8007
J , Phys, Chem. 1991, 95, 8007-8013
Rotatlonal Alignment of the CD3 Fragment from the 266-nm Photodlssoclatlon of Cb,It Maurice H. M. Janssen, David H. Parker, Molecular and taser Physics, Department of Physics, Catholic University of Nijmegen, Toernmiveld, 6525 ED, Nijmegen, The Netherlands
Greg 0. Sitz, Physics Department, the University of Texas at Austin, Austin, Texas 78712
Steven Stolte, Laser Centre, Free University Amsterdam, De Boelelaan 1083, 1081 H V Amsterdam, The Netherlands
and David W . Chandler* Combustion Research Facility, Sandia National Laboratories, Livermore, California 94550 (Received: December 21, 1990)
The alignment of CD3 fragments created by photodissociation of CD31with linearly polarized 266-nm light is characterized by using the ion imaging technique. A linearly polarized probe laser is used for (2 1) resonance.-enhancedmultiphoton ionization (REMPI) of the methyl fragment. The three-dimensional velocity distribution of the state-selected CD3 ion is subsequently "crushed" onto a two-dimensional detector. Each position in the two-dimensional image corresponds to a different methyl fragment velocity, v. By measuring the dependence.of the REMPI signal on the angle between the probe laser polarization and ihe photolysis laser polarization for specific parts of the image, the population n(N,K) and the alignment moments Ah2) and 4')of the angular momentum distribution of recoiling CD3fragments are obtained with respect to v. These velocity-selective alignment moments describe the 0.N correlation. The alignment moments extracted for single rotational levels (N,K)indicate that the rotational excitation produced in the photodissociation is about an axis perpendicular to the I-(CD3) axis and that the initial rotation about the C3axis of the parent is conserved in the methyl fragment. The alignment moments of the fragments recoiling along the direction of the photolysis transition dipole approach the maximum values expected for a purely axial recoil process, Le., for a methyl fragment in the N,K rotational state, (NKMN)= (NKK).
+
Introduction In recent years, experiments have begun to reveal extensive and intimate information on photodissociation processes. Particularly interesting are measurements of the energetic and directional correlations between the many quantities involved in the event, such as the transition dipole moment, recoil velocity, electronic and rovibrational channel branching, and angular momentum alignment. l-3 Methyl iodide has been the subject of many experimentaleIs and theoreticallbM studies of photodissociation for several reasons. From a theoretical point of view, methyl iodide has attracted much attention because although it is a "largen molecule (five atoms) and therefore not seemingly well-suited for detailed quantum dynamical modeling, photodissociation in the A band around 260 nm involves a parallel transition and thus preserves the C3symmetry axis. This restricts the number of possible vibrational modes excited in the methyl fragment to just two, the symmetric stretch, w I , and the umbrella mode, w2. Furthermore, the dissociation is highly axial, i.e., very fast and directed along the symmetry axis, so very little rotational excitation is expected. For these reasons the basic photodynamics have been modeled successfully with a two-parameter potential considering methyl iodide as a linear psuedotriatomic moIecule.16 Early mea~urements6~ inferred final-state distributions of the methyl fragment from deconvoluted time-of-flight mass spectra of fragments ionized by non-state-selective electron impact. Detailed information on methyl rotational excitation was not available, and even the problem of distinguishing u2 from vI excitation, following dissociation a t 193 nm, turned out to be challenging.6*21 Resonance-enhanced multiphoton ionization (REMPI) has been proven to be a sensitive technique for stateselective detection of polyatomic photofragments." REMPI offers the additional advantage in that information about vectorial 'Research supported by the U S . Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences.
0022-365419 112095-8007$02.50/0
correlations in the fragmentation can be obtained by exploiting the polarization of the detection laser beam.1.2.23*24 (1) (2) (3) (4) (5)
Simons, J. P. J . Phys. Chem. 1987, 91, 5378. Houston, P. L.J. Phys. Chem. 1987, 91, 5388. Hall, G. E.; Houston, P. L. Annu. Reu. Phys. Chem. 1989, 40, 375. hley, S.J.; Wilson, K. R. Faraday Dfscuss. Chem. Soc. 1972,53,132. Sparks, R. K.; Shobatake, K.; Carlson, L. R.; Lee, Y . T.J. Chem.
Phys. 1981, 75, 3838. (6) van Veen, G. N. A.; Mohammed, K. A.; Baller, T.; de Vries, A. E. Chem. Phys. 1983, 74,261. van Vctn, G. N. A.; Ballcr, T.; de Vries, A. E.; van Veen, N. J. A. Chem. Phys. 1984,87,405. (7) Barry, M. D.; Gorry, P. A. Mol. Phys. 1984, 52, 461. (8) Leone, S. R. Adu. Chem. Phys. 1982,50, 255. Has, W. P.; Kohler, S.J.; Haugen, H. K.; Leone, S.R. J . Chem. Phys. 1986,84, 2143. (9) Loo,R. 0.;Hall, G. E.; Haerri, H.-P.; Houston, P. L.J. Phys. Chem. 1988,92,5. Loo,R. 0.; Haerri, H.-P.; Hall, G. E.; Houston, P. L. J. Chem. Phys. 1989,90,4222. Loo,R. 0.;Straw, C. E.; Haerri, H.-P.; Hall, G. E.; Houston, P. L.; Burak, I.; Hepburn, J. W. J . Chem. Soc.,Faraday Trans. 2 1989, 85, 1185.
