J . Phys. Chem. 1990, 94, 4839-4846
4839
Photofragment Imaging: The 266-nm Photolysis of CD,I David W. Chandler,* Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551
Maurice H. M. Janssen, Molecular and Laser Physics, Department of Physics, Catholic University of Nijmegen, Toernooiveld, 6525 ED Nijmegen. The Netherlands
Steven Stolte, Department of Physical and Theoretical Chemistry, Free University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
Robin N. Strickland, Department of Computers and Electrical Engineering, University of Arizona, Tucson, Arizona 8571 1
John W. Thoman, Jr., Chemistry Department, Williams College, Williamstown, Massachusetts 01 267
and David H. Parker Chemistry Department, University of California at Santa Cruz, Santa Cruz, California 95064 (Received: October 30, 1989; In Final Form: February 8, 1990)
Internal state and velocity distributions of methyl fragments from the 266-nm photodissociation of CDJ in a supersonic beam are measured by using photofragment imaging. Methyl radicals are state-selectively ionized by using ( 2 + 1 ) resonance-enhanced multiphoton ionization (REMPI) via the 3p, RydbeLg state, and the imaging technique records the velocity distribution of the ions. A line-by-line rotational analysis of the 3pz X 0; band, including conservation of the parent molecule’s ortho:para ratio in the planar fragment molecules, indicates that about 90 cm-l of rotational excitation about a C2axis in CD3 results from the photolysis. The shapepf the probability distribution for rotational energy excitation upon dissociation is extracted from the analysis of the 3p, X 0; band. The photodissociation appears to conse-we the initial (low) rotational excitation about the C, axis of the (cold) parent molecule. From the previously derived 3p,-X Franck-Condon factors the branching ratio for the v = 2/v = 0 levels of the umbrella mode is determined to be 1.15 0.13. Propensity ratios for forming channel are obtained the selected fragment state via the ground-state iodine 1(2P3,2)(I) or excited-state iodine 1(2P,,2)(1*) from the images. I / I * ratios are obtained while resonant on the O;, 2;. 2:, 21, 2:, 2:, and 1 f transitions. The [/I* branching ratio is found to increase rapidly with increasing vibrational excitation. For u2 L’ = 0, I , 2, and 3 we find I/I* ratios of (0.04 i 0.02), (0.09 i 0.03), (0.27 i 0.08), and (1.4 & 0.2), respectively.
-
+-
*
Introduction
Methyl iodide photolysis has drawn considerable attention over the past 20 years as an “instantaneous” pseudolinear dissociation that may be described by a two-dimensional potential energy surface. The availability of pulsed laser light resonant with the first dissociative state has made methyl iodide particularly amenable for study using time-of-flightl-8 or spectroscopic techniques.”” Such data spurred many theoretical effort^,'^-^^ es( I ) Riley, S. J.; Wilson, K. R. Faraday Discuss. Chem. SOC.1972,53, 132. (2) Kasper, J. V. V.; Pimentel, G . C. Appl. Phys. Left. 1984, / I , 231. (3) Porret, D.; Goodeve, C. F. Proc. R. SOC.(London) 1938, 165, 31. (4) Sparks. R. K.; Shobatake, K.; Carlson, L. R.; Lee, Y. T. J . Chem. Phys. 1981, 75(8), 3838. (5) van Veen, G.N. A.; Mohammed, K. A,; Baller, T.; de Vries, A. E. Chem. Phys. 1983, 74, 261. (6) Penn, S. M.; Hayden, C. C.; Carlson Muyskens, K. J.; Crim, F. F. J. Chem. Phys. 1988, 89, 2909. (7) Barry, M. D.;Gorry, P. A. Mol. Phys. 1984, 52, 461. (8) van Veen. G . N. A.; Baller, T.; de Vries, A. E.; van Veen, N. J. A . Chem. Phys. 1984, 87, 405. (9) Leone, S. R. Adu. Chem. Phys. 1982, 50, 255. Hermann, H. W.; Leone, S. R. J. Chem. Phys. 1982, 76, 4766. Hess, W. P.; Kohler, S. J.; Haugen, H. K.; Leone, S. R. J . Chem. Phys. 1986, 84, 2143. (10) Imre, D.; Kinsey, J. L.; Sinha, A,; Krenos, J. J . Phys. Chem. 1984, 88, 3956.
