4364
J. Phys. Chem. 1995,99, 4364-4372
ARTICLES N,K Rotational Level Populations of CD3 from the 266 nm Photofragmentation of IJKM) State-Selected CD3I Dae Young Kim, Nathan Brandstater, Leonard Pipes, Timothy Garner, and Delroy Baugh* Department of Chemistry and Biochemistry, University of Califomia, Los Angeles, Califomia 90024-1569 Received: August 30, 1994; In Final Form: November 22, 1994@
The photofragmentation of IJKM) = 1111) state-selected CD31 was performed at 266 nm. The INK) rotational energy level distribution of the resulting vibrationless CD3 photofragment was determined using ( 2 1) resonance-enhanced multiphoton ionization. The INK) distribution showed that the dominant mechanism during the dynamics on the excited 3Q0surface was A K = 0 scattering between the initially excited parent CD31 and the CD3 fragment, i.e., no relative orbital motion about the original C3 axis of the parent, in agreement with previous non-state selected experiments. In addition, smaller but significant amounts of A K = f 3 scattering also occurred. The outline of a model is provided which attributes the effect of nonhelicity conservation and the A K = f 3 propensity to scattering from regions near the conical intersection between the 3 Q and ~ 'QIsurfaces and in particular to the coupling term between these surfaces. It is therefore suggested that the relative population of the CD3 INK) energy levels for a given N might provide a quantitative measure of the strength of the nonadiabatic coupling between the two surfaces that correlate asymptotically to the 2P3/2 and 2 P ~ /spin-orbit 2 energy levels of the atomic iodine photofragment. The experimental INK) rotational distributions are also compared to two recent quantum calculations and are found to be in good agreement for the total scattering into all K levels for a given N . Experimental evidence is also provided, although not analyzed, for the first observation of a detailed photofragmentation differential cross section.
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I. Introduction
One of the primary objectives in the field of experimental molecular photofragmentation dynamics is full initial quantum state selection.'-2 This means, for excitation from a known electronic potential energy surface (PES), selecting not only the initial rovibrational energy level IJK{v}) (where J is the total parent angular momentum, K is its projection in the molecular frame, and { Y } is the set of all relevant vibrational quantum numbers), but also the initial magnetic quantum number M as well. This would allow "active control" of the photofragmentation scattering procem2 Moreover, if the photofragment products are also detected in a quantum state-specific manner, such experiments would truly be quantum state to quantum state measurements. Here we report our results on the rotational
energy level populations of CD3 photofragments in their ground vibronic level resulting from the 266 nm photodissociation of IJKM) state-selected (i.e. polarized) CD31(eq 1);the multipole moments for each CD3 rotational level will be reported el~ewhere.~ Although only energy level populations are reported here, we believe this to be the first example of the direct dissociation of a IJKM) state-selected molecule to molecular products that are state-specifically detected as opposed to when only the initial energy level is selected and products are statespecifically detected (e.g.,in the pioneering rovibrational energy level selected photodissociation of H z O ) . ~ ,Measurement ~ of ~
'Abstract published in Advance ACS Absrracrs, February 1, 1995.
the state-specific CD3 angular distributions would then yield the maximum amount of information possible from a photofragmentation experiment (i.e., the magnitude and the phase of the transition dipole or T matrix) as was shown in calculations by Seideman: and in earlier work by Balint-Kurti and Shapiro? These measurements are now in progress in our laboratory and are only in part reported here. The photofragmentation of methyl iodide in the region of its first absorption maximum -260 nm, the A band, has been extensively studied both experimentally*-'8 and the~retically.'~-~* The primary reasons for this ever-increasing level of interest is the apparent simplicity of the dynamical models required to describe the fragmentation of this rather "large" molecule.* Indeed, methyl iodide has become a model system on which to test the most recent photofragmentation theories as was recently demonstrated in a multidimensional (5 degrees of freedom) dynamical wave packet calculation by Kosloff and co-workers.22 Central to this supposed simplicity is the heretofore assumed preservation of the C3 symmetry axis during excitation between the ground PES X('A1) and the excited ACQo) adiabatic surface (Le., a parallel transition), at least in the Franck-Condon region, and the consequential conservation of the K or helicity quantum number during the evolution of the fragmentation process on the adiabatic excited PES between the CD31 parent and the methyl and iodide fragments.*-"~~~-*~ Indeed, the conservation of K is assumed to hold even after the crossing from the initially excited 3Q0 diabatic surface, which correlates to the Z(2Pl,z) channel, to the 'QI diabatic surface, which correlates to the I(2P3/2)channel, at the intersection between these two surfaces. However, since one photon excitation via the A-band continuum necessarily precludes rotational resolution, the conservation of K could only be inferred.*-'* If K is indeed conserved in the
0022-365419512099-4364$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 13, 1995 4365
N,K Rotational Level Populations of CD3 n
.-C e
-
v
.-A 5e
v)
deo#ra
C
U
co C ._ m
. .