(IO) Black, J. F. Ph.D. Thesis, University of Nottingham, 1987. Black, J. F.; Powis, I. J. Chem. Phys. 1988,89, 3986. Black, J. F.; Powis, I. Chem. Phys. 1988, 125, 315. (11) Powis, I.; Black, J. F. J . Phys. Chem. 1989, 93, 2461. (12) Chandler. D. W.: Houston. P. L. J. Chem. Phvs. 1987. 87. 1445. (13) Chandler,'D. W.;Thoman, J. W., Jr.; Janssen, hi. H. M.{Pa;ker, D. H. Chem. Phys. Len. 1989,156, 151. (14) Chandler, D. W.; Janssen, M. H. M.; Stolte, S.;Strickland, R. N.; Thoman, J. W., Jr.; Parker, D. H. J. Phys. Chem. 1990, 91, 4839. (15) Chandler, D. W.; Thoman, J. W., Jr.; Sit& G. 0.;Janssen, M. H. M.; Stolte, S.;Parker, D. H. J. Chem. Soc., Faraday Trans. 2 1989,85, 1305. (16) Shapiro, M.; Bersohn, R. J . Chem. Phys. 1980, 73,3810. Kanfer, S.; Shapiro, M. J . Phys. Chem. 1984,88,3964. Shapiro, M. J . Phys. Chem. 1986, 90, 644. (17) Lee, S.-Y.; Heller, E. J. J . Chem. Phys. 1982, 76, 3035. (18) Gray, S.K.; Child, M. S.Mol. Phys. 1984, 51, 189. (19) Yabushita, S.;Morokuma, K. Chem. Phys. Lerr. 1989, 153, 517. (20) Swaminathan, P. K.; Stodden, C. D.; Micha, D. A. J. Chcm. Phys. 1989, 90, 5501. (21) Contenetti, B.; Balko, B. A.; Lee, Y. T. 1. Chem. Phys. 1988, 89, 3383. (22) Parker, D. H. In Lllrrasenrltlue Lmer Spectroscopy;Academic Reas: New York, 1983; Chapter 4.
0 1991 American Chemical Society
8008 The Journal of Physical Chemistry, Vol. 95, No. 21, I991
Mrrlr
I\
EnrworPlae
I\
I\
Figure 1. Schematic of apparatus used to perform the velocity selected REMPI study of the polarization dependence of the CD, ion intensity following CDJ photolysis.
In this study the alignment of the methyl fragment rotational angular momentum distribution is measured by using the recently developed REMPI-based two-dimensional imaging technique.Ivs Methyl iodide is photodissociated by 266-nm linearly polarized light and the methyl fragment is state-selectively ionized by (2 1) REMPI shortly after the dissociation via the intermediate 3p, (2A”2)Rydberg ~ t a t e ~ ~byJ ’a tunable linearly polarized probe laser. The three-dimensional spatial distribution of the fragments is subsequently “crushed” onto a two-dimensional detector. The photolysis laser polarization is set parallel to the normal of the detector plane, along the direction of the molecular beam. In this configuration the image is a nearly uniform intensity circle. Velocity-selected polarization measurements are performed by only detecting light from the center portion of the two-dimensional image while the polarization axis of the ionization laser is rotated with respect to the photolysis laser’s polarization axis. Analysis of the ion intensity as a function of angle allows the extraction of the alignment moments, Ah2) and Ah4), of the cylindrically symmetric angular momentum d i s t r i b u t i ~ n . ’ ~ * ~ * * ~ ~ Multiphoton ionization has been used recently in determining the alignment of molecules scattered and desorbed from surf a c e ~and ~ ~CD3 * ~ fragments ~ from photodissociation of CD3I.I1 Sitz et a1.29measured the alignment and orientation of the angular momentum distribution of N2 scattered from Ag[ 1111 using (2 2) REMPI and observed an increasing alignment of J perpendicular to the surface normal with increasing rotational level J, for high J levels. Jacobs et al.30 used (1 + 1) REMPI to investigate the alignment of NO inelastically scattered and trapped/desorbed from Pt( 1 11). Winniczek et al.31used the same 1 + 1 scheme on NO to investigate the dissociation dynamics of CH30N0. To obtain information on the NO similar to that which we obtain here for the CD3, they velocity-selected the NO fragments and angularly resolved the cations formed. Powis and Black1’measured the alignment of CD3 fragments using 2 + 1 REMPI via the 4P, Rydberg state following the 266-nm photodissociation of CD31. An “overall alignment
+
+
(23) See the discussions of the Faraday Symposium 24, in: J. Chem.Soc., Faraday Trans. 2 1989,85. (24) Hall, G. E.; Sivakumar, N.; Houston, P. L. J. Chem. Phys. 1986,84, 2120. (25) Thoman, J. W., Jr.; Chandler, D. W.; Parker, D. H.; Janssen, M. H. M. Laser Chem. 1988, 9, 27. (26) Hudgens, J. W.; Di Guiseppe, T. G.; Lin, M. C. J. Chem. Phys. 1983, 79, 571. (27) Parker, D. H.; Wang, Z. W.; Janssen, M. H. M.; Chandler, D. W. J. Chem. Phys. 1989, 90, 60. Zare, R. N. J . Chem. Phys. 1986,85, (28) Kumme!, A. C.; Sitz, G. 0.; 6874. (29) Sitz,G. 0.; Kummel, A. C.; Zare, R. N. J. Vac.Sci. TechnoZ.A 1987, 5, 513. (30) Jacobs, D. C.; Kolasinski, K. W.; Madix, R. J.; Zare, R. N. J. Chem. Phys. 1987, 87, 5038; J . Chem. Soc., Faraday Trans. 2 1989, 85, 1325. (31) Winniczek, J. W.; Dubs, R. L.; Appling, J. R.; McKoy, V.; White, M.G . J . Chem. Phys. 1989,90,949.