0022-3654/90/2094-4839$02.50/0
pecially in the generation of semiempirical potential energy surfaces. In this paper we employ the photofragment imaging t e c h n i q ~ ethat ~ ~ couples * ~ ~ time-of-flight velocity measurements ( 1 1) Hale, M. 0.;Galica, G . E.; Glogover, S. G.; Kinsey, J. L. J . Phys. Chem. 1986, 90,4997. (12) Oaorzalek Loo, R.; Hall, G. E.; Haerri, H.-P.; Houston. P. L. J . Phys. Chem. 1998, 92, 5. (13) Ogorzalek LOO,R.; Haerri, H.-P.; Hall, G . E.; Houston, P. L. J . Chem. Phys. 1989, 90,4222. (14) Ogorzalek Loo, R.; Straws, C. E.; Haerri, H.-P.; Hall, G . E.; Houston, P. L.; Burak, I.; Hepburn, J. W. J . Chem. SOC.,Faraday Trans. 2, 1989, 17. (15) Chandler, D. W.; Houston, P. L. J. Chem. Phys. 1987, 87, 1445. (16) 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, 375. (17) Shapiro, M.; Bersohn, R. J. Chem. Phys. 1980, 73, 3810. (18) Shapiro, M. J . Phys. Chem. 1986, 90, 3644. Shapiro, M. Chem. Phys. Leu. 1981, 81, 521. (19) Lee, S.-Y.; Heller, E. J. J . Chem. Phys. 1982, 76, 3035. (20) Billing, G. D.; Jolicard, G . J . Phys. Chem. 1984, 88, 1820. (21) Gray, S. K.; Child, M. S. Mol. Phys. 1984, 51, 189. (22) Kanfer, S.; Shapiro, M. J. Phys. Chem. 1984,88, 3964. (23) Henriksen, N. E. Chem. Phys. Left. 1985, 121, 139. (24) Yabushita, S.; Morokuma, K. Chem. Phys. Left. 1988, 153, 517.
0 1990 American Chemical Society
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The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
with state selectivity, obtained by using resonance-enhanced multiphoton ionization (REMPI), to further explore methyl iodide photolysis. This paper reports studies of CD3 produced from CDJ photolysis; previous work26 addressed imaging studies of CH,I photolysis. Because the excited electronic states of CD3 are less predissociative than those of CH3, more detailed information on the 266-nm dissociation process is obtained from the study of CD31. Recently Loo et aI.l3 published results on 266-nm photolysis of CD31 using their one-dimensional technique and we direct the readers to that paper for an excellent review of the previous work in the field. The photofragment imaging technique is a two-dimensional analogue of the time-of-flight methods used by Welge'sZ7and Houston'sI2 groups. Photofragment imaging uses the position of selectivity ionized photofragments at the time-of-flight detector along with their arrival time to determine the full (angle and speed) velocity distribution of fragments populating a single internal state. This is achieved by the following series of events. Several nanoseconds after photolysis of CD31 by polarized 266-nm radiation the methyl fragments are state-selectively ionized by using (2+1) REMP1.28,29A few microseconds later, after the ions travel down a IO-cm-long time-of-flight tube, the ions impact a position-sensitive ion detector. The image created is a two-dimensional projection of the three-dimensional spatial distribution of the selected fragments captured at the time the ions arrive at the detector. If all fragments are detected with equal probability the cylindrical symmetry of the dissociation process ensures that the two-dimensional image (the raw data) is all that is necessary to regenerate the three-dimensional distribution of photofragments produced by the dissociation. Because the fragments are ionized with a polarized laser beam, the images, although symmetric, reflect alignment of the fragment angular momentum created by the photolysis event.I5 In a following paper30 we describe the CD3 alignment and its implications for the dissociation mechanism. Three properties characterize the images: (a) the angular distribution, which for CD,I is indicative of an absorption via a parallel transition followed by a nearly "instantaneous" dissociation (6 = 1 .8);12 (b) the speed distribution of the fragments, which is dominated by the presence of two channels, production of ground-state iodine (I(2P3/2) = I) or excited state iodine (1(2P,/2) = I*), giving many of the images a double-ringed appearance; and (c) the angular momentum alignment of the fragments, which makes the image sensitive to the direction of the polarization vector of the ionizing laser beam. This paper focuses on the variation of the product channel (I/I*) ratio with fragment internal state as well as spectroscopic analysis that reveals the distribution of rotational and, to lesser degree of detail, vibrational energy released by the dissociation event. Experimental Section
As described in previous papers15~25~26 and shown in Figure 1 the apparatus consists of a pulsed molecular beam that is skimmed and directed through a repeller plate toward the center of a position-sensitive ion detector. The molecular beam is produced by flowing He at 7 bar over CD31 in an ice-cooled sample holder and into a piezoelectric-pulsed valve (Laser Technics) equipped with a 0.3-mm orifice. A 50-V pulse is applied to open the valve, and the initial part of the 250-ps-long gas pulse is photolyzed. A quadrupled Nd:YAG laser beam at 266 nm (-2 mJ/pulse) with its polarization axis aligned perpendicular to the molecular beam (vertical polarization) is loosely focused on the molecular ( 2 5 ) Thoman, Jr., J. W.; Chandler, D. W.; Parker, D. H.; Janssen, M. H. M . Laser Chem. 1988, 9, 27. (26) Chandler, D. W.; Thoman, Jr., J. W.; Janssen, M. H. M.; Parker, D. H . Chem. Phys. Left. 1989, 156, 151. ( 2 7 ) Krautwald, H . J.; Schneider, L.; Welge, K. H.; Ashfold, M . N. R. Faraday Discuss. Chem. Soc. 1986. 82. (28) Hudgens, J . W ; DiGiuseppe, T. G.; Lin, M . C. J. Chem. Phys. 1983. 79. 571. (29) Parker, D. H.; Wang, Z. W.; Janssen, M. H. M.; Chandler, D. W. J . Chem. Phys. 1989, 90, 60. (30) Janssen, M . H. M.; Stolte, S.; Parker, D. H.; Sitz, G . 0.;Chandler, D. W., manuscript in preparation.
