϩ 1 g,0ϩ A u,Ϯ1 , 3 tions between ground and excited states. Buijsse et al.,3 have recently published results of a detailed velocity-map imaging SO Ќ 3⌺Ϫ ↔ 3⌸ → 3⌺Ϫ ͑ ͒ study of photodissociation in the Herzberg continuum. The X g,Ϯ1 1 g,Ϯ1 A u,0Ϫ . 4 velocity map experiments measured the directions of veloci- Here, we have given the projection ⍀ϵ⌳ϩ⌺ of total angular momentum on the bond axis as an additional subscript on ⌺ϩ Ϯ a͒ 2 1⌳ Ј 3⌬ Present address: School of Chemistry, University of Edinburgh, Edinburgh the term symbol, g/u,⍀ . The transitions to A u and Ϫ EH9 3JJ, UK. c 1⌺ are purely perpendicular in character. b͒ u Present address: College of Chemistry, University of California, Berkeley Adiabatically, the A, AЈ, and c states correlate to give O CA 94720-1460. ͒ ϭ 3 ϩ 3 c Author to whom correspondence should be addressed. Electronic mail: atoms with j 2, i.e., O( P2) O( P2). Several studies have 3 ϭ 5–7 [email protected] shown significant populations of O( P j) with j 0,1.

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3 ϭ ϳ Buijsse et al. measured the j 0:1:2 branching ratio as of 400 Torr. The O2 was photolyzed using linearly polar- 1.00:3.33:9.00. Clearly a significant amount of nonadiabatic ized light in the 218–239 nm wavelength range. The second interaction takes place during the dissociation. There are a harmonic ͑532 nm͒ ofaNd3ϩ:YAG laser ͑Continuum total of eight states of ungerade symmetry correlating to the PL9020͒ was used to pump a dye laser ͑Continuum ND6000, 3 ϩ 3 O( P) O( P) dissociation limit, these include three rhodamine 590ϩ610 dye͒ to produce tunable radiation in the Ј 1⌸ Herzberg states (A, A , and c) and five others (1 u , region 550–616 nm, which was doubled to 275–308 nm 3⌸ 3⌺ϩ 5⌸ 5⌺Ϫ 1 u ,2 u ,1 u , and 1 u ). The ungerade states using a KDP crystal. The resulting doubled light was then may couple through long-range SO interaction, and the ͑ ͒ 3 ϩ 3 ϩ mixed with the residual fundamental 1064 nm of the A ⌺ and 2 ⌺ states may also interact by radial deriva- ϩ u u Nd3 :YAG laser in a second KDP crystal to produce tunable tive coupling due to the radial kinetic energy operator. Un- photolysis radiation from 218 to 239 nm. Measurements of fortunately, angular distribution and branching ratio mea- product O(3P ; jϭ1,2) atom alignment were made at pho- surements do not reveal clues to the specific states involved j tolysis wavelengths of 221.667 and 237.049 nm; for brevity, in the nonadiabatic dissociation. we shall refer to these wavelengths as 222 and 237 nm, re- Recently, van Vroonhoven and Groenenboom8 ͑VG͒ cal- spectively. Measurements of O(3P ) atom orientation were culated ab initio potentials for the eight ungerade states, and 2 made at several photolysis wavelengths in the range the SO and radial derivative couplings between them. These 3 ϭ potentials were used in semiclassical calculations of the elec- 218.521–238.556 nm. The O( P j ; j 0,1,2) atom products ϩ ͑ tronic state-resolved branching ratios and ␤( j) parameters as were ionized by 2 1 REMPI resonantly enhanced multi- ͒ 3 3 a function of the dissociation energy, and the calculations photon ionization via the 2p 4p( P jЈ) intermediate state were compared with the experimental results of Buijsse using wavelengths of 226.233, 226.059, and 225.656 nm for ϭ et al.9 Significantly, VG also calculated electronic state re- j 0, 1, and 2, respectively. Polarization measurements are 3 ␳(k) ϭ ϭ not possible for O( P0) because this state has zero total an- solved alignment moments 0 ( j)(k 2,4; j 1,2), but at that time no experimental data were available for compari- gular momentum. Tuneable probe radiation around 226 nm son. The alignment moments are sensitive to nonadiabatic was produced by frequency doubling the 450 nm output of a 3ϩ ͑ transitions between states, and their experimental determina- second Nd :YAG pumped dye laser Spectra Physics DCR- tion would provide a useful test of ab initio and dynamical 2A, PDL-3, coumarin 450 dye͒. The probe and photolysis calculations. laser beams were counterpropagated and both loosely fo- In this article, we present measurements of electronic cused ͑ϩ50 cm focal length͒ to overlap at the center of the ϩ 3 pulsed expansion in the TOF. The resulting O ions were orientation and alignment of O( P j) atoms following dissociation via the Herzberg continuum in the region 218–239 collected with the TOF spectrometer operating under 12 nm. The O-atom polarization is obtained in terms of mol- velocity-sensitive conditions. (k) The direction of the linear polarization of the photolysis ecule frame polarization parameters aq (p) that distinguish between atoms produced by parallel (ʈ) or perpendicular (Ќ) beam was controlled using a double Fresnel rhomb ͑Optics transitions, or coherence due to mixed transitions.10 The For Research͒, and the direction of the probe linear polariza- measured alignment parameters allow a detailed comparison tion was switched on a shot-by-shot basis using a photoelas- with the recent semiclassical calculations of VG. The photo- tic modulator ͑Hinds PEM 80͒ allowing difference measure- dissociation of O2 with linearly polarized light results in pro- ments to be made very accurately. For the orientation duction of O atoms that are oriented in the molecule frame. measurements, the probe beam was circularly polarized us- The orientation results from interference between dissocia- ing a Soleil-Babinet compensator ͑Special Optics͒, and was tive states of parallel and perpendicular symmetry. The switched between left- and right-circular polarization using phase-dependent orientation should prove to be a very sen- the PEM. The experimental geometries used were the same sitive test parameter for the shapes of the dissociative poten- as described by Rakitzis et al.11 The TOF profiles are labeled F tial energy curves for O2 , and the nonadiabatic transitions by their geometry as IG , where F indicates the geometry of between states. The paper is arranged as follows: in Sec. II the photolysis polarization, and G indicates the geometry of we describe the experiment and extraction of the polarization the probe polarization. The laboratory Z axis lies along the parameters. The experimental results are presented in Sec. III TOF direction, and the Y axis lies along the photolysis laser in comparison with the semiclassical results of VG and our propagation direction. Left and right circular polarization is own semiclassical calculations of the interference between X indicated by L and R respectively. For example, for the IR excited dissociative states. Conclusions are given in Sec. IV. profile, the photolysis laser would be linearly polarized along the X axis, with the counterpropagating probe laser being right circularly polarized. For the alignment experiments, a total set of 4 profiles were recorded. These were obtained in II. METHODS two experiments using the PEM to flip the probe laser polar- The experimental methods have been described in detail ization between the X and Z axes on a shot-by-shot basis: elsewhere,11,12 and a brief overview is given here. A 1:9 mix- first with the photolysis polarization along X, and second ͕ X X͖ ͕ Z ture of oxygen ͑Matheson, 99.9%͒ and helium was made and along Z. This gives two pairs of profiles: IZ , IX and IZ , Z͖ expanded into the source region of a Wiley–Mclaren time- IX . TOF profiles that are sensitive to the O-atom velocity, of-flight ͑TOF͒ mass spectrometer via a pulsed nozzle ͑Gen- but approximately independent of product atom alignment ͒ Z ϭ Zϩ Z X ϭ Xϩ X eral valve, series 9, 0.6 mm orifice with a backing pressure are calculated as Iiso IZ 2IX and Iiso IZ 2IX . TOF pro-