,
.
2.60 2.64 Time Of Flight (Ps)
2 ( I dipole fEld)
IhermrlMdcculph (with anriclusrn moui)
LIKM>seleclcd Molecular &am
Figure 1. Schematic of the experimental arrangement. The inset shows the CD+3 ion time-of-flight from the (2 by the 266 nm photolysis of II 1 I ) state-selected CD3I.
photofragmentation of methyl iodide, then by selecting the initial IJKM) state of the parent only the same K level should be populated in the methyl fragment. We have used the UCLA electrostatic hexapole to select the 111-1) and the 11-11) rotational states of CD31(Le., the initial molecular state is ideally characterized by the density matrix &Jj) = I/*{ 11- 11)(1- 11I 111-1)(11- 1I}) and detected the CD3 fragment using ( 2 1) resonance-enhanced multiphoton ionization (REMPI).
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II. Experimental Section Only a brief description of the experimental setup (Figure 1) will be given here; a complete discussion can be found elsewhere.23 A 400 ms-', -100 ps pulsed beam of 5% CD3Y Xe was state-selectively focused by the three-lens UCLA electrostatic hexapole source 380 cm downstream from the exit of a pulsed valve (PO= 800 Torr, d = OS"), into a 1-2 mm diameter spot in the photofragmentatioddetection chamber (2 x Torr). The focused molecular beam is crossed in the photofragmentatioddetection chamber at 90" by collinear, counter-propagating photolysis and probe laser beams. Both lasers were linearly polarized, and their polarization directions were independently controlled by i1/2 plates. For the one photon dissociation of CD31the electric vector of the linearly polarized (calcite polarizer) 266.2 nm photolysis laser (1.7 mJ/pulse focused with a 1 m lens) was aligned parallel (AM = 0) to the electric vector of a homogeneous dipole field (210 V/cm)-the 2 direction in Figure 1-which was used to adiabatically orient the molecular dipoles after the molecules had exited the stateselecting hexapole field. The electric field vector of the linearly polarized probe laser (2-3 mJ/pulse focused with either a 30 or 50 cm lens) was aligned at varying polar angles 0 (0= 54.7" in Figure 1) with respect to the experimental 2 axis. The ( 2 1) REMPI signal intensity, I(N,K), from each CD3 INK) rotational energy level can be written as24
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I(N,K) = C(det.)n(N,K)x A@,K)C(N,K:O)
(2)
k.*9
Here C(det.) is an experimental sensitivity constant which includes the laser power dependence, detector efficiency, etc., n(N,K) is the population of the rotational level INK), (A:) are
+ 1) REMPI of CD3 produced
the moments which describes the distribution of N (the rotational angular momentum of CD3) averaged over electron spins (ie., are the moments of the reduced density matrix ,o(N,K) of the CD3 fragment), are the two-photon line strength moments for each INK) level and the sum extends over rank k up to 4 (twice the spin of the two photons) or 2N, or (Wj 2 ) for velocity integrated cross sections, whichever is smaller, and over components with Iql Ik. Since the M state of the parent is selected, all 2N ranks of (At) can be measured even if I(N,K) results from ion signals that are integrated over all CD3 velocities as long as N IJmax= Ji 1. This is one of the main differences, and in our case an advantage, of JJKM) stateselected experiments versus experiments with unpolarized parent molecules, since in the latter case moments of ranks higher than 2 can only be obtained from angle-resolved product-state mea~urements.2~ The zero components (q = 0) for each rank are the only moments that are allowed in these measurements since the experimental geometry is cylindrically symmetric about the dipole field and the polarization direction of the photolysis laser, Figure 1. Also, no odd-ranked moments can occur for the N distributions since the initial parent rotational angular momentum vector is only aligned and not oriented (Le., as characterized by the moments of @(Ji)). Furthermore, since the photolysis laser is linearly polarized, it cannot impart any net angular momentum orientation to the parent molecule, i.e., introduce odd-ranked moments. Moreover, only the even ranks (0, 2 , and 4) can be measured with linearly polarized photons in (2 1) REMPI without angular resolved detector of the photoelectrons. Therefore only the population, n(N,K)(A: = l), and the alignment moments A i and A: can be measured. The highest rank (k = 4) associated with the maximum total angular momentum therefore limits complete characterization in the present experiments to only two product rotational levels: those with the rotational quantum numbers N = 1 and 2 for our angle-integrated IJKM) state to IJKM) state cross sections. Prior to entering the state-selecting hexapole, the pulsed CD31 molecular beam was skimmed and chopped into 40 ps pulses for the best speed resolution in some experiments and left unchopped for others. Since the signals were 4 times larger