Chandler et al.
4
i
I
Figure 1. Schematic of the photofragment imaging apparatus. A pulsed molecular beam of CDJ seeded in He enters the photodissociation region of the apparatus through a hole in a repeller plate of a time-of-flight mass spectrometer. A 266-nm laser beam intersects the molecular beam and dissociates the methyl iodide. A few nanoseconds later a tunable U V (-334 nm) laser beam intersects the fragments and resonantly ionizes them. A few microseconds later the ions impact a position sensitive ion detector creating a two-dimensional projection of the ion distribution. The image is recorded on a C C D camera. In order to obtain REMPI spectra a photomultiplier is used to monitor the detector.
beam (50-cm-focal-length lens). A tunable (360-320 nm), collinear, counterpropagating, linearly polarized laser beam (- 1 mJ/pulse) from a frequency-doubled tunable dye laser pumped by an injection-seeded single-mode Nd:YAG laser is also loosely focused 10 ns later into the photolysis region (20-cm-focal-length lens). The focal points of the lasers are adjusted away from the molecular beam such that signals from either laser alone are only a few percent of the two-laser signal. To avoid alignment effects when recording a spectrum the polarization axis of the ionization laser beam is rotated 5 4 O (the "magic angle")3' from the polarization axis of the photolysis laser by a 1 / 2 wave plate. Ions are accelerated along the molecular beam axis into a wide-bore (40 mm diameter) time-of-flight mass spectrometer with a dual-chevron microchannel plate/phosphor-screen detector. Electric fields are adjusted in the accelerating region so that the selectivity ionized fragments move 1 cm (due to the velocity gained from the dissociation process) off-axis before they strike the front plate of the detector. For nascent methyl radicals this takes -2.5 ks. A significant improvement in mass selectivity and spatial resolution resulted from removing the ion shutter electrode from in front of the detectorI5 and instead pulsing the voltage applied to the face of the first microchannel plate when the ion of interest arrives. The front face of the first microchannel plate is normally at ground potential. Coincident in time with the arrival of the CD3+ ions, a -700-V, 100-ns-duration voltage pulse is applied to the front face. The pulse accelerates the ions into the detector and turns on the gain of the microchannel plate at the same time, since the back face of the first microchannel plate is held at 300 V . An electronic camera records the images from several thousand laser pulses, and background is removed by subtracting an image collected with the ionizing laser tuned off-resonance. We obtain velocity-selected REMPI spectra of the methyl fragment by using a mask to pass light from selected regions of t h e phosphor screen (correlating to fragments with different speeds) to a photomultiplier tube. The fast (50 ns) phosphor allows us to record a mass-resolved time-of-flight spectrum using a boxcar averager. The measured image is a two-dimensional projection, along the direction of ion acceleration (which coincides with the molecular beam axis), of the three-dimensional velocity distribution of the ionized photofragments. By orienting the polarization axis of the dissociation laser parallel to the face of the ion detector, we ensure that this image captures all the information needed for reconstructing the three-dimensional distribution. Each digitized line
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(31) Kummel, A. C.: Sitz. G. 0.;Zare, R. N.J . Chem. Phys. 1986, 85, 6874
Photofragment Imaging
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4841
of data, taken perpendicularly to the cylindrical symmetry axis of the image, is the one-dimensional projection of a latitudinal cross section of the ion cloud. These cross sections are circularly symmetric and can therefore be recovered by an inverse Abel transform of the corresponding p r o j e c t i ~ n . By ~ ~ Abel inverting the projections line by line, we create a stack of two-dimensional cross sections that together reconstruct the three-dimensional photofragment distribution. The integral transform approach to the Abel inversion is computationally simple.33 The transform technique involves a Fourier transform, implemented by the standard fast Fourier transform algorithm, followed by an inverse Hankel transform, based on a modification of Candel’s algorithm.34 As with other forms of the Abel inversion, any noise in the projection data appears in amplified form in the final reconstruction. This noise in the reconstruction has a well-known inverse proportionality to the distance from the symmetry axis discussed above, which in our case means that the noise is greatest on the line joining the two poles of the reconstructed ion distribution. Fortunately, the regions most affected are those in which the ion signal is greatest. A dramatic reduction in the noise in the reconstruction is achieved by presmoothing the two-dimensional projection data with a small (typically either 5 X 5 or 9 X 9 pixel) Gaussian convolution mask. A typical image is about 200 pixels in diameter.