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(k) TABLE I. Interpretation and range of molecule frame polarization parameters aq (p) used in the present work. The column headed ‘‘Physical Direction’’ gives the direction of alignment (kϭ2) or orientation (kϭ1) if the parameter is positive (ϩ) or negative (Ϫ).

Range

Parameter Interpretationa Physical direction jϭ1 jϭ2

(2) ʈ Ϫ 2 ϩ ʈ Ϫ Ќ Ϫ ••• ϩ Ϫ ••• ϩ a0 ( ) c2͗3 j z j ͘ ( ) z,( ) z 1.000 0.500 1.000 1.000 (2) Ќ Ϫ 2 ϩ ʈ Ϫ Ќ Ϫ ••• ϩ Ϫ •••ϩ a0 ( ) c2͗3 j z j ͘ ( ) z,( ) z 1.000 0.500 1.000 1.000 ͓ (2) ʈ Ќ ͔ Ϫ ͱ ϩ ϩ ʈ Ϫ Ϫ ʈ ϩ Ϫ ••• ϩ Ϫ ••• ϩ Re a1 ( , ) c2 3/2͗ j z j x j x j z͘ ( ) x z,( ) x z 0.866 0.866 1.000 1.000 (2) Ќ ͱ ͗ 2Ϫ 2͘ ϩ ʈ Ϫ ʈ Ϫ ••• ϩ Ϫ ••• ϩ a2 ( ) c2 3/2 j x j y ( ) x,( ) y 0.866 0.866 1.000 1.000 ͓ (1) ʈ Ќ ͔ ͱ ϩ ʈ ϩ Ϫ ʈ Ϫ Ϫ ••• ϩ Ϫ ••• ϩ Im a1 ( , ) c1 1/2͗ j y͘ ( ) y,( ) y 0.500 0.500 0.577 0.577 a ϭ ϩ Ϫ1/2 ϭ ϩ Ϫ1 c1 ͓ j( j 1)͔ , c2 ͓ j( j 1)͔ .

XϪZ XϪZ files that are sensitive to product atom alignment are calcu- obtain left IL and right IR TOF profiles respectively. Z ϭ ZϪ Z X ϭ XϪ X lated as Ianiso IZ IX and Ianiso IZ IX . In the orientation Orientation-sensitive and velocity-sensitive composite TOF XϪZϭ XϪZϪ XϪZ XϪZϭ XϪZ experiments, the photolysis radiation was polarized at 45° profiles are defined as Ianiso IL IR and Iiso IL Ϫ ϩ XϪZ 13–16 with respect to the TOF axis, along the (X Z) direction. IR respectively. The probe radiation was switched between left and right cir- Following Rakitzis and Zare,10 we write the relative cular polarization on a shot-by-shot basis with the PEM to ͑2ϩ1͒ REMPI intensity I as

͓⌰ ⌽ ␪ ␤ k͑ ͔͒ϭ ϩ␤ ͑ ␪ ͒ϩ ͑ ͒ ␪ ␪ ͓ (1)͑ʈ Ќ͔͒ͱ ⌰ ⌽ϩ ͑ ͒ ͑ ⌰͓͒͑ ϩ␤͒ I , , ⑀ , ,aq p 1 P2 cos ⑀ s1 j sin ⑀cos ⑀ Im a1 , 2sin sin s2 j P2 cos 1