Janssen et al. moment” Ah2)= 0.5 f 0.2 was reported for methyl fragments from the dissociation of CD31 in a relatively warm (300 K) effusive beam. A positive alignment moment was interpreted as indicating preferred spinning rotation of the (rotationally warm) CD3 fragment around the C3 axis. In this paper alignment measurements of individual N,K states of the CD3 fragments following the 266-nm dissociation of cold CD31molecules in a pulsed molecular beam are reported. We have reported our measurement of the rotational populations and iodine electronic branching ratios 1(2P3/2)/1(2P1/2) previously.131s
Experimental Section The experimental setup used has been described in detai112J3*25 and is shown schematically in Figure 1. A pulsed molecular beam of CD31seeded in He is skimmed and directed through a repeller plate toward the center of a position-sensitive ion detector. A quadrupled Nd:YAG laser beam of 266 nm (-2 mJ/pulse) photons with its polarization axis aligned parallel to the molecular beam (horizontal polarization) is mildly focused on the molecular beam with a 50-cm focal-length lens. The polarization of the 266-nm light is set by a double Fresnel rhomb and filtered by a Glan-Thompson prism. About 10 ns after the photolysis pulse a tunable ( E 333 nm) counter propagating, linearly polarized laser beam (- 1 mJ/pulse) from a frequency-doubled dye laser, pumped by an injection-seeded single-mode Nd:YAG laser, is focused with a 20-cm focal-length lens into the photolysis zone. The tunable probe laser beam first passes a Glan-Thompson polarizer and subsequently a 1/2X wave plate mounted on an automated rotator stage before it is focused into the photolysis region. Both the probe and photolysis laser beam polarization are checked after they exit the vacuum chamber to ensure that birefringence in the windows on the apparatus is not scrambling the polarizations of the laser beams. Methyl fragments produced by the 266-nm dissociation laser are state-selectively ionized by (2 + 1) REMPI and the ions are accelerated collinearly to the molecular beam into a 40-mm-diameter, 80-mm-long time-of-flight mass spectrometer equipped with a dual-chevron microchannel plate/phosphor screen detector. A mask on the back side of the phosphor screen is used to pass light from only the central part of the image onto a photomultiplier. This part corresponds to methyl fragments travelling parallel to the polarization direction of the photolysis laser. The mask hole is approximately one-seventh size of the image and defines a cone with a full acceptance angle of about 15’. This size aperture gave the best compromise between signal level and spatial velocity selection. A photomultiplier tube is used to detect the light emitted from the phosphor, and a boxcar averager processes the output. Rotation of the probe laser polarization is controlled by a microcomputer which also stores the output from the boxcar averager. With the Crobe laser set at a certain rotational transition of the ~P,(*A”~) - X(2A”2) 000 band of CD3, the rotator makes steps of typically 3 or 5’. At every position of the rotator the ion signal is averaged for 50-100 shots. Data is taken for a full (360’) revolution of the rotator, which means that every set angle 8 between the polarization axis of the probe laser and the polarization axis of the photolysis laser is measured four times. Note that when the half-wave plate rotates over an angle 4, the polarization rotates over an angle 8 = 24. Because the probe laser is linearly polarized, the angles B and (T + 0 ) probe the same angular dependence. Simultaneously, with the signal at an angle 8 the 266-nm laser power and the probe laser power are stored by the microcomputer. After the polarization data are taken at one rotational line, the probe laser frequency is changed to another line and the same measuring procedure is started again. Velocity-selected (masked image) scans and velocity-integrated (no mask) scans are recorded. Sample data for the P(3) transition is shown in Figure 2. Owing to predissociation of the intermediate 3p, Rydberg state14 and to the cold temperature (- 15 K) of the parent beam which leads to cold CD3 fragments (N,,, C lo), K structure is not resolved for any of the N-specified 0, P, R, or S bands studied.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8009
CD, Fragment
Rotational Alignment of the
P(3) WITHOUT MASK 3400
rzi 2550 ". Y
1.
Simulated
Experimental
'
"
..
' *
#
f -.071
0 1
0
. %*a*
.
,
.a
3.
J
*:
1
I
I
100
200
300
ANGLE
e''
500
600
P(3) WITH MASK 3400
5
i
1700
850
0
29875
L 0
100
'oo*NyJE
io0
500
600
Figure 2. ( 2 + 1) REMPI signal on the P(3) transition of the 3pz-X 08 band of CD3versus the angle 0 between the polarization axis of the probe laser beam and the horizontal (parallel to the molecular beam axis) polarization of the photolysis laser beam, without a mask blocking the detector, thereby monitoring all velocity groups (top panel), and with a mask blocking the detector, thereby allowing only certain velocity fragments to be detected (lower panel). Rotator angles of Oo, 180°, 360°, and 540' correspond to parallel polarization of the dissociation and probe laser; at rotator angles of 90°, 2 2 5 O , and 315' the polarization axes of the two lasers are perpendicular to each other. A comparison of part of the angular scan of the P(3) transition with the calculated intensity is given by the solid curve, by using the average alignment moments found in Table 1. The P(3) probes K = 1 and 2.
For the polarization rotation scans, the REMPI laser wavelength is set at the peak signal and is believed to sample all K sublevels equally. The setting of the laser on the peak of the line may introduce a small amount of bias for particular K states because the laser resolution is of the same magnitude as the width of the K stack. To guard against K-level selectivity, we collect REMPI spectra at fixed probe polarization angles. While these spectra are more susceptible to long-term drifts of the photolysis laser power and to ionization laser intensity changes due to the laser dye gain curve than the polarizer scans, they sample populations along with the alignment moments and provide complementary information. Velocity-integrated (no mask) spectra and velocity-selected (with mask) spectra are recorded. Velocity selected spectra are shown for B equal Oo, 30°, and 90° in Figure 3 along with simulated spectra incorporating the populations, alignment moments, heterogeneous (N,K dependent) predissociation of CD, and experimental line width.I4
Results and Analysis Angular Momentum Alignment. A molecule with rotational quantum number J has 2J + I sublevels with MJ = -J, -J + 1, ..., J = 1, J , where MJ is the projection of J onto a space-fixed axis. If levels with different IM,I are unequally populated, the sample is said to be aligned. Kummel et aLZ8(hereafter referred to as KSZ) have presented the angular momentum algebra needed to determine the rotational states populations and alignment moments A:) of a distribution when a sample is probed by twophoton excitation with linearly polarized light. We use their formalism and angular momentum machinery to analyze our
29875 29925 29975 30025 29925 29975 30025 Probe Laser Frequency (cm')
Figure 3. Experimental and model spectra of the 3pz-X 4 band of CD3 for three angles 0 of the probe lasers polarization axis relative to the horizontally (parallel to the molecular beam axis) polarization of the photolysis laser beam. The model spectra are generated using the information in Table 1.