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Kim et al.
4366 J. Phys. Chem., Vol. 99, No. 13, 1995
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Voltage (kV) Figure 2. Experimental focusing curves obtained via the CD3I+ ion peak and the optimum simulation. The inset is the time-of-flight mass spectrum of CDJ produced by single laser excitation at 339.1 nm with the hexapole set to -6 kV.
for the unchopped beam, most experiments were performed in this mode. The chopped beams gave better CD31 [ J K M ) state resolution, although the unchopped beams also provided sufficient resolution to clearly resolve different IJ K M ) rotational states as can be seen in Figure 2. The experimental focusing curve in Figure 2 was measured by recording the CD31f ion signal-shown in the inset time-of-flight (TOF) mass spectrum-generated by using the probe laser alone for (2 1) REMPI at 339.1 nm via the Q-branch of the strongly predissociative 6; vibronic band of CD31 as a function of the hexapole rod voltage. Spectra are recorded by setting the hexapole rod voltage to -6.0 kV, the peak of the 111-1) and the [ 1- 11) states, hereafter referred to as the 1111) state. The simulated focusing curves were obtained as previously described,26except that here the (2 l ) REMPI rotational line strengths will affect the relative peak heights for the various states presented in Figure 2.27328The hexapole voltage at which states with a given KMIJ(J 1) value and a specific speed are focused was determined by treating the hexapole as a thick lens.26 All states with a given IJK) value were then weighted by their relative thermal populations, including all degeneracies that arise due to nuclear spin statistics,28 and the resulting distribution was convoluted with the velocity distribution of the incident molecular beam. The temperature characterizing the relative population was then adjusted until the best fit to the experimental focusing curve was obtained. The optimized fit to the focusing curve gave a beam temperature of -6 K. It was also assumed that the room temperature ortho:para ratio is maintained throughout the supersonic expansion; this is consistent with the results from prior experiments in our laboratory on the state-selective focusing of ND3.27.28
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111. Results
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The asymmetric TOF distribution of the (2 1) REMPI generated CD3+ ion signals, obtained with both the probe and photolysis lasers (Figure 1 inset), definitely shows that the parent CD31 is indeed IJKM) state-selected. This was also clearly demonstrated by Bemstein et al. for the I atoms produced from the 286 nm photofragmentation of CH31.29 The two outer peaks of the CD3+ ion signals correspond to fragments resulting from
the 266 nm photolysis beam and the -333.8 nm probe together, while the inner peak results primarily from multiphoton processes associated with the probe laser alone. We were clearly able to distinguish, and thus separate, the CD3+ ions resulting from these two different processes. Moreover, the intensity of the CD3+ ion signal resulting from probe laser fragmentation was significantly reduced, and in some experiments completely eliminated, by using an iris to decrease the probe laser spot size on the focusing lens. This reduces the incident probe laser fluence and is used to control signals from processes requiring more than three photons. Contrary to the implications of the semiclassical models assumed p r e v i o ~ s l y , ~the ~ .asymmetry ~~,~~ of the CD3+ ion TOF distribution produced from the photodissociation of CD31, followed by (2 1) REMPI of the CD3 radical, reflects not only the initial laboratory frame (dipole) orientation of the CD31 molecule (Le., iodine atom in the direction of the dipole field vector), but also the angular distribution of the CD3 velocity resulting from the coherent excitation of scattering wavefunctions with total angular momentum J = l and 2 ( i e . , resulting from transitions AJ = 0,l; AJ = -1 is not allowed since AM = 0 and IMII = 1) on the 3QoPES and includes interference between these total angular momentum states. Note that CD3 fragments that correlate with either Z(*P1/2) or z(2P3/2)and that are in a single INK) level travel at a single speed, i.e., have a A function speed distribution in the center of mass frame since they result from photofragmentation of a state-selected CD31parent which has a specific energy and therefore the peak shapes are due solely to the different directions of the CD3 velocity and not to distributions in its magnitude. Also, since the velocity distribution of the parent CD31is very narrow (Le., Av/v 0.01) with an angular spread of 1.6 x steradians (as determined from the acceptance aperture of the hexapole lens and the distance from the exit aperture of the hexapole to the detection volume), the center of mass velocity distribution can be known with high precision. The TOF of the CD3+ ion signal shown in the inset in Figure 1 is then in essence identical to the state-selected angular distribution of the CD3 photofragments in the laboratory frame, i.e., the photoionization process is not expected to significantly change the angular distribution of the CD3+ ions from that of
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J. Phys. Chem., Vol. 99, No. 13, 1995 4367
N,K Rotational Level Populations of CD3
n
.-E
v1
-
4
3-
a
1
I
0
Y
E
; I *
I
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5
-$ W
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I
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1
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333.3
333.4
333.5
333.6
333.7
333.8
Wavelength (nm) Figure 3. C D ~ ( V = ” 0) (2
+ 1j REMPI spectrum obtained from the 266 nm photolysis of 1111) state-selected CD3I.
the neutral CD3 photofragments. The INK) level selected CD3+ laboratory-frame velocity distribution therefore directly reflects the center of mass angular distribution (Le., the IJKM) to IJKM) state or detailed differential cross section) shifted in the direction of the molecular beam by -400 d s . The state-to-state integral cross sections reported here are derived from spectra such as those shown in Figure 3. This (2 1) REMPI spectrum of the R(AN = f l ) and S(AN = f 2 ) rotational branches of the 0; vibronic band of the corresponding (3p2A2 2p2Ai) electronic transition was recorded at 0 = 54.7” where p‘, = 0 (Le., only the population and hexadecapole moments can affect the line intensities). Many such spectra were recorded by integrating the area under the outer peaks of the CD3+ ion signals in the TOF spectrum displayed in the inset in Figure 1 which, as mentioned above, results exclusively from the action of both the pump and probe lasers. Indeed, the CD3+ ion signal generated solely by the probe laser drops precipitously at wavelengths away from the Q-branch maximum (333.84 nm), which is not shown. Some spectra were therefore recorded by integrating over the entire CD3+ TOF distribution and, except for slight increases in the Q-branch intensity (typically less than 5%), these spectra differed little from those recorded by integration over only the two major peaks in the wings of the TOF distributions. All recorded spectra were analyzed on a line-by-line b a s i ~ .The ~ ~resulting ~ ~ ~ INK) rotational energy populations were then averaged and are presented in Figure 4A. The R and S, and the P(AN = -1) and O(AN = -2) branches were recorded separately in some spectra; the 0 and P branches are not shown. This was done in order to avoid any long-term drifts that might occur during the course of recording a spectrum, which required more than an hour per scan: 200-400 spectral points; 200-400 laser shots per spectral point at 10 Hz. This level of signal averaging was necessary in order to achieve reliable signal to noise levels. Also shown in Figure 3 is the corresponding simulated spectrum using the populations obtained from the line-by-line analysis. Clearly there is excellent overall agreement between the simulated and the experimental spectra. Again, since 8 = 54.7”,the line intensities are not sensitive to A i and since A: by normalization is unity, only n(N,K) and A i were used to simulate the spectrum. Varying the A: values used in the