Results and Discussion Velocity-selected spectra of nascent CD, have been published in a previous articlez9 in which we determined the rotational and vibrational constants and Franck-Condon factors used in the present populatio_n analysis. Houston and co-workersI3 have also X REMPI spectra of the nascent CD, using a reported 3p, one-dimensional analogue of the i m a e n g technique. Black and X transition to monitor the Powis16 have recently used the 4p, nascent methyl fragments from the photolysis of room-temperature CD31. Both the 4p, and 3p, electronic states predissociate at a rate increasingly competitive with photoionization as their rotational and vibrational energy content increases. As a consequence, rotational-population information can be reliably extracted only for transitions involving the u = 0 level of the excited electronic state. Less detailed information on the higher levels of the vz umbrella motion and u = 1 level of_the v 1 symmetric stretch can also be obtained from the 3p, X transition. Rotational Population Distributions in the u = 0 I* Channel. The_bottom panel (b) of Figure 2 shows the 0; band of the 3p, X transition. Images reveal that very little (-4%) of this signal arises from CD, formed through the channel producing groundstate iodine, I . Except for a small background contribution at 334.15 nm, indicated by the arrow in Figure 2, which we assign to the 1 ; transition, Figure 2 reflects the population of the I* channel. This spectrum represents the coldest CD, distribution obtained and was produced by photolyzing the leading edge of the molecular beam pulse. Photolysis during the middle part of the gas pulse produces fragments with higher rotational excitation and a large number of fragments with low kinetic energy. Cluster formation presumably warms the beam and cluster dissociation results in the low-velocity signal.3s We use two approaches to fit the observed spectra. Both approaches, a line-by-line deconvolution of the spectrum and a two-temperature model, produce acceptable fits to the data. The simulated spectra are calculated by using a symmetric-top twophoton transition line-shape program similar to that of Hudgens et aLZBThe upper panel (a) of Figure 1 displays the simulation obtained by the line-by-line deconvolution of the data. Heteroand homogeneous broadening are also included in the fits following +-
+ -
+ -
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(32) Bracewell, R. N . The Fourier Transform and its Applications; McGraw Hill: New York, 1986; p 262. (33) Smith, L. M.; Keefer, D. R.; Sudharsanan,S. I. J . Quanr. Spectrosc. Radiat. Transfer 1988, 39, 361. (34) Candel, S . M. IEEE Trans. Acoustics, Speech, Signal Processing 1981, 29, 963. (35) Donaldson, D. J.; Vaida, V.; Naaman, R. J . Chem. Phys. 1987.87, 2522.
la)
I
I
I
0:;
CD3
5
3p-x
2
P
59800
5
2
-
0 1
5
1
5
k
59900
S
60000
FRERUENCY (cm-’)
Figure 2. Experimental (bottom panel) and simulated (top panel) (2+1) REMPI spectrum of the 0 : band of CD, following the 266-nm photolysis of CD,I. The spectrum was obtained by observing all velocity components of CD3 fragments while the lasers’ polarizations were crossed at 5 4 . 7 O . The populations used to generate the upper spectrum are obtained from a line-by-line analysis of the experimental spectrum as described in the text.
the formulas of Black and Powis.16 The rotational constants used were derived p r e v i o u ~ l y . ~ ~Both J ~ simulations conserve in the methyl fragment the ortho:para ratio (1 1:16)of the parent methyl iodide before the supersonic expansion. Only two parameters, TN and TK,are needed to produce the two-temperature simulation. In this model, populations, n(N,K), follow a modified “Boltzmann” distribution given by n ( N , K ) = nogN,+(-EV”K)/kBTN)e(-E(K,K) / TK) (1) where TN,the “temperature” describing the distribution of population among the N manifold, is combined with TK,the “temperature” defining the K manifold population within each N manifold, gN& accounts for the proper statistical weight of the level ( N , K ) , and kB is Boltzmann’s constant. The K quantum number represents the projection of the molecular rotation, N , along the figure axis. For the vibrationless ground state E ( K , K ) is defined by the formula for the rotational level of a symmetric top molecule, E ( N , K ) = BN(N + 1) ( C - B ) P , replacing N by K . Here B and C a r e the r_otationalconstants of CD3.z9 For the vibrationless ground state X z A F , gNK = 8(2N + 1) for para levels ( K # 3n with n integer). For ortho levels with K # 0 ( K = 3n, n > o), g N , K = 1 l ( 2 N 1 ) ; g N , K = (2N + 1 ) for K = 0, N even, and gN& = lO(2N + 1 ) for K = 0, N odd. For the beam conditions used to obtain the spectrum shown in Figure 2 , the best-fit values of TN and TKare 150 and 20 K, respectively. A small value of TKrelative to TN implies that the low K levels are preferentially populated and rotational excitation is predominantly perpendicular to the figure axis (tumbling). The lower the value of TKthe higher is the preferential population of the low K states. Following the approach of Black and Powis16 we account for the effect of homogeneous and heterogeneous predissociation on the spectral Lorentzian shape of the REMPI spectrum using a homogeneous predissociation line width of Avo = 0.75 cm-’ and a rotational state dependent line width of Avrrol= s(N’(N’+ 1) - KO} with (N’,K’)the upper resonant level and s = 0.015 cm-’. Due to the rotation-dependent predissociation the integrated peak intensity of the ion signal at a particular transition (N‘,K’) ( N , K ) is reduced by a factor 1/F = 1 / ( 1 + A ~ , , , / A U ~To ).~~ account for the experimental line shape the total spectrum is
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(36) Frye, J. M.; Sears, T. J.; Leitner, D. J . Chem. Phys. 1989, 88, 5300.