ϫ 2␪ (2)͑ʈ͒ϩ͑ Ϫ␤ ͒ 2␪ (2)͑Ќ͔͒ϩ ͑ ͒ ␪ ␪ ͓ (2)͑ʈ Ќ͔͒ͱ cos ⑀a0 1 /2 sin ⑀a0 s2 j sin ⑀cos ⑀ Re a1 , 3/2 ϫ ⌰ ⌽ϩ ͑ ͒͑ Ϫ␤ ͒ 2␪ (2)͑Ќ͒ͱ 2⌰ ⌽ ͑ ͒ sin2 cos s2 j 1 /2 sin ⑀a2 3/2 sin cos 2 . 5

(k) ⌰,⌽, and ␪⑀ describe the position of the probe and photoly- The molecule frame polarization parameters aq (p) are sis polarization vectors with respect to the TOF laboratory spherical tensor moments of j in the molecule frame,14 with frame, ␤ is the translational anisotropy parameter, and the z axis being the recoil velocity vector v, assuming that (k) aq (p) are molecule frame polarization parameters. It should the dissociation occurs in the limit of axial recoil. Equation be noted that we have multiplied by a factor of ͓1 ͑5͒ has been derived by rotating the molecule frame into the ϩ␤ ␪ ͑ ͒ ͑ ͒ (k) P2(cos ⑀)͔ that appeared in the denominator of Eq. 16 laboratory TOF frame. The aq (p) are identified by the ͑ ϩ ͒ in Ref. 10. The sk( j) are 2 1 REMPI polarization sensi- symmetry of the parent dipole transition moment (p), which 3 ʈ Ќ tivities for O( P j) atoms, and were calculated from the Ik( j) is parallel ( ) or perpendicular ( ) to the diatomic internu- geometrical factors derived by VG,9 using the conversion clear axis. The symmetry of the transition depends upon the projection of the angular momentum along the O2 bond axis, ͱ͑2kϩ1͒͑2 jϩ1͓͒ j͑ jϩ1͔͒k/2 ⍀ ͑ ͒ϭ ͑ ͒ ͑ ͒ . For parallel transitions, the change in the projection of sk j Ik j , 6 ⌬⍀ϭ c͑k͒͗ jʈJ(k)ʈ j͘ angular momentum is 0, and for perpendicular transitions ⌬⍀ϭϮ1. ϭ ϭͱ 13 (k) where c(1) 1, c(2) 6 are constants, and the reduced The interpretations of the aq (p) are summarized in ͗ ʈ (k)ʈ ͘ 14 (2) ʈ (2) Ќ matrix elements j J j have been listed elsewhere. Us- Table I. The a0 ( ) and a0 ( ) represent cylindrically- ϭͱ ϭϪͱ ing I2(1) 1/2 and I2(2) 7/10 from VG, we calculate symmetric alignment of j about v that arise from incoherent ϭ ϭϪ 17 s2(1) 1 and s2(2) 1. For REMPI by circularly polar- parallel and perpendicular excitations respectively. The pa- ͓ (2) ʈ Ќ ͔ ͓ (1) ʈ Ќ ͔ ized light, it is possible to obtain the sensitivity factor using rameters Re a1 ( , ) and Im a1 ( , ) arise from the the simplified expression of Mo and Suzuki,15 where the broken cylindrical symmetry of j about v resulting from co- SF Ik ( ji , j f ) of VG are equivalent to Pk of Mo and Suzuki. The herent superposition of parallel and perpendicular excita- calculated Pk can be combined with branching ratios to the tions. These coherent paramaters vanish in the limit of pure (2) Ќ excited state as described by VG, and converted to sk using parallel or perpendicular transitions. The a2 ( ) results Eq. ͑6͒ above. Orientation measurements were only carried from coherent superposition of perpendicular transitions. The ϭ ϭͱ (2) Ќ out for j 2, for which we calculate s1(2) 8/3. A prime a2 ( ) may occur as a result of simultaneous excitation of advantage of measuring polarization of O atoms, is that no ͉⍀͉ϭ1 states with different energies, or as a result of the hyperfine depolarization occurs because O atoms have zero excitation of degenerate ⍀ϭϮ1 components of an ͉⍀͉ϭ1 nuclear spin. On the other hand, experiments that attempt to transition.17 It should be noted that relationships between (k) Ј measure angular distributions of O atoms may be signifi- aq (p) and the dynamical functions f k(q,q ) of Siebbeles cantly distorted if they do not explicitly account for the ef- et al.17 that appeared in Appendix A of Ref. 10 were incor- fects of polarization on the detection sensitivity.16 rect. Correct relationships between the molecule frame pa-

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3 3 FIG. 1. Isotropic and anisotropic TOF profiles of O( P2) products at pho- FIG. 3. Isotropic and anisotropic TOF profiles of O( P1) products at pho- ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z tolysis wavelength 222 nm: a Iiso , b Iiso , c Ianiso , d Ianiso . Experi- tolysis wavelength 222 nm: a Iiso , b Iiso , c Ianiso , d Ianiso . Experi- mental data are shown as dashed lines, fitted data are solid lines. mental data are shown as dashed lines, fitted data are solid lines.