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simulations between the cases where the CD3 N vectors were on average aligned either parallel or perpendicular to the laboratory Z axis did not cause any significant changes in the simulated spectrum, Le., the line intensities for the various branches were all within 10% of values calculated assuming “maximum alignment” along Z,9 Le., IMN~= [Kl. Since these populations are determined from angle-integrated cross sections, maximum alignment is an assumption regarding the nature of the photofragmentation process. It would not be so in experiments where angularly resolved CD3 products were detected parallel to the polarization vector of the photolysis laser, since in this case detection is biased against CD3 fragments with lKl f l M ~ assuming l that K of CD3 is equal to the K of CD31. That is, the MN resolved differential cross section can be expanded in products of rotation matrices that depend on the direction of the fragment velocity and which are zero for detection parallel to Z, the polarization direction of the photolysis laser, except if MN = K . This was clearly shown in the photofragmentation theory developed by Shapiro and Balint-Kurti’ and more recently by Seideman.6 As was mentioned above, we are currently in the process of measuring A i and Ai; these values will then be used to redetermine n(N,K) values and any significant changes will be given el~ewhere.~ The averaged experimental INK) level populations presented in Figure 4A were within 10% of the populations derived from all spectra analyzed to date. As can be seen in the spectra in Figure 3, rotational levels up to N = 5 were easily discernible (and in the 0 and P branches and other more recent spectra up to N = 7 and higher).3 Also, note that although the initial CD31 state was selected to have 1K1 = 1 (with better than 94% certainty at 6 kV, Figure 2) and that while CD3 1KI = 1 levels were dominant, levels with lKl f 1 are also significantly populated, approximating experimental populations in Figure 4A. There was a total contribution of -6% (less in the chopped beams) from all parent molecules in states that have no first-order Stark shift, Le., states with K = 0 and/or M = 0, which were thus not state-selectively focused and from states with the product K M > 0 which were defocused. The contributions from parent states with 1K1 # 1 is expected to be well within our experimental error of -10%. Moreover, since the beam temperature was -6 K, it is unlikely that CD31 molecules in levels with lKl 2 2 could have made any
4368 J. Phys. Chem., Vol. 99, No. 13, 1995
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Experimental
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Expcrimcntal
--
0.75
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State INK) I
H 0.75 --
.-
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a 2
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PJ
Experimental Theoretical (Kosloff et al.)
0.5
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2 0.25
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Figure 4. Experimental CDJ rotational distribution (A) from the 266 nm photolysis of 11 1 I ) state-selected CDJI which is compared, respectively, in B and C to the theoretical results of Guo and Kosloff et nl.
significant contributions to the spectrum shown in Figure 3, since their thermal populations were low-definitely less than that of the J = 2, K = 2 level which occurs at about -4.3 kV, Figure 2. It is also possible, although unlikely, that CD3 radicals in rotational levels with IKl = 2 were populated from an overlap of the 1222) peak at (-4.4 kV) with the 11 1 1) peak (-6.1 kV), see Figure 2, but the relative number of parent molecules in the 1222) state at 6 kV is much smaller than the overall CD3 population that is present in rotational states with lKl = 2 (Figure 4A). This argument holds true even more for CD3 fragments in the IKl = 4 rotational levels, since at the beam temperature of 6 K parent CD3I in states with K = 4 (e.g., the 1444) which occurs at -3.7 kV) were not populated.