polarization data. Note that in our analysis we assume that the final ionization step in the 2 1 REMPI process has no dependence on the probe laser polarization. In general, the two-photon excitation intensity Z(Ni,Ki)from the ground electronic state level (Ni,Ki)to a two-photon resonant level (Nf,Kf)is expressed asz8
+
I(Ni,Ki)= Cn(Ni,Ki)C~(Ni,Ki;Nr,Kr;Q) Aik)(Ni,Ki) (1) kq
where C is a proportionalit constant, n(Ni,Ki)is the population of the level (Ni,Ki),the 4(Ni,Ki;N,K;Q) are the two-photon line-strength factors for the system geometry labeled by Q, the Aik)(Ni,Ki) are the spherical tensor moments of the ground-state angular momentum distribution and k is the rank and q the component with k taking on values of 0-4 and q taking on values 0-k. Because the photolysis laser is linearly polarized, the anisotropy induced in the dissociation has cylindrical symmetry about the direction of polarization of the photolysis laser and k is restricted to values of 0,2, and 4, and q must be zero. Furthermore, when the photofragment angular momentum distribution is averaged over velocity the k = 4, q = 0 moment (Ah4))must vanish because of the Iptpho,12 averaging of the single-photon photodissociation. Using the conventions of KSZ the moments Ah0),Ah2),and Ah4) are related to the expectation values of N Z and N, (note that we use N and N,, rather than J and J, to describe the rotational angular momentum of the fragment because the spin of the unpaired electron couples to the frame rotation N to form a resulting total angular momentum J, and we will be presenting alignment moments of N): Aho) = 1
Abz' = ( (Ni1(3NzZ- N2)/N21Ni))
(2)
(3)
,464)
((NiI(35N: - 30N,ZN2 + 3N4 + 25N: - 6Nz)/(8N4)INi)) (4)
The single-photon photodissociation restricts Ah2)such that -z/s C Ahz' C +4/5 (again when averaged over velocity and with the
8010 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
quantization axis now along the polarization of the photolysis laser for this special case).32 These limits on Ab2)and the restriction that Ab‘) = 0 noted earlier are relaxed when the velocity of the photofragment is resolved. From eq 3 it can be seen that Ab2’ ranges from -1 < Ai2) < +2 and higher order moments can be nonzero. A distribution with Ab2) = -1 has N perpendicular to the quantization axis (taken to be the direction of the photolysis laser polarization) while a value of Ab2) = +2 means that N is perfectly aligned along the quantization axis. These limits are valid in the high-N limit, e.g., for N = 10 the maximum value of Ai2)is only +1.727. Remembering that the quantization axis is parallel to the velocity vector we note that the alignment moments for the velocity selected ionization signal are equivalent within a normalization factor to the V-J correlation coefficients of D i ~ o n . ~ ’ The two-photon line-strength factors P’k)(Ni,Ki;Nf,Kf;52)in eq 1 depend on the initial level (Ni,Ki), the Anal level (Nf,Kf),and the experimental geometry, 52, which in our case is characterized by the angle 0 between the horizontal polarization of the photolysis laser and the polarization of the probe laser. When considering transitions in a symmetric top molecule such as CD,, the K quantum number replaces the A quantum number used in KSZ for a diatomic molecule. The spin of the unpaired electron in the CD, fragment is assumed to be spatially isotropic and unaffected by the photodissociation. The angular momentum associated with this spin couples with the angular momentum of the nuclear rotation and can reduce the observed alignment. With the measured spinrotation constant for CD, in the vibrationless ground state)‘ the fine structure splitting can be calculated and is found to be larger than 4.5 X lo-’ cm-’ for all rotational states with N > 1. This means that the electron spin S couples to N on a time scale less than 1.2 ns. This is shorter than the time between photolysis and probe laser pulses and therefore will reduce the observed alignment. These fine-structure depolarization effects are accounted for by correcting the f$k)(Ni,Ki;Nf,Kf;52)line-strength factors.28 This correction is largest for low-N levels. The nuclear spin of the D atoms also couples to rotation; however, the time scale on which this occurs is much longer than the photolysis probe delay,35and no correction for hyperfine depolarization is needed. Model for Maximum Alignment. We define a purely axial photodissociation process to be one in which no torque acts perpendicularly to the axis (in this case the C3axis of the CD31parent molecule). Assuming that initial tumbling motion in the parent CDJ with N perpendicular to the C3axis is transformed to orbital angular momentum of the fragments for a purely axial dissociation, it is possible to populate only one IMA sublevel in CD, starting from a given 1 4 state of CD,I, Le., IMAcD, = 14cD,l.If however the CD3top axis becomes nonparallel to the CD31top axis during the photodissociation event, tumbling will be induced about a C2 axis in the CD3fragment and IMdcD,will not necessarily be l~c,,,, Zero-point motion in the u6 mode or motion induced by anisotropy in the potential energy surface for the system are two possible origins of tumbling. In this model the spinning K of CD,I is transformed to spinning K of the CD3fragment, Le., KcD,, = Kcs. The total rotational angular momentum, N, for CD, contains then N - K quanta of tumbling rotation about a C2axis obtained from the photodissociation event and the K units of angular momentum about the C,axis obtained from the parent CD,I molecule. A schematic drawing of the vector orientations for this model is given in Figure 4 indicating the maximum alignment obtainable for each lNKMN) state of a particular N quantum number. The upper limits to the value of the alignment moments that can be expected for a particular N,K state of CD3can be estimated from the axial model for dissociation. In the analysis of the rotational population distribution in the CD3fragment reported before,14 the initial K quantum number of the parent molecule (32) Greene, C. H.; Zare, R. N. J . Chem. Phys. 1983, 78, 6741. (33) Dixon, R. N. J. Chem. Phys. 1986, 85, 1866. (34) Frye, J. M.;Scars, T. J.; Leitner, D. J . Chcm. Phys. 1988.88,5300. (35) Altkorn, R.: Zare, R. N. Annu. Rev. Phys. Chem. 1984, 35, 265.