III. RESULTS (k) ␣ rameters aq (p), the k polarization parameters of Vasyutin- A. Branching ratios skii and co-workers,18 and the dynamical functions of Siebbeles et al.17 have been tabulated by Alexander.19 At the fixed photolysis wavelength 226 nm, we mea- 3 As has been described in detail elsewhere,10 a set of sured the total ion intensity for O( P j) atom REMPI for j F F ϭ0,1,2. The ion signals were corrected for variations in isotropic and anisotropic basis profiles Biso and Baniso were simulated by Monte Carlo sampling of Eq. ͑5͒. The ␤ probe laser energy. We found the relative branching ratio to ϭ parameter was varied to produce BF that gave good fits be 1.00:2.90:8.65 for j 0:1:2. Our results are in good iso Ϯ Ϯ to the IF , agreement with the branching ratios 1.00 0.26:3.33 0.43: iso 9.00Ϯ0.70 reported by Buijsse et al.3 Using branching populations and excitation factors in Tables II and III of VG,9 we F ϭ F F ͑ ͒ Iiso c Biso , 7 obtain a semiclassical estimate at 226 nm of 1.00:4.32:9.73, which agrees well with the experimental results. where cF is a weighting coefficient that was subsequently used to fit the anisotropic profiles: B. Alignment F ϭ Isotropic and anisotropic TOF profiles IG (F X,Z) are ͑ ͒ ͑ ͒ 3 IF ϭ ͚ a(k)͑p͒cFBF . ͑8͒ shown in Figs. 1 222 nm and 2 237 nm for O( P2) prod- aniso q aniso 3 k,q,p ucts, and Figs. 3 and 4 for O( P1). The resulting alignment parameters are given in Table II, and plotted in Fig. 5. The (2) ʈ ϭ For the alignment experiments, the FϭX and FϭZ profiles incoherent parameter a0 ( ) has opposite signs for j 1 ϭ (2) Ќ are fitted simultaneously, and the sum in Eq. ͑8͒ includes compared with j 2, and the same is true for a0 ( ). For a a(2)(ʈ), a(2)(Ќ), Re͓a(2)(ʈ,Ќ)͔, and a(2)(Ќ). For the orien- particular j at a given photolysis wavelength, we also find 0 0 1 2 (2) (2) (2) ϭ Ϫ ͓ (1) ʈ Ќ ͔ that a (ʈ) and a (Ќ) have opposite signs. The a (ʈ) tation experiments, F (X Z) and Im a1 ( , ) is the 0 0 0 only polarization parameter fitted by Eq. ͑8͒. does not appear to change, within uncertainties, from 222 nm (2) Ќ compared to 237 nm and the a0 ( ) appears to decrease at

3 3 FIG. 2. Isotropic and anisotropic TOF profiles of O( P2) products at pho- FIG. 4. Isotropic and anisotropic TOF profiles of O( P1) products at pho- ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z ͑ ͒ X ͑ ͒ Z tolysis wavelength 237 nm: a Iiso , b Iiso , c Ianiso , d Ianiso . Experi- tolysis wavelength 237 nm: a Iiso , b Iiso , c Ianiso , d Ianiso . Experi- mental data are shown as dashed lines, fitted data are solid lines. mental data are shown as dashed lines, fitted data are solid lines.

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␤ (2) 3 TABLE II. Experimental beta parameters ( ) and molecule frame alignment parameters aq (p) for O( P j) atoms at photolysis wavelengths 222 and 237 nm. (2) ͓ (2) ʈ Ќ ͔ (2) Ќ The calculated semiclassical a0 (p) from Table III are also shown here for convenience. The calculated Re a1 ( , ) and a2 ( ) were obtained using methods outlined in Sec. III C.

jϭ1 jϭ2 Parameter 222 nm 237 nm 222 nm 237 nm

␤ 0.51Ϯ0.10 0.25Ϯ0.15 0.55Ϯ0.10 0.50Ϯ0.10 (2) ʈ ϩ Ϯ ϩ Ϯ Ϫ Ϯ Ϫ Ϯ a0 ( ) 0.158 0.043 0.123 0.048 0.090 0.037 0.125 0.030 calculated ϩ0.055 Ϫ0.007 Ϫ0.060 Ϫ0.191 (2) Ќ Ϫ Ϯ Ϫ Ϯ ϩ Ϯ ϩ Ϯ a0 ( ) 0.223 0.071 0.052 0.057 0.081 0.066 0.015 0.050 calculated Ϫ0.131 Ϫ0.048 ϩ0.073 ϩ0.000 ͓ (2) ʈ Ќ ͔ Ϫ Ϯ ϩ Ϯ ϩ Ϯ Ϫ Ϯ Re a1 ( , ) 0.115 0.042 0.069 0.035 0.090 0.037 0.001 0.027 calculated Ϫ0.348 Ϫ0.036 (2) Ќ ϩ Ϯ ϩ Ϯ Ϫ Ϯ Ϫ Ϯ a2 ( ) 0.019 0.035 0.061 0.023 0.094 0.033 0.009 0.021 calculated Ϫ0.086 Ϫ0.049