IV. Analysis So with the caveat that the values of A;',(N,K) used in our analysis might cause the value of n(N,K) to be in error by -lo%, it is clear from the populations presented in Figure 4A that while the AK = 0 scattering channel dominates, significant contributions also apparently arise from channels with AK = K(CD3) - K(CD3I) = 1 and 3. We believe that the AK = 1 scattering channel (i.e., K(CD3) = f 2 ) results from scattering on the excited PES out of the initially excited K(CD3I) = -1 state by AK = +3 and out of the K(CD31)= 1 state by -3, giving rise to K(CD3) = +2 and -2, respectively. This is consistent with the preponderance of theoretical and experimental evidence supporting a primarily parallel transition CAK(CD3I) = 0) in the photoexcitation step at 266 nm from the CD3I ground 'AI to the excited 'Qo PES,8-13-19-22 and thus excited CD3I molecules should primarily have only one unit of rotational angular momentum about their C3 axis. If this is true then CD3
Kim et al. products with K = f 2 could not arise from perpendicular (AK(CD3I) = f 1 } transitions during photoexcitation at 266 nm and must result from AK(CD3) f 0 scattering during the "half-collision" on the excited PES(s). This means that the heretofore assumed conservation of the helicity quantum number during the dynamics on the excited PES(s) between the excited parent CD3I and the CD3 product appears not to be rigorous. This assumption was made in previous methyl iodide photofragmentation experiments and was justifiable because of the lack of initial K state selection.x-'O Indeed, the AK = f 3 effect was probably observed in previous experiments as well, although not recognized as such, particularly in the recent work of Nibler and co-workers.' I Their comparisons of the initial thermal rotational energy level populations for the CH3I parent with those of the u" = 0, CH3 photofragment produced by 266 nm light, clearly shows a strong propensity for AK = 0 and f 3 . However, these experiments were conducted under non-nascent conditions (ca. three collisions before detection), and collisional effects could therefore modify nascent distributions. All theoretical treatments of methyl iodide photodissociation have invoked helicity conservation during the dynamics on the excited PES. Since it is not immediately obvious from the spectra (Figure 3) which specific INK) level is populated, the occupation of such levels had to be determined in a systematic manner; below, K is used to represent both the f K levels. The procedure is similar to that used by Chandler et aL8 except that since the initial parent K level is selected, the analysis is more straightforward. First, the population in the N = 1 , K = 1 level, n( 1, I), was determined from the R ( l ) line since selection rules only allow Q (AN = 0), S, and 0 transitions from K = 0 levels, so this transition can only probe the K = 1 level. In addition, for N = 1 Ai = 0, R( 1) measures directly the n( 1,l) population at 54.7'. The population in the N = 2, K = 1 level, n(2,1), was determined next from the P(2) line since this transition is again limited by the selection rules to probe only the K = 1 levels. The population of the N = 2, K = 2 level is then determined from the R(2) and S(2) line intensities. The R(2) transition is sensitive to the populations in both N = K = 2 and K = 1 levels, while the S(2) line is sensitive to all three K levels for N = 2: K = 0, 1 , and 2. Since the population in the N = 2, K = 1 level is known from the P(2) line, this contribution can be accounted for in the R(2) intensity and the N = 2, K = 2 population can be determined. The S(2) line is then used as a check since the initial CD31state is K = 1 and is of para nuclear symmetry. Because the D atoms are not exchanged during the reaction, states with IKI = 3m, with m = 0, 1,2, ..., etc., which are of ortho nuclear symmetry, therefore cannot be populated. This argument is used to eliminate all ortho states from further consideration, so only para levels 1K1 3 m are allowed, starting from para CD31with IKI = 1. Therefore, even though the R(2) and S(0) transitions overlap, the latter makes no contribution to the line intensity since it probes the N = K = 0 level which is of ortho nuclear symmetry and is therefore not populated. The N = 3, K = 2, and K = 1 levels were then treated in a similar manner by first using the P(3) line which overlaps the zero intensity O(2) line and which is only sensitive to the N = 3, K = 1, and K = 2 levels. The P(3) line intensity is fitted with the relative populations obtained from the N = 2, K = 1 and 2 levels by adjusting the overall N = 3 population. The S(3) line is fitted next by adjusting the relative K = 1 and K = 2 populations until the best fit is obtained. The sensitivity of the R(3) line to both the overall N = 3 population and the relative K = 1 and K = 2 populations is then used to optimize n(3,2) and n(3,l). Finally, the O(3) line overlaps with the P(5)