Janssen et al.
U
LASER POLARIZATION
Figure 4, Schematic drawing of the maximum expected orientation of the angular momentum vectors and velocity vector in space relative to the detection system as given by a linear impulsive dissociation model described in the text. appears to be conserved in the dissociation as the K quantum number of the methyl fragment. The rotational excitation induced by the photolysis can be directed into tumbling motion only around an axis perpendicular to the C-D, axis. This implies that for the methyl fragments the recoil velocity is parallel to the transition dipole axis and the maximum expected projection of N on the quantization axis (polarization axis of photolysis laser beam) is K, Le., the maximum (parallel) alignment is obtained for the rotational state INK&) = INKK). If K for CD, is not created perfectly parallel to K for CD31,the alignment moments will be smaller than their maximum value. The maximum expected alignment moments, A&:L and A&MX, can be calculated from eqs 3 and 4 with N, = K: Ab%aX = Ab%, = 35K4 - 30K2N(N
3K2 - N(N + 1) N ( N + 1)
(5)
+ 1) + 3 M ( N + 112 + 2 5 P - 6N(N + 11
Table I gives A&*Land Ab4& for the rotational states analyzed. Experimentaj Determination of the Abk)Alignment Moments. How do we determine the experimental alignment moments for a particular N,K quantum state? Most features in the spectra of Figure 3 contain contributions from several different N,K states. The alignment measured, while resonant with one of these assigned features, is then a linear combination of the individual alignment moments wei hted by the population of each N,K state and the appropriate ,(Ni,K(;Nt,Kr;Q) line-strength factors. Because the different spectral branches (O,P,R,S) have different line-strength factors, each transition is sensitive to differing degrees to the individual N,K states and their alignment moments. When several K levels contribute to the total ion intensity from a particular branch, b a t an angle 0 of the polarization probe laser with the symmetry axis, Ib(Ni;O) is given by
$
Ib(Ni;O) = Cc
2
PoZk(NiKi;O)Aba)(Ni,Ki) n(Ni,Ki) (7)
Kik-0
where the range of Ki levels is determined by the particular branch, b (0,P, R, or S), and k = 0, 1, or 2. Measurement of the ion intensity as a function of 8 allows us to determine the alignment moments, A&2k).We term these intensity plots polarization scans which can be written as I(cos 0) = Co+ C2P2(cos 0) + Cg,(cos e), where P2(c0s 0) and P~(COS 0) are Legendre polynomials. Polarjzer scans are taken on all rotational lines of the vibrationless 3pz-X, 0; band with quantum number N < 6. Two representative plots are shown in Figure 2 for the P(3) transition (Nf = 2, Kf = Ki) (Ni = 3, Ki). The upper scan is without the mask and the lower scan with a mask transmitting the central part of the image with an aperture one-seventh the diameter of the image. Figure 2 clearly shows the periodic modulation of the ion signal with changing direction of the polarization of the probe laser. As explained above, a full 360° scan of the half-wave plate gives four repetitions of the modulated ion signal.
-
Rotational Alignment of the CD3 Fragment TABLE I: Population and Alignment Moments 4') and Ai4) of the Angdir Momentum Distribution of the CD3 Fragment from the 266-nm Photodissociation of CDJ (Values Listed in the Columns Labeled Measured Were Used To Generate the Model Spectra of Figure 3) population' A62) Ah') N K from ref 14 measd measd modelb measd' modelb 0.V 0.0 0.85 -I.@ -1.0 1 0 0.8 0.62 0.50 0.5 1 0.62 0.V 0.0 0.15 -1.0 -1.0 0.12 0.25 2 0 0.11 -0.02 -0.167 0.85 -0.45 -0.5 1 0.8 0.29 0.986 1.0 0.042e 0.042 2 0.4 3 0 1.2 1.2 -0.7 -1.0 0.3e 0.313 0.71 -0.65 -0.75 0.05 0.052 1 0.8 0.4 0.00 0.0 -0.2 -0.365 2 0.4 0.20 1.25 1.25 0.156e 0.156 3 0.18 ' 4 0 0.13 0.1 -0.8 -1.0 0.338r 0.338 0.169 -0.85 0.1 0.8 -0.65 I 0.8 -0.40 -0.21 -0.206 0.4 -0.4 2 0.4 0.21 0.2 0.35 -0.394e -0.394 3 0.15 1.40 0.025 1.4V 0.263e 0.263 4 0.03 'The populations for each (N,K) reproduced from ref 14, and the newly obtained populations from analysis of the polarization data presented here. For (N,K) = (0,O)a population of 0.08 is used in the spectral simulation of Figure 3. bMaximum expected A&*) and Ah') from eqs 6 and 7 respectively (see text). 'The P transitions are relatively sensitive to the Ah') moment; therefore, only Ah4)moments for K values sampled by a P transition are adjusted. d N o unblended transitions in the spectra sensitive to this moment. eAlignment moment set to maximum because data insensitive to value. IAh2)values set to be about 80% of maximum value to be consistent with values found for lower N transitions. Due to the many contributing ( N , K ) states to a single line and the limited number of independent lines available, no unique inversion of the Ab2)and Ab') moments can be obtained.