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The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
TABLE I: Best-Fit Populations for Individual (N,K ) Levels from a Line-by-Line Analysis of the Spectrum of Figure 2'
N
K
0 I 1 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5
0 O 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2
best-fit Douulation
N
K
best-fit Dooulation
0.04 0.8 0.62 0.1 1 0.8 0.4 I .2 0.8 0.4 0.18 0.12 0.8 0.4 0.15 0.025* 0.8 0.6 0.3
5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7
3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7
0.16 0.02* 0.0025* 0.076 0.50 0.20 0.12 0.02. 0.002" 0.0001* 0.45 0.20 0.13 0.08* 0.01 * 0.0015* 0.00 1o* 0.0002*
'Asterisks indicate populations to which the line-by-line analysis of the present data is insensitive; these values are determined from adapting the populations obtained with the two-temperature fit to be consistent with the half-collision model described in the text. convoluted with a Lorentzian line shape having a full width at half-maximum of 1 cm-I. The contribution of the isotropic part to the strong Q branch is estimated from comparison of the peak height of the Q branch to the S(2) line and is included in the simulation. Individual rotational state populations, given in Table I, are derived by the line-by-line analysis. Although spectral resolution of the K states is not possible for the low rotational level of CD3 populated by the photolysis (predissociation processes in the 3p, Rydberg state produce spectral line widths larger than the K state splitting), the contributions of individual K states to each N band are extracted by the procedure outlined below. First the populations obtained from the two-parameter temperature fit were used as a start in an iterative procedure. Subsequently the populations of all K states from a certain N level were individually adjusted to fit all the lines originating from this N level, the different 0, P, R, and S branches. Because we detect via a parallel transition, the AK = 0 selection rule dictates that some lines originate from single ( N , K ) states. For instance, the R ( l ) line probes the (N,K) = (1,l) level and the P(2) transition probes the (N,K) = (2,l) level only. The populations of the (N,K) levels were iteratively adjusted under the constraint of conservation of the ortho:para ratio of 11:16 of the CD31 parent beam. The same predissociation line widths as used for the temperature fit are included in the line-by-line simulation. The populations in some states are too low to contribute to the overall intensity of the transition in a significant way and are adjusted by a separate procedure described below. These states are designated with asterisks in Table I. Most are high-K states populated by dissociation of hot parent molecules and thus are very sensitive to the conditions of the molecular beam. We describe below a method for deconvoluting the effect of the CDJ beam temperature from the CD3 rotational distribution. In Table I1 the average values for the rotational quantum numbers ( N ) , ( K ) and the total average rotational energy ( E ( N , K ) )and the calculated average rotational energy around the figure axis ( C P ) are given, using the populations of Table I. Here (E(N,K)) is defined as z W , K ) E(N,K) ( E ( N , K ) )=
N,K
XW , K )
(2)
N.K
Inspection of Table I1 gives insight into the photodissociation process. To estimate the amount of rotational excitation in the fragment from the photodissociation we assumed the parent beam
Chandler et al. to be cooled to a rotational temperature of 15 K while conserving the initial ortho:para ratio of 11:16 of the gas a t the stagnation room temperature. The temperature of 15 K is estimated from a comparison of the temperatures obtained by Bernstein and co-workers3' for their beam expansion conditions. This is also the rotational temperature Loo et ai.', assumed for their methyl iodide molecular beam of similar design. We will show that a beam temperature of 15 K is consistent with our observed spectrum. The average rotational energy of the CD3 fragment, as reported in Table 11, is 94 cm-' of which 90 em-' is tumbling motion and 4 cm-' is rotation around the C3 symmetry axis. The average K levels, (K), for both the ortho and the para stacks in the CD, fragment are almost exactly the same as the initial K population in the cooled parent CD31 beam at the temperature of 15 K. This implies that in the photodissociation K is conserved. For comparison