longer wavelengths for both j, most signiﬁcantly for jϭ1. ͑2 jϪ1͒͑2 jϩ1͒͑2 jϩ3͒ 1/2 (2) Ќ ϭ a(2)ϭͫ ͬ ␳(2) . ͑9͒ The coherent parameter a2 ( ) is positive for j 1 and 0 5 j͑ jϩ1͒ 0 negative for jϭ2, at both wavelengths.20 Currently there have been no theoretical estimates of the The semiclassical calculations of VG were obtained at ener- effects of coherence on the atomic alignment for dissociation gies equivalent to photolysis wavelengths 204, 216, 226, 21 236, and 240 nm and our experimental results were obtained of O2 . Balint–Kurti et al. have recently reported an ab initio study of the dissociation of HF, in which they used a at 221.667 and 237.049 nm. We have made linear interpola- time-dependent wave packet approach to obtain the photo- tions of the results of VG in order to compare with our ex- ␳(2)͑ ͒ fragmentation matrix, T. The T matrix elements contain the perimental data: these were calculated as 0 222 nm ϭ0.5667ϫ␳(2) ͑226 nm)ϩ0.4333ϫ␳(2)(216 nm͒, and phase and amplitude information that is required for calcula- 0 0 ␳(2)(237 nm)ϭ 0.7377ϫ␳(2)(236 nm)ϩ0.2623ϫ␳(2)(240 tion of the coherent polarization parameters Re͓a(2)(ʈ,Ќ)͔ 0 0 0 1 nm͒. The resulting ␳(2) were converted to a(2) , using Eq. ͑9͒, and a(2)(Ќ), and a similar study for the O system would 0 0 2 2 and are given in Table III. Also shown in Table III are inter- allow a detailed comparison with our experimental results. polated semiclassical excitation branching ratios to each of We have, however, made approximate semiclassical calcula- the Herzberg states, and their respective ␤ parameters. ϭ ϩ tions of these coherent alignment moments for j 2 atoms, From Table III we see that dissociation via A 3⌺ has ͑ ͒ ͑ ͒ u,Ϯ1 using Eqs. 12 – 14 as outlined in Sec. III C. We found a both parallel and perpendicular contributions. For example, large discrepancy between the experimental and semiclassi- if ␤ϭ1.219 we determine that (␤ϩ1)/3ϭ0.740 is the par- ͓ (2) ʈ Ќ ͔ ϩ cal Re a1 ( , ) at 222 nm. Overall, however, the agree- 3⌺ allel branching fraction of the A u,Ϯ1 state dissociation at ment between the semiclassical and experimental coherent 222 nm. The total parallel branching fraction for O2 disso- alignment parameters is good. ciation at 222 nm is 0.735ϫ0.740ϭ0.544. From Table III, The molecule frame alignment tensor moments ␳(2) cal- (2) ϭ ϭϪ 3⌺ϩ 0 a0 ( j 2) 0.111 for the A u,Ϯ1 state at 222 nm. We culated by VG ͑Ref. 9͒ can be related to the molecule frame calculate the total parallel contribution to alignment as (2) (2) alignment parameters a (ʈ) and a (Ќ) of Rakitzis et al.,10 (2) ʈ ϭϪ ϫ ϭϪ 0 0 a0 ( ) 0.111 0.544 0.060. The last two rows in Table III are the weighted sums of the contributions from parallel and perpendicular transitions, and the calculated (2) a0 (p) results are compared to the experimental results in (2) Table II. Comparing the experimental and calculated a0 (p) in Table II, we see good quantitative agreement overall, within experimental uncertainties. There appears to be greater discrepancy between experimental and calculated re- (2) ʈ ϭ sults for a0 ( ), particularly for j 1 atoms. The dissociation of O2 via the Herzberg continuum ap- proaches the threshold for the O(3P)ϩO(3P) dissociation limit, and we must consider the potential effects of nonaxial 3⌺Ϫ recoil. In the X g electronic state there are only odd rotational J states, with the lowest populated level being Jϭ1. The estimated rotational temperature of our expansion is 15 K, and we calculate fractional Boltzmann populations as ϭ FIG. 5. Molecule frame alignment parameters a(2)(p) for O(3P ) atoms at 0.787, 0.197, and 0.016 for J 1, 3, and 5, respectively. The q j 0 ϭ Ϫ1 222 nm ͑squares͒ and 237 nm ͑circles͒. Solid symbols are jϭ2 atoms, open dissociation energy of O2 is D0(O2) 41268.6 cm . As- ϭ ϭ symbols are j 1 atoms. suming dissociation from O2(J 1) to give two ground state

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␤ TABLE III. Herzberg excitation branching ratios pn⍀ and state-speciﬁc anisotropy parameters n⍀ for different molecular eigenstates, calculated from Table ͑ ͒ (2) ϭ II of VG Ref. 9 . Semiclassical alignment parameters a0 ( j 1,2) were calculated by interpolation from the results of VG, see text for details.

␤ (2) ϭ (2) ϭ State pn⍀ n⍀ a0 ( j 1) a0 ( j 2) 222 nm 237 nm 222 nm 237 nm 222 nm 237 nm 222 nm 237 nm 3⌺ϩ Ϫ Ϫ Ϫ A u,1 0.735 0.727 1.219 1.253 0.102 0.012 0.111 0.350 3⌺ϩ Ϫ Ϫ Ϫ Ϫ A u,0 0.191 0.181 1 1 0.648 0.154 0.378 0.235 1⌺Ϫ Ϫ Ϫ c u,0Ϫ 0.021 0.027 1 1 0.174 0.254 0.435 0.271 3⌬ Ϫ Ϫ Ϫ Ϫ Ϫ Ϫ AЈ u,1 0.021 0.026 1 1 0.244 0.254 0.492 0.278 3⌬ Ϫ Ϫ Ϫ Ϫ AЈ u,2 0.031 0.039 1 1 0.824 0.482 0.720 0.531 3⌬ Ϫ Ϫ AЈ u,3 0.001 0.001 1 1 0.500 0.500 0.436 0.377 total ͉͉ 0.544 0.546 ϩ2 ϩ2 0.055 Ϫ0.007 Ϫ0.060 Ϫ0.191 total Ќ 0.456 0.454 Ϫ1 Ϫ1 Ϫ0.131 Ϫ0.048 0.073 0.000