The masked polarization data for the P(3) line (lower frame of Figure 2) clearly exhibits extra intermediate maxima at angles of 90°, 270°, and 450°, of the polarization of the probe laser with respect to the horizontally polarized photolysis laser. These pronounced intermediate maxima ori inate from the fact that P lines are relatively sensitive to the A t ) moment, and the angular-dependent line-strength moment e(Ni,Kiflf,Kr;Q) (see eq 1) is proportional to the Legendre polynomial P~(COS 6) = (35 cos4 6 - 30 6 + 3)/8.28 By comparison of the overall alignment of a transition to its sibling transitions, a consistent set of populations and alignment moments for individual N,K states can be found that will satisfy the intensity and angular dependence for each transition. For the transitions with values of N > 3 the fit is not unique due to the few number of transitions (maximum of four branches 0, P, R, S) and the large number of contributing N,K states. For transitions with small numbers of contributing states unique fits are possible. In particular the R ( l ) line samples only the N,K = 1,l state and the P(2) line only samples the N,K = 2,l state. A detailed description of our inversion procedure is given below. Except for a few bands, the measured REMPI signals from a single N band result from the contribution of several different K levels, e.g., for the O(4) line the levels (N,K) = (4,0), (4,1), and (4,2) (note we have AK = 0 transitions) and for the P(4) line the levels (N,K) = (4,1), (4,2), and (4.3) are probed. As mentioned previously, resolution of K structure in the spectra is not experimentally possible, so the K population distribution within each N manifold must be obtained indirectly by comparing different branches for the same N. In some cases branches overlap; for instance, R(4) overlaps with S(1) and thus cannot be included in the set used to determine n(4,K) (or A&') (4,K)). O(2) and P(3) also overlap, as do S(0) and R(2). A good knowledge of n(N,K) (to which A&') is scaled in eq 2) is thus vital in determining the separate K-level contributions to the polarization rotation signals. In our previous analysis14the n(N,K) populations were obtained from direct fits of a velocity-integrated magic angle spectrum (e = 57O, A&') = A&') = 0), using a residual minimizing routine along with the requirement that the parent ortho-para ratio is conserved in the fragment. The magic-angle spectrum populations of ref
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8011 14 obtained by a line-by-line fit are listed in Table I. We found that the fragment rotational energy content is strongly affected by that of the parent CDJ molecule, which in turn is determined by the supersonic expansion conditions. Although we attempted to keep the pulsed valve parameters constant, daily fluctuations in the beam temperature (even as small as 2K) cause observable variations in the fragment spectra. In this study we compare spectra and polarizer rotation scans taken on several occasions. We use both the polarizer rotation scans and the spectra taken at different fmed polarizer angles to determine the set of alignment moments and populations listed in Table I. Additional information on the K-state population distributions within an N manifold can be gleaned from these polarizer scans and then used to better define n(N,K). The results of this polarizer-angle-based analysis is also listed in Table I as a final set of populations n(N,K). Only minor differences arise between this final n(N,K) distribution and the distribution determined from the single magic-angle spectrum.I4 To determine the alignment moments for individual N,K, states we start by assuming the population distribution determined in ref 14 and listed in Table I. Next, the best-fit values for Ai2)and Ah4) for the polarizer scans for lines with only a single N,K origin are determined, i.e., P(2), along with their uncertainties. Scans on lines of the same N value that sum progressively more K-level origins are analyzed, Le., R(2) is sensitive to both K = 1 and 2. The previously determined values of Ai2)and A&')and the population ratio of ref 14 are used to subtract out the contribution of already determined K states to the transition. A best-fit A&')and Ai4) are extracted for the remaining states. Obviously, the moments, Aik),for the same (N,K) level obtained from different branches must be consistent. We then iteratively adjust the original and newly found values within their error bars to get an overall best fit. Alignment moments are constrained in this fit not to exceed the maximum allowed by the impulsive dissociation model described above. This procedure becomes unstable as soon as a transition is sensitive to more than a few K levels. In practice we can work up to around N = 4 with reasonable confidence. If there are no transitions for a particular N value that sample only one K state, we start by assuming the maximum possible alignment for each N,K state defined by eqs 6 and 7 and the population ratio found in ref 14. The alignment moments are adjusted downward in order to fit the data. If the polarization scans cannot be fit to within their signal-to-noise by this procedure, then the populations are adjusted in order to find a consistent set of populations and alignment moments that fit all the transitions originating from states having a common N quantum number. As an example we outline in detail our procedure for determining the alignment moments and populations for the N = 2 states. For the N = 2 level the P(2), R(2), and S(2) lines are used to extract the moments. The R(2) line coincides with the S(0) line, but from the population analysis reported beforeI4 it was found that the (N,K) = (0,O)level has about 10% or less of the population of each of the K levels of the N = 2 level, so this isotropic contribution is subtracted from the total polarizer scan intensity of the R(2) line. The P(2) line probes only the (N,K) = (2,l) level and is used to obtain a first fit of Ai2)(2,1) and Ai4)(2,l). Next, the R(2) line, which probes the K = 1 and 2 levels, is fitted to extract the moment for (N,K) = (2,l) and (2,2). We do this by subtracting from the data the contribution that is due to the (N,K) = (2,l) state assuming the population ratio of ref 14. The remainder is fit to extract the Ah2)(2,2)and Ah4)(2,2) moments. The S(2) line, which probes all three K = 0, 1, and 2 levels, is then fitted in a similar manner. To get a better agreement between the fitted moments for this line and the moments extracted from the P(2) and R(2) line, the populations of the (N,K) = (2,O) and (2,l) levels are increased slightly and the (2,2) level decreased compared to the population from ref 14. The moments obtained from the fits to the P(2), R(2), and S(2) lines are listed in Table I. Table I contains two main pieces of information that result from this study: (a) the best-fit population distribution n(N,K); (b) the set of alignment moments for on-axis recoiling fragments. Both