Table I1 includes the same quantities obtained from the rotational populations of the 0; band of CH, from the 266-nm dissociation of CH31 reported previously.26 An extended analysis of the populations reported in ref 26 results in slightly different rotational energies in the CH, fragment. The (N,K) = (4,3) population of 0.7 was adjusted to a value of 0.1 because the accidental overlap with the 1 band, although noted in the data presentation, was not taken into account in the population analysis. The preferred values for CH3 are also given in Table 11. Summarizing, by inspection of Table I1 for both CD31and CH31, the K quantum number appears to be conserved in the photodissociation and accounts for the observed rotational excitation around the C, axis of methyl. Due to the closeness of the center of mass of the C H J molecule to the position of the iodine atom, initial parent rotation perpendicular to the C, axis is transformed more than 99% into orbital angular m 0 m e n t ~ m . lTherefore ~ the dissociation-induced rotational excitation energy E,,,, defined as ( E ( N , K ) )- ( C P ) ,of the fragments in the vibrational ground state can be calculated by subtracting the rotational energy about the symmetry C, axis, resulting in E , = 90 cm-' for CD3 and E , = 114 cm-' for CH,. In an effort to better characterize the dissociation dynamics we formulate a half-collision model for the rotational excitation of the CD3 fragment. We assume (1) the K quantum number is conserved upon dissociation; (2) the tumbling motion of the parent molecule, N-K, is converted into orbital angular momentum of the fragments; and (3) the ortho:para ratio (1 1:16) of the parent CD31 is retained in the dissociation process, because no C-D bonds are broken. These assumptions imply that the population found in a particular N,K state of the CD, can be described by PopCD3(N,K) =
Pop,C,2i(K) gCD3(N,K)ProbCD3({Zf+;, f ) EgCD'(N,K)ProbCD3(F=g+, f ) (3) N
Here PopCD3(N,K)is the pulation in a particular N,K state of the methyl radical, PopE$(K) is the population of a particular K state of the parent methyl iodide (summed over all populated N states) for the temperature of the molecular beam, ,&'(N,K> is the degeneracy of the N,K rotational state of the methyl f) is the probability that a methyl fragment and ProbCD'($=:+, radical born in a particular N = K state obtains tumbling angular momentum, Ah', as the molecule dissociates, thus ending up with N = K U units of angular momentum. This gain in angular momentum is in tumbling around a C, axis and is of value N K . Note that by using the degeneracy factors for free CD, we are assuming a statistical distribution of CD3 product states. This includes the even/odd alteration of the K = 0 manifold which originates from the planar nature of CD, and is clearly evident in the spectrum of Figure 2. Taking the populations in Table I and dividing them by the appropriate degeneracies and methyl iodide K populations for a 15 K beam temperature, we obtain a set of probabilities of pop-
+
(37) Choi, S. E.; Bernstein, R. B. In Special Issue on the Dynamics of Molecular Processes; Isr. J . Chem., in press.
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4843
Photofragment Imaging
TABLE 11: Rotational Energy Distribution of the Methyl Fragment from the 266-nm Dissociation of CDd and CHd CD3" CD3P CH3' ortho para total ortho para total ortho para total ortho population 11/27 16/27 1 11/27 16/27 1 112 112 1 112 3.67 3.64 6.0 6.1 6.1 2.16 2.71 2.74 5.2 (N) 3.60
CHJd para
total
112 5.4 1.2 18.4 8.1
1 5.3 0.6 14.9 4.6
1.33 0.98 0.5 1.4 1.o 0.2 1.26 0.73 0.1 (K) 0.48 90.9 94.0 14.5 16.1 15.4 136 104 120 11.4 (E(N,K))/cm-' 98.5 5.0 4.4 4.3 5.8 5.1 2.8 8.5 5.1 1.0 (CKZ)/cm-' 3.5 "Obtained from the populations of Table I. 60btained assuming a part:nt rotational temperature of 15 K and orthofpara conservation in the cooling of the parent beam expansion. 'Obtained from the extended analysis of the spectra and populations of Table I of ref 26 (see text). dObtained assuming a parent rotational temperature of 15 K and ortho/para conservation in the cooling of the parent beam expansion as applied to the data of ref 26.
~50.40 1
?
0.35
0.20 d
9 0.15
0
0.05 U
:0.00 0
1
2
3
4
5
0
0
6
7
8
AN Figure 3. Probability distribution for rotational energy transfer upon dissociation as defined by the half-collision model described in the text. The probabilities are obtained from analysis of the spectrum in Figure 2 and lead to the populations in Table I.