3 O( P2) atoms, we estimate the final center-of-mass velocity lenging to obtain correlated experimental data. It is possible, of O atoms to be 1681 m sϪ1 at 222 nm and 832 m sϪ1 at however, that the effects of the implicit averaging could be 237 nm. Following Wrede et al.20 we calculated the total assessed in future calculations. (2) quasiclassical angle of rotation ␥ that accumulates during the In summary, the semiclassical a0 of VG agree well with dissociation, i.e., ␥ is the angle between the asymptotic ve- our experimental results. We expect that a fully quantum locity vector of the O atoms and the position of the internu- model of the Herzberg excitation and dissociation, which ϭ clear axis at the time of excitation. For O2(J 1) we find could include calculation of the coherent alignment param- ␥ϭ ␥ϭ that 1.4° at 222 nm and 2.5° at 237 nm, and for O2 eters, would improve the agreement between theory and (Jϭ3) ␥ϭ3.5° at 222 nm and ␥ϭ6.2° at 237 nm. The experiment.22 effect of these deviations from axial recoil are small: for ␥ ϭ6.2° ␤ would be degraded to only 0.98 of its axial value.20 A further complication in our experiment is that we are C. Orientation Ϫ unable to determine the correlated alignment between jA and X Z Typical isotropic and anisotropic TOF profiles IG at jB for the two atoms, so there is an implicit averaging over photolysis wavelength 223.543 nm are shown in Fig. 6. The ϭ ϳ the co-fragment with j 0,1,2. The energy separation 100 resulting Im͓a(1)(ʈ,Ќ)͔ obtained from measurements over a Ϫ1 3 1 cm between j levels of O( P) would make it very chal- range of photolysis wavelengths 218.521–238.556 nm are shown in Fig. 7, and tabulated in Table IV. The ͓ (1) ʈ Ќ ͔ Im a1 ( , ) parameter represents orientation along the molecule-frame y axis resulting from interference between states of parallel and perpendicular symmetry.10 The ͓ (1) ʈ Ќ ͔ Im a1 ( , ) contains both amplitude and phase information. For the simple case of interference between two states ͑one parallel, one perpendicular͒ we can write

͓ (1)͑ʈ Ќ͔͒ϰ ⌬␾ ͑ ͒ Im a1 , sin , 10

where sin(⌬␾)ϭsin(␾ЌϪ␾ʈ) is the sine of the asymptotic phase difference between the radial parts of the dissociative wave functions for the perpendicular and parallel states. The photodissociation of O2 involves more than one pair of interfering electronic states. A fully quantum mechanical simulation of the dissociation is outside the scope of the present study. However, as a base to compare with our experimental results, we have calculated the energy dependence of the semiclassical phase difference using the O2 potential energy curves of VG.8 ͓ (1) ʈ Ќ ͔ We begin by writing the Im a1 ( , ) in terms of the 17 dynamical functions f k(q,qЈ) of Siebbeles et al.

͒ 6Im͓ f 1͑1,0 ͔ Im͓a(1)͑ʈ,Ќ͔͒ϭϪ . ͑11͒ 1 ͱ ͓ ͑ ͒ϩ ͑ ͔͒ 3 2 f 0 0,0 2 f 0 1,1 FIG. 6. Isotropic and anisotropic TOF proﬁles of O( P2) products at pho- ͑ ͒ XϪZ ͑ ͒ XϪZ tolysis wavelength 223.543 nm: a Iiso , b Ianiso . Experimental data are shown as dashed lines, ﬁtted data are solid lines. The dynamical functions can be written as21

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TABLE IV. Experimental molecule frame orientation parameters ͓ (1) ʈ Ќ ͔ 3 Im a1 ( , ) for O( P2) atoms.