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J. Phys. Chem., Vol. 99, No. 13, 1995 4369
N,K Rotational Level Populations of CD3 transition but probes only the n(3,l) population, so this transition was used as a final check of this population once the N = 5 levels were fitted. The same procedure was followed for the N > 3 levels, except that all K levels excluding the ortho levels had to be considered. In order to fit these high N levels we relied on the sensitivity of the various branches on the magnitude of K. In general the S branch is more sensitive to low K's, e.g., K = 0 and 1, than to higher K ' s , while the R branch is more sensitive to the population in levels with K > 2 . When allowed by the twophoton selection rules for AK = 0 transitions, the 0 and P branches have K-level dependences similar to that of the S and R branches, respectively. As an example, we will consider the N = 4 levels, K = 1, 2, and 4. As before, the same relative K = 1 and 2 populations for a given N are used to fit the intensity of the P(N f 1) line. For N = 4 we therefore used the same total population as in the N = 3, K = 1, 2 levels to fit the P(4) line intensity. The relative populations of the K = 1 and 2 levels were then adjusted to obtain the best fit to the O(4) line. Since the R(4) line is more sensitive to K = 4 than is the S(4), and since the P(4) and O(4) line intensities only reflect the K = 1 and 2 populations, once the latter two transitions were fitted, the magnitude of n(4,4) was increased until a best fit was obtained for R(4) without any significant changes in the S(4) intensity. Although the R(4) and S(1) lines overlap, this was not a serious problem because the K = 0 level was assumed not to be populated and n(1,l) was already known from R(1). If any final refinement was needed, the value of Ai(4,K) was adjusted, although in most cases the best fit to the observed line intensities were obtained with IMI of CD3 set equal to K. The condition of setting IMNI = K was referred to as the maximum alignment model by Chandler et aL9 However, under their experimental conditions (photolysis laser polarized in the direction of detection) MN is automatically equal to K of the parent CD31, as was mentioned earlier. The primary assumption in their model is therefore that K of CD3 is equal to K of CD31. If any torque is generated about the C3 axis of CD3I during the dissociation process on the excited surface, then K of CD3 would be different and this assumption no longer holds. Indeed, detection of CD3 parallel to the photolysis laser polarization direction would introduce a bias against detecting CD3 fragments with K not equal to K of CD31 since these fragments would have components in their velocity vectors in directions perpendicular to the detector. In our experiment, where the parent CD31was polarized and where final angles were integrated over, detection was sensitive to CD3 products in all states. Contrary to the case for the photodissociation of unpolarized parent molecules and angle-integrated cross sections,25moments of the photofragment rotational distribution of ranks greater than 2 could still be measured in our experiment. Also, since the initial CD3I was M-state aligned with its dipole oriented along the laboratory fixed Z axis, it is therefore not surprising that the average alignment of the CD3 rotational angular momentum vector N assumes its maximum value along Z. Of course, confirmation of this can only be obtained from spectra taken at polarization angles other than 54.70G3
V. Discussion In Figure 4B, we compare our experimental rotational distribution with the results from a recent 3-dimensional, pseudotriatomic quantum calculation by Guo.*' We have also compared our distributions in Figure 4C to those from a recent 5-dimensional quantum calculation by Kosloff and co-workers for CH31.22 Although the latter comparisons are necessarily qualitative due to the differences between CH31and CD31,they
Experimental 0 Guo
1
1
Id Kosloff et 01.