d a t i n g the rotational states in the dissociation process. The degeneracies must be normalized such that for a given starting K state the sum of e D , ( N , K )ProbCD3($i+, f ) over all possible N is I . This ensures conservation of the parent methyl iodide ortho:para ratio. For instance, at 15 K 33% of the parent methyl iodide is in the K = 0 state. These molecules can obtain rotational excitation about a C2axis in the dissociation process and populate a range of N states of the methyl radical with K = 0. The sum of these states must represent 33% of the product molecules. The results of this analysis are shown in Figure 3 where ProbCD3(Gi+, f ) is plotted versus AN. This plot is the probability distribution for obtaining rotational energy upon dissociation. All of the points fall on the same curve (to within our ability to determine the populations), implying that the probability of obtaining rotational energy is independent of starting rotational state K . One would expect the energy-transfer function to be independent of the starting K because the dissociation is rapid compared to the rotational frequency. Our data is only sensitive to K < 5. Populations for states with their K values larger than 5 are adjusted to fall on the curve of Figure 3 and are marked by asterisks in Table I. These high K populations are typically so small that the shape of the calculated spectrum is insensitive to their exact value. We note that the probability of transferring rotational energy upon dissociation declines almost exponentially with AN. The amount of rotational energy transfer upon dissociation is small, with the probability of AN = 6 an order of magnitude smaller than AN = 0. The fact that the data falls on a single curve suggests that the parent molecular beam is indeed 15 K. Using the energy-transfer function of Figure 3, we find that the simulated spectrum fit the data only when a molecular beam temperature near 15 K is used. The analysis was performed using molecular beam temperatures of 10 and 20 K, and in those cases the data indicates that if the temperature is correct then the transfer function must not be independent of the starting K state. Now that we have quantified the amount and distribution of rotational energy obtained by the methyl radical upon dissociation
of methyl iodide by 266-nm photons we turn our attention to the origins of this energy. There are two sources for rotational excitation of the methyl fragment. First, the zero-point, I-C-D3 bending vibrational energy (for CD31the classical turning point is about l o o bent) can be transferred into rotational excitation, the extent of which can be calculated by modeling the process as a sudden dissociation of a linear pseudo triatomic molecule. Applying the treatment of Morse and Freed38yields the average rotational excitation in the tumbling motion of the methyl fragment, ( E ( N , K ) ) - ( C p ) , assuming conservation of angular momentum during the adjustment of the fragment planar structure, as 40.3 and 64.3 cm-' for CD, and CH3, respectively. A second origin for rotational excitation can arise from the curve crossing between the 2Al(3Qo)surface to which the excitation (at 266 nm) takes place and the 3E(IQ,) surface. Recently Morokuma and c o - ~ o r k e r scalculated ~~ these low-lying surfaces for methyl iodide. The minimum energy configuration for the two A' curves (from 2A, 3E) at the conical intersection is at a bent geometry. The A' surface, correlating with the I(2P3/2)channel (I) has an energy difference of 43 cm-' between the minimum energy geometry at 0 = 6.4" and the linear geometry at 0 = Oo, where 0 is the angle between the C-H3 axis and the linear I-C-H3 geometry. The other A' surface correlates with the I(zP,/2) channel (I*) and has an energy difference of 18 cm-1 between the minimum and linear geometry. These bent surfaces will lead to exertion of a torque that will create additional rotational energy in the fragments, less for the I* channel than the I channel due to the magnitude of the bend for the different states and the shape of the potentials after the crossing. By comparing the estimated values for the rotational excitation due to zero-point motion of 40.3 cm-' for CD, and 64.3 cm-' for CH3 to the experimental values of 90 and 114 cm-l we conclude that about half of the energy rotation in the fragments comes from dynamics occurring at the curve crossing and about half from the zero-point motion of the parent methyl iodide molecule. Our analysis should be compared to the result of Loo et al.13J4 They fit their CD, spectrum with a normal Boltzmann temperature of 105 K but artificially increase the population of the K = 0 levels by a factor of 6, resulting in an ortho:para ratio of 1.8:l (the expected ratio from the parent molecule is 11:16). For C H 3 a rotational temperature of 120 K and a boosting factor of five for the K = 0 levels was used to simulate their measured spectrum. This gives a ortho-para ratio of 2.6:l in contrast to the parent ratio of 1:l. Using the temperatures of Loo et al. and the enhancement factor for the K = 0 levels we calculate using eq 2 an average rotational energy of ( E ( N , K ) ) for (CH,) = 104 cm-' and ( E ( N , K ) ) for (CD,) = 94 cm-', which is close to the values obtained from analysis of our data. The fact that such different fitting procedures arrive at similar average energy content for the fragments is somewhat reassuring but the details of which states are inferred to be populated by the dissociation are quite sensitive to the fitting procedure used. Correct determination of the populations is important in order to understand the dynamics of dissociation as is demonstrated in Figure 3. Because the methyl fragments are highly aligned by the photodissociation process, the populations can also be obtained,
+
(38) Morse, M. D.; Freed, K.R.J . Chem. Phys. 1981, 74, 4395.
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The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
I -
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O(5) Line of 0; Band 2; Band Q Branch
1; Band Q Branch
Figure 4. Measured two-dimensional images and reconstructed three-dimensional images for three different state-selected CD, fragments. The left column is obtained with the probe laser set on the O(5) transition of the 0; band, the middle column is obtained with the laser set to the 2; band (at 60 98 1 ~ m - ' ) ,and ~ ~ the right-hand column is obtained with the laser set on the Q branch of the I : band. The second row shows the experimental two-dimensional images. The first row gives an intensity profile of a line through the center of the image along the direction of the polarization of the photolysis laser beam. The smaller outer and larger inner peaks correspond to CD, fragments born in coincidence with the I(2P3/2),I, and I(2P1/2), I*, respectively. The third row shows a cross section through the reconstructed three-dimensional image. Rotation about the horizontal axis of the image, along the polarization axis of the photodissociation laser beam, generates the three-dimensional distribution. The fourth row shows an intensity profile along this symmetry axis. Note that integration of the three-dimensional distributions of row 3 along the ordinate recovers the intensity profiles shown in row 1 .
along with extra information about the dissociation dynamics, by analysis of the dependence of the ion signal on the population ~ ~shall direction of the ionization laser. In a future p u b l i ~ a t i o nwe report our polarization measurements of the individual rotational lines. The populations obtained here from a magic angle spectrum are consistent with those found from the polarization study.