͑ ͒ ͓ (1) ʈ Ќ ͔ Wavelength nm Im a1 ( , ) 218.521 0.020 221.667 0.034Ϯ0.002 222.293 0.030 222.918 0.033 223.543 0.049 224.789 0.048 225.566 0.052Ϯ0.007 226.031 0.071 226.341 0.076 227.888 0.060 ͓ (1) ʈ Ќ ͔ 3 FIG. 7. Molecule frame orientation parameter Im a1 ( , ) for O( P2) 238.556 0.041Ϯ0.011 atoms vs photolysis wavelength. Circles are experimental points. The solid line is the semiclassical simulation obtained using potential energy curves of VG ͓see Eq. ͑15͒͑Ref. 8͔͒. The dashed line incorporates a reduction in the term involving the c0 state. See text for details. ϭ ϫ ϩ␤ parallel component pA1ʈ pA1 (1 )/3 of the branching fraction to A1 has been used. Taking the positive root we ϩ ϩ⍀Ј ␲ ͒ϭ Ϫ ͒k jA A have introduced a factor of uncertainty in the phase for f k͑q,qЈ ͚ ͑ 1 ⍀ ⍀ ⍀ ⍀Ј n, , A ,nЈ, Ј, each pair of interfering states in f 1(1,0). A ␾ ϵ ⍀ The total semiclassical phase n for state n n was j j k ϫͩ A A ͪ found by numerical integration using the adiabatic Hund’s Ϫ⍀ ⍀Ј Ϫ Ј case ͑c͒ potential energy curves of VG with the expression23 A A q q ϫT n⍀ ͑T nЈ⍀Ј ͒ ␲ ϱ j ⍀ j ⍀ j ⍀Ј j ⍀ * ␾ ϭ ϩ ͵ ͓ ͑ ͒Ϫ ͑ϱ͔͒ Ϫ ͑ϱ͒ ͑ ͒ A A B B A A B B n kn R kn dR kn Tn , 13 4 Tn Ϫ ␾ ␾ ϫ i n⍀ i nЈ⍀Ј ͑ ͒ rn*⍀rnЈ⍀Јe e , 12 where R is the O2 bond length, Tn is the classical inner where we have combined Eqs. ͑6͒ and ͑13͒ of Ref. 21. The turning point for state n at a given available energy E. The dissociation gives two fragments with angular momenta j ϭ ␯Ϫ 0 ␯ A available energy E h D0(O2), where h is the energy of and j , having projections ⍀ and ⍀ on the molecule B A B the photolysis photon. The de Broglie wave number kn(R)is frame z axis. The indices n⍀ label the excited state with ⍀ ϭ⍀ ϩ⍀ . To be brief, we shall refer to the six Herzberg 1 A B ͑ ͒ϭ ͱ ␮͕ Ϫ ͑ ͖͒ ͑ ͒ states of Table III as A1, A0, c0, AЈ1, AЈ2, and AЈ3. As kn R ប 2 E En R , 14 ⍀ explained by Balint–Kurti et al., summation over B is im- ͑ ͒ Ϫ Јϭ⍀ Ϫ⍀Јϭ⍀ ␮ plicitly included in Eq. 12 , and q q A A where is the reduced mass of O2 , and En(R) is the poten- n⍀ Ϫ⍀Ј. The coefficients T ⍀ ⍀ are expansion coefficients tial energy of state n. The centrifugal potential due to rotation jA A jB B of the molecular electronic states in the product atomic basis of the dissociating O2 was found to be insignificant in our ͑ ͒ ͉j ⍀ ͉͘j ⍀ ͘, which can be calculated by diagonalizing the calculations and has not been included in Eq. 14 . The case A A B B ͑ ͒ long-range quadrupole–quadrupole potential interaction ma- c potentials were obtained by diagonalization of the matrix T n⍀ ˆ ϭ ˆ ϩ ˆ trix in the atomic basis. ⍀ ⍀ coefficients for O2 have elements of the Hamiltonian H HCoul HSO in the basis of jA A jB B ⍀ϭ been given in Table I of VG.9 the electronic states for 0, 1, 2, and 3, respectively, as a The dynamical function f (1,0) represents a sum over function of the internuclear separation, R. The eigenvalues of 1 ˆ (ʈ,Ќ) pairs of interfering states. No interference occurs be- the Coulombic Hamiltonian HCoul correspond to the elec- tween dissociation paths that start with different values of the tronic adiabatic Born–Oppenheimer ͑ABO͒ states, and the ⍀ ˆ ground state i . Since the only parallel transition involved matrix elements of HSO are the spin–orbit couplings between is from ground state X1→A1 ͓see Eq. ͑2͔͒, the only perpen- ABO states.24 → ͑ ͒ ͑ ͒ ͓ (1) ʈ Ќ ͔ dicular transitions to be considered in f 1(1,0) are X1 A0, Equations 11 – 14 show how Im a1 ( , ) is related c0, and AЈ2. to the potential energy curves En(R) through the phase ac- ␾ ͑ ͒ The coefficients rn⍀ and n⍀ in Eq. 12 are amplitudes cumulated during dissociation at a given available energy E. and phases of the photofragment T matrix. For their work on When the available energy is much larger than the potential HF photodissociation,21 Balint–Kurti et al. calculated the T energy difference between parallel and perpendicular curves, matrix from time-dependent wave-packet dynamical calcula- the phase difference ⌬␾ does not vary much, and the ͓ (1) ʈ Ќ ͔ tions. In the present case, we approximate by using the semi- Im a1 ( , ) will change very slowly as a function of the classical results of VG to obtain amplitudes as the ͑positive͒ photolysis energy. Nearer to threshold, however, ⌬␾ varies root of the branching ratios in Table III. For parallel transi- more rapidly with E, and measurement of the energy depen- ϭ 1/2 ͓ (1) ʈ Ќ ͔ tions rn⍀ (pn⍀) , and for perpendicular transitions rn⍀ dence of Im a1 ( , ) can be a very sensitive test of the ϭ 1/2 25 (pn⍀/2) . The branching ratios pn⍀ depend on the pho- shapes of the potential energy curves. For the present case, tolysis wavelength, and are given in Table II of Ref. 9. The we calculate