8012 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 of these can be discussed in terms of the simple axial dissociation model described previously. In summary, the populations extracted from the polarization analysis appear to be in most cases in good agreement with the populations reported before.I4 For the higher K levels, the alignment moments fitted to the polarization dependence of the REMPl signal of the velocity-selected CD3 fragment turn out to be close to the values expected for the maximum alignment of fragments in rotational states with M N = K . For higher N levels we are unable to extract reliable polarization information from the data due to the large number of overlapping transitions with the same Nand differing K . The populations of these states are assumed to be the same as was previously determined." The closeness of the measured alignment moments with the model prediction gives us confidence that the model incorporates the essential physics of the photodissociation event. Zero-point bending of the parent molecule would be expected to reduce the alignment moments by diluting the pure (linear) axial character of the dissociation process. The measured Ai2)moments are in general about 10%smaller than predicted and the Ai') moments range from their predicted value to about half of the predicted values. Rotational Population Analysis. The assumptions that the K quantum number is conserved upon dissociation and that the tumbling motion of the parent molecule, N - K of CD31, is converted into orbital angular momentum dictates that the ortho/para ratio (1 1/ 16) of the parent CD31 is conserved upon dissociation. The ortho/para ratio of the product CD3 should be the same as the parent. The ortho/para ratio of the populations given in Table I summed over the first seven rotational states, N I6, is 0.69. The assumption of conservation of K upon dissociation allows us to determine the parent CD31temperature. Addition of all of the populations of the different N states for a particular K quantum number and plotting this sum against K allows us to compare our populations with theoretical K populations from CD31at different temperatures. Comparison of our summed K populations with these calculated populations indicates that the populations of Table I are consistent to a CD31population of 1SK f 2K. We will use this CD31 parent beam temperature in the analysis of the populations. A conclusion of the analysis of the polarization data is that on the order of one M Nstate is populated for each N,K state produced, i.e., the CD3 is highly aligned. This means that the analysis done in ref 14 deducing the probability of energy transfer from the population distribution is in error. That analysis assumed a degeneracy of 2N l M N states for each N,K state produced. We have reanalyzed the populations given in Table I assyming the degeneracies for the vibrationless ground state of CD3 X2AN2gFx = 8 for para levels ( K # 3n with n integer). For ortho levels with K # 0 ( K = 3 4 n > 0) g N , K = 11, gN,K 1 for K = 0, N even, and gN:! = 10 for K = 0, N odd. The rotational excitation probability
+
is defined by the equation
ppCD3(N,K) =
Here popCD,(N,K)is the pulation in a particular N,K state of the methyl radical, popz$(K) is the population of a particular K state of the parent methyl iodide (summed over all po ulated N states) for the temperature of the molecular beam, fg(N,K) is the degeneracy of the N,K rotational state of the methyl fragment, and
Janssen et al. 0.5 0.4
>
2m 0 . 3 U
pm 0.2 P
0.1
-
0 0
0
I
I
I
1
I
i
50
100
150
200
250
300
A
E (cni')
Figure 5. Relative probability of rotational energy transfer for a given energy gap during the dissociation of CD31following absorption of a 266-nm photon. This probability is extracted from the data assuming the perfect alignment of the CD3 fragments as defined by the model of Figure 4.
is the probability that a methyl radical born in a particular N = K state obtains tumbling angular momentum, AN, as the molecule dissociates, thus ending up with N = K + AN units of angular momentum. This gain, AN, in angular momentum is in tumbling around a C2axis and is of value N - K . The degeneracies used here include the even/odd alternation of the K = 0 manifold which originates from the planar nature of CD3 and is clearly evident in the spectrum of Figure 3 but not the (2N 1) degeneracy of the M Nstates. This (2N 1) degeneracy is dropped because the model for alignment of CD3constrains Mc~:McD,= KcD, = Kcw. In Figure 5 we have plotted the probability for obtaining an amount of rotational energy in the dissociation event
+
+
probCD3
N=K (N=K+m
">
K
versus the appropriate energy gap associated with the transfer. We find the fairly smooth curve indicating an energy-gap dependence on the transfer of rotational energy. Not all of the data fall on the smooth curve drawn in Figure 5. The points that fall furthest from the best fit curve come from K = 0 states. These K = 0 states exhibit the strong N = even:odd variation of the degeneracy due to the nuclear spin statistics. Previously we had reported a smooth variation with rotational quantum number change (a momentum gap law), but the use of the restricted degeneracy factors in the analysis eliminates the smooth variation with quantum number change and serves to point out the importance of taking the alignment of the fragments into account when performing such population analysis.
Discussion Of the many systems studied in photodissociation experiments the most detailed information about vector correlations is obtained for ICN,ZJ6-39H202,@CH31, CD31,e12*ls*2s and CH30N0.3i Very recently, studies by Houston and co-workers9 and Black and PowisioJ1were reported investigating the rotational excitation and alignment of the methyl (CH3, CD,) fragment from the photodissociation of methyl iodide (CH31, CD31). Houston and co-workers9 found rotational excitations of 125 and 109 cm-' for CH, and CD3, respectively, from the dissociation of a cold pulsed (36) Hall, G. E.; Sivakumar, N.; Houston, P. L. J. Phys. Chem. 1986,81, 2120. (37) OHalloran, M. A.; Joswig, H.; Zare, R. N. J . Chem. Phys. 1987,87, 303. ( 3 8 ) Hasselbrink, E.; Waldeck, J. R.; &re, R. N. Chem. Phys. 1988, 126, 191. (39) Black, J. F.; Waldeck, J. R.; Hasselbrink, E.; Zare, R. N. J . Chem. Soc., Faraday Trans. 2 1989,85, 1044. (40)See,e.g., the following reviews: August, J.; Brouard, M.; Docker, M. P.; Hodgson, A.; Milne, C. J.; Simons. J. P. Eer. Busen-Ges. fhys. Chem. 1988.92, 264. Comes,F. J.; Gericke, K.-H.;Grunewald, A. U.; Klee, S.Eer. Eusen-Ges. Phys. Chem. 1988, 92, 273.