Black and Powis'6 have obtained nascent rotational populations of methyl following 266-nm photolysis of room-temperature methyl iodide. They find most of the population is in the highest K levels for a given N value, in contrast to our findings for cold parent molecules. This observation is reconciled to our observation of low K levels being most populated by conservation of the K
Photofragment Imaging quantum number between parent and fragment. At room temperature the higher K levels of methyl iodide for a given N manifold are most populated. Summarizing, from the rotational analysis we conclude that approximately half of the rotational excitation can be accounted for by transformation of the zero-point bending vibrational energy of the parent into rotation of the methyl fragment. The remaining amount of rotational energy into the I* channel may originate from a small bending induced at the crossing of the IQ0 and 3Q0 surfaces. W e also determine the shape of the energy-transfer function which dictates the observed rotational state populations and find that gain of rotational energy is independent of starting K state for low K . Predissociation and spectral congestion make rotational analysis of the higher u2 transitions impractical. The S branches of the higher bandsz9 are similar in appearance to those of the 0; band; thus we believe that the amount and partitioning of rotational energy in the excited vibrational levels of uz is roughly similar to that of c = 0. Observation of u I Symmetric Stretch Excitation. A small feature, marked by the arrow in Figure 2, is seen in the REMPI spectrum of the 0; band near P(6). Velocity-selected REMPI (scanning the frequency of the ionization laser while observing only that part of the detector corresponding to a single dissociation channel) reveals that this weak band corresponds to predominantly faster moving fragments which we assign to the I channel of the 1 I Q branch. This is borne out by inspection of an image, shown in Figure 4, taken while resonant on the 1 ! band. Scaling of the ground and electronic state energies for the symmetric C H stretching mode of CH, by the Teller-Redlich 2-'12 isotope dependence predicts a 64-cm-l shift of the l ! band.2639 The assigned 1 band red shift from the 0; band agrees to within a few cm-I with the red shift observed for the C H , 11 transition. Relative to the 0; band the 1; band appears stronger in the CH, REMPI spectrum than in CD, sqectrum. Direct comparison of the strength of u l versus v2 excitation is not possible due to the unknown Franck-Condon factors, but we believe that the 1; band is too strong to result from the dissociation of u l = 1 parent molecules. Dissociation of CH,I with 193-nm photons produces greater amounts of u1 excitation in the resultant CH3.@ An image taken on the 1 band (right-hand column of Figure 2) and analyzed as described in the following section reveals an I / I * ratio of 1.3 f 0.2. This is a lower limit since the Q branch overlaps the tail of the P(5) and O(3) transitions of the 0; band which has only inner ring, I*, character. [ / I * Branching Ratios for u2 u = 0, I , 2,s. Three representative measured images are shown in the second row of Figure 4. Column a, the O ( 5 ) transition of the 0; band, shows very little I channel (fast CD,) signal, while columns b and c, Q branches of the 2: and 1; bands, respectively, show increasing population of the fast channel. Above the images, row 1, are plots of the intensity through the center of the image, parallel to the polarization vector gf the photolysis laser. Below the images, row 3, are the three-dimensional reconstruction of the images using the inverse Abel transform as described above. Shown below the reconstructed images, row 4, are intensity profiles taken on a line through the poles of the three-dimensional reconstructions. Note that the two channels are completely separated in the reconstructions. Rotation of the reconstructed image around the central axis will generate the three-dimensional distribution of ionized fragments. Branching ratios are calculated from the intensity profile of the two-dimensional image, row 1 of Figure 4, by first subtracting the (extrapolated) tail of the fast channel from the base of the slow channel, multiplying the fast component by 1.69 to correct for its additional spread of the ions in space (proportional to the velocity squared, with the fast/slow velocity ratio = 1.3), and then
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4845 dividing the two signals. This procedure is insensitive to the resolution of the laser and the Doppler width of the transition.25 A comparison of the branching ratios obtained by the procedure outlined above with that found by analysis of the intensity profile through the three-dimensional reconstruction yields equivalent ratios. The analysis of the data from the two-dimensional image is more convenient. I/I* ratios obtained from images recorded while the ionization laser is resonant on the Q branches of transitions originating from v2 L: = 0, 1, 2, and 3 are (0.04 f 0.02), (0.09 f 0.03), (0.27 f 0.08), and (1.4 f 0.2) respectively. The latter two values are averaged from the Au = -2 and Au = 0 transitions. Overlap with unassigned bands causes uncertainty for the Au = 0 transition^'^^^^ as does overlap with strong methyl-producing methyl iodide resonances for the Au = 2 transitions. These ratios differ from those we reported in an earlier preliminary reportz5 because of the inadvertent omission of the 1.69 (1.32) factor due to the different velocities. Loo et al.I2-l4 report I / I * values of