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͓ (1)͑ʈ Ќ͔͒ϭ ͑⌬␾ ͒ dicular states. Semiclassical calculations of the energy- Im a1 , f A0rA0rA1ʈ sin A0 dependent orientation were made using Hund’s case ͑c͒ potential energy curves of VG, and were shown to give good ϩ f r r ʈ sin͑⌬␾ ͒ c0 c0 A1 c0 agreement with the experimental results. The photodissociation of O via the Herzberg continuum ϩ ͑⌬␾ ͒ ͑ ͒ 2 f AЈ2rAЈ2rA1ʈ sin AЈ2 , 15 reveals a surprisingly rich photochemistry involving motions ⌬␾ ϵ ␾ Ϫ␾ on—and interactions between—more than one electronic po- where sin( n⍀) sin( n⍀ A1) and the constants f A0 ϭϪ ϭϪ ϭϪ tential energy surface that correlates to the separated open- 1.060, f c0 1.325, and f AЈ2 1.458. Recall that we have no knowledge about the sign of each term in Eq. ͑15͒. shell atomic photofragments. This work brings out the inad- equacy of the Born–Oppenheimer approximation in We have therefore chosen the coefficients f n⍀ to have the same sign, which qualitatively matches the experimental describing the dissociation of simple molecules when the data. The results of the semiclassical calculation of Eq. ͑15͒ dissociating state lies in the midst of other excited states of are shown as the solid line in Fig. 7. Even with uncertainty in different symmetry. The Herzberg continuum serves as a fun- the relative signs of the three terms in Eq. ͑15͒, the magni- damental example of nonadiabatic photodissociation. As fur- ͓ (1) ʈ Ќ ͔ ther theoretical studies are carried out, we hope that our ex- tude of the calculated Im a1 ( , ) is remarkably close to the experimental points. There are pronounced ripples in the perimental results will provide additional tests for our orientation: the frequency of the ripples increase at longer understanding of this important atmospheric process. wavelength, as the available energy decreases on approach to the threshold. At wavelengths around 225 nm, the magnitude of oscillation in the calculated orientation is larger than ex- perimentally observed. The oscillations in this energy region are mostly due to the interference component involving the ACKNOWLEDGMENTS c0 state. By fitting the experimental data using a nonlinear least-squares algorithm, we investigated the effect of reduc- The authors thank Mirjam van Vroonhoven and Gerrit ing the contribution from the c0 state. We find that the ex- Groenenboom for helpful discussions about their work, and perimental results are more closely followed if the contribu- Fe´lix Fernańdez-Alonso for useful discussions about oxygen tion from the c0 state is reduced by multiplying the second atom REMPI. Z.H.K. gratefully acknowledges receipt of a term in Eq. ͑15͒ by a constant factor of 0.15. The resulting Dr. Franklin Veatch Memorial Fellowship. This work was orientation is shown as the dashed curve in Fig. 7. The re- funded by the National Science Foundation under Grant No. duction factor is equivalent to reducing the branching frac- CHE-99-00305. ϫ Ϫ4 tion pc0 in Table III at 222 nm from 0.021 to 4.5 10 . This is a sizable reduction, and it is very doubtful that this is the sole source of discrepancy between the experiment and our semiclassical calculations. Unfortunately, the maximum 1 D. H. Parker, Acc. Chem. Res. 33, 563 ͑2000͒. 2 observed in the calculated results at around 230 nm can only W. B. DeMore, S. P. Sander, D. M. Golden, R. F. Hampson, M. J. Kurylo, C. J. Howard, A. R. Ravishankara, C. E. Kolb, and M. Molina, JPL Pub- be inferred in our experimental data as it covers a region that lication 97-4, 1997. was difficult to access with our photolysis nonlinear mixing 3 B. Buijsse, W. J. van der Zande, A. T. J. B. Eppink, D. H. Parker, B. R. setup. Despite the simplicity of our semiclassical calcula- Lewis, and S. T. Gibson, J. Chem. Phys. 108, 7229 ͑1998͒. 4 ͑ ͒ tions, the results show reasonable agreement with the experi- R. N. Zare and D. R. Herschbach, Proc. IEEE 51, 173 1963 . 5 Y. Matsumi and M. Kawasaki, J. Chem. Phys. 93, 2481 ͑1990͒. mental results. 6 Y. -L. Huang and R. J. Gordon, J. Chem. Phys. 94, 2640 ͑1991͒. 7 K. Tonokura, N. Shafer, Y. Matsumi, and M. Kawasaki, J. Chem. Phys. 95, 3394 ͑1991͒. 8 M. C. G. N. van Vroonhoven and G. C. Groenenboom, J. Chem. Phys. IV. CONCLUSIONS 116, 1954 ͑2002͒. 9 M. C. G. N. van Vroonhoven and G. C. Groenenboom, J. Chem. Phys. 3 116, 1965 ͑2002͒. We have made a detailed study of the O( P j) atom 10 T. P. Rakitzis and R. N. Zare, J. Chem. Phys. 110, 3341 ͑1999͒. alignment and orientation following photodissociation of O2 11 T. P. Rakitzis, S. A. Kandel, A. J. Alexander, Z. H. Kim, and R. N. Zare, in the Herzberg continuum in the region 218–239 nm. The J. Chem. Phys. 110, 3351 ͑1999͒. polarization parameter formalism used has allowed us to de- 12 W. R. Simpson, A. J. Orr-Ewing, S. A. Kandel, T. P. Rakitzis, and R. N. termine alignment contributions from parallel or perpendicu- Zare, J. Chem. Phys. 103, 7299 ͑1995͒. 13 A. J. Orr-Ewing and R. N. Zare, Annu. Rev. Phys. Chem. 45,315͑1994͒. lar transitions, and alignment resulting from coherence be- 14 R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Phys- tween excited dissociative states. Experimental alignment ics and Chemistry ͑Wiley, New York, 1988͒. parameters were found to be in reasonably good agreement 15 Y. Mo and T. Suzuki, J. Chem. 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J. Chem. Phys. 116,6064͑2002͒. 23 Y. Asano and S. Yabushita, J. Phys. Chem. A 105, 9873 ͑2001͒. 21 G. G. Balint–Kurti, A. J. Orr-Ewing, J. A. Beswick, A. Brown, and O. S. 24 M. C. G. N. van Vroonhoven and G. C. Groenenboom, J. Chem. Phys. Vasyutinskii, J. Chem. Phys. 116, 10760 ͑2002͒. 117, 5240 ͑2002͒. 22 M. C. G. N. van Vroonhoven and G. C. Groenenboom ͑personal commu- 25 T. P. Rakitzis, S. A. Kandel, A. J. Alexander, Z. H. Kim, and R. N. Zare, nications͒. Science ͑Washington, D.C., U.S.͒ 281, 1346 ͑1998͒.

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