8013
J. Phys. Cbem. 1991, 95.8013-8018 parent beam. Excessive population in the K = 0 levels was observed, indicating a preferred rotation of the methyl fragment around a C, axis. A quite differing, but to some extent complementary study, was done by Black and Powis,’OJ’ who photolyzed an effusive warm methyl iodide beam. Rotational population in levels up to N = 15-20 was found, and mainly high-K levels were populated in the methyl fragment. From an analysis of the changes in the REMPI spectrum form perpendicular plarization of the photolysis and probe laser to the magic angle REMPI spectrum (polarization of probe laser at 5 4 . 7 O ) an ‘‘overall” alignment moment Ah2)= 0.5 f 0.2 was extracted. This positive alignment is in agreement with the expectation for a parallel dissociation of an internally warm parent molecule. The initial relatively high-K quantum number of the parent is conserved in the dissociation to the spinning rotation of the methyl fragment and N will be directed preferentially along the C3 symmetry axis. The maximum attainable alignment from the total recoil distribution of the photofragments is Ag) = 0.8.39A somewhat smaller extracted average alignment of A&) = 0.5 was proposed to originate from the rotational excitation induced in the photodissociation from the Yg wagging mode, populated to about 7% in the CD31at room temperature, and zero-point energy, lowering the initial parallel alignment on N along the C3 axis.” From inspection of Figure 5 it can be seen that the rotational energy transfer to the fragment CD3 has a smooth dependence on energy gap. It is also noted that as the value of N becomes larger the energy gap between (N”, K” = N’? and (N‘ = N”+ 1, K’= N ’ - l ) , the smallest allowed rotational energy transfer, increases. By N = 9 this smallest energy gap, (9,9) (10,9), is 100 cm-I, and the probability of rotational energy transfer can be seen by inspection of Figure 5 to be small. This is why Black and Powis’o*’’observe an increasing propensity for N = K in the CD3 fragments at the higher rotational states where they are able to resolve the transitions from the individual K states.
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From inspection of the Ah2)moment in Table I, it is observed that especially for the higher K levels within a certain N stack the measured Abz) is very close or equal to the maximum for these (N,K) states. This can be explained from the fact that the high-K levels originate from the initial rotational excitation around the C3 axis in the parent molecule. As the K quantum number is expected to be conserved in the photodissociation, a methyl fragment in a high-K state, e.g., K = A’, has not been rotationally excited from the photodissociation. It means no rotational excitation from zero-point bending or from the curve crossing of the two potentials involved in the dissociation“Jg is induced. The fragment in final state (NX)= (K,K) is dissociated collinear to the C3axis, which was parallel to the direction of the polarization of the photolysis laser. This rotational state will then have the maximum parallel alignment expected.
Conclusion We have determined the alignment moments and population distribution for the CD3 fragment following the 266-nm photodissociation of CD31. These alignment moments are explained in terms of a simple linear dissociation model assuming conservation of K quantum number and conservation of the parent ortho/para ratio upon dissociation. A reanalysis of the rotational populations for the ground vibrational state of the CD3 fragment taking into account this high degree of alignment of the CD3 fragments reveals an energy gap law for rotational energy excitation from the dissociation process. Acknowledgment. We thank Mark Jaska and Mitch Williams for their expert technical assistance in the laboratory and Diana Atwood for help with the figures. M.H.M.J., S.S.,and D.H.P. gratefully acknowledge the Sandia National Laboratories’ Visiting Scientists Program and the National Science Foundation, Grant 8619803, for support. Registry No. CDJ, 865-50-9; CD,,2122-44-3.
Observation of a Parallel Recoil Dlstribution from a Perpendicular Absorption Transition in HCO and DCO Scott H. Kable? Jean-Christophe Loison,$ David W. Neyer, Paul L. Houston,* Department of Chemistry, Cornel1 University, Ithaca. New York 14853- 1301
Itamar Burak, School of Chemistry, Tel Aviv University, Tel Aviv, Israel
and Richard N. Dixon School of Chemistry, The University, Bristol BS8 1 TS, England (Received: February 5. 1991) We report results and calc_ulalionsof the recoil anisotropy of H and CO photofragments following laser dissociation of HCO and DCO radicals. The A-X transition of HCO/DCO is known to lie perpendicular to the molecular plane. Excitation using linearly polarized light, however, gives rise to fragments recoilingparallel to the axis of polarization. The degree of spatial anisotropy was found to depend as expected on the value of K (the projection of J onto the a axis) for the upper electronic state, but also to depend on the initial value of K in the lower state, contrary to normal expectation. The anisotropy parameter, p, was measured for the following K’+ K” transitions: 1 0, j3 = 1.0 0.1; 1 2, j3 = 0.0 f 0.15;0 1, Q branch, @ = 0.25 f 0.15;0 1, R branch, @ = 0.0 f 0.15; and 2 1, j3 = 0.1 f 0.2 These unusual results are explained by examining the detailed mechanism of the Renner-Teller interaction and by calculating the angle of recoil of the H atom with respect to the CO molecule.
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*
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I. Introduction The use of Doppler profile techniques to measure the translational energy distribution of recoiling photofragments has become
widespread as lasers and molecular beam technology have been increasingly applied to molecular photodissociation dynamics.’-’*
‘Current address: Environmental Division, Proctor and Gamble, Egham, Surrey TW20 9NW, England. *Currentaddress: Laboratoire de Photophysique Moliculaire, UniversitE de Paris-Sud, Orsay, France.
(1) Simons, J. P. Gas Kinetics and Energy Transfer; Royal Society of Chemistry: London, 1977; Vol. 2, pp 58-95. (2) Ashfold, M. N. R.; Macpherson, M. T.; Simons, J. P. Top. Curr. Chem. 1979, 86, 1-90.
0022-3654/91/2095-8013$02.50/0
0 1991 American Chemical Society