2 3 4 5 Rotational Quantum Number (N)
6
Figure 5. The experimental rotational distribution with the population summed over the K levels for a given N compared to the theoretical distributions of Guo and Kosloff er al.
are nonetheless insightful. The PES'S used in both calculations were based on the ab initio surfaces calculated by Morokuma et ~ 1 . , *and ~ therefore differences between the theoretical results reflect mostly differences between the respective models. The theoretical distributions were normalized to include 95 and 5% contributions from the Z*(2P1/2) and Z(2P3/2) channels, respectively. Our experiments did not distinguish the contributions from these two channels, although the I channel contribution to the CD3 v" = 0 populations are expected, from previous experiments, to be less than 5%.83'0 Since the theoretical rotational distributions were calculated assuming that the parent does not rotate about its C3 axis ( i e . , K = 0) and that levels with any quantum number N and the same K have populations n(N,K) that reflect the initial parent K or helicity quantum number distribution, Le., K is conserved. This behavior is shown to some degree in the rotational distributions of Chandler et al. where the assumption of helicity conservation was used to fit their experimental ~ p e c t r a . ~The .~ calculated n(NK = 0) distributions should then apply for any initial parent K as long as K 5 Nand energy is conserved. This implies that if the methyl iodide parent molecules are in a level with K = 2, then the methyl radical fragment cannot populate the N = 1 level or any other level with K f 2. Using this A K = 0 criteria and assuming K = 1 for the calculations, the theoretical and experimental distributions were then scaled to the rotational energy level with the maximum population, which was the N = 2, K = 1 level for all three distributions. The CD3 ortho levels were forbidden by the conservation of nuclear symmetry in our experiments and are therefore not shown in the Figure 4. The agreement between both theoretical distributions and that derived from the state-selected experiment was reasonable for the K = 1 populations. Due to the neglect of off-diagonal elements in the half-collision matrix which couple scattering states with different helicity quantum numbers, scattering into K states different from those of the methyl iodide parent was not considered and no comparisons can be made regarding AK t 0 scattering. The neglect of AK f 0 scattering in effect assumes that the projection of the orbital angular momentum of the relative photofragments along the original C3 axis of the parent CD31 is zero. That is, no torque is generated about the C3 axis of the excited complex during the dissociation. In light of this approximation, a more meaningful comparison would be to the total scattering into final states with rotational quantum number N , Figure 5. As expected, the agreement between experiment and theory is much more reasonable. The experimental distribution, however, still rises faster and falls
4370 J. Phys. Chem., Vol. 99, No. 13, 1995
Kim et al.
off more slowly than both theoretical distributions. The shape of the rotational distribution as a function of the quantum number N is related to the variation of the potential with bending away from the C3 symmetry axis and can be produced from zero-point bending motion and/or from the bending which occurs at the conical intersection between the excited surfaces. Although the shape of the experimental and theoretical distributions are slightly different, the average experimental rotational energy of -70 cm-’ is in excellent agreement with Guo’s average rotational energy -71.5 cm-I, which was calculated with the 5% contribution from the I channel, assuming K = 1 and that N,,, = 6 as was the case in the experiment. The only apparent disagreement between Gou’s results and our experiment is due to scattering out of the initially prepared helicity state and thus to the angular dependence of the excited PES, especially in the region of the conical intersection. The coupling term between the 3Qo(A‘) and the ‘Ql(A’) diabatic surfaces contains a periodic dependence, sin(3~), on the angle&) conjugate to the helicity quantum number.20.22This coupling term is here believed to be responsible for the AK f 0 (Le., AK = f 3 ) scattering on the 3QoPES in regions near the conical intersection. Inclusion of the nonhelicity conserving components in the scattering could be sufficient to bring the theoretical calculations into even better agreement with our experimental results although some adjustment to the model andor the angular dependence of the PES might also be necessary. Guo has also shown that 266 nm photodissociation produces CH3 that is rotationally colder than CD3.21 If this trend is also observed in future 5-D calculations for CD31, then this more extensive model should be in even better agreement with our experimental results, providing that the AK = f 3 n scattering channels are also included in the new calculations. The AK = &3n propensity rule has also been observed in the inelastic scattering of atoms from symmetric tops, e.g., NH3/ Ar, et^.^^ Since NH3 and CD3 have similar symmetries, C3, and D3h, respectively, it should not be surprising that final state interactions between the departing I atom and CD3 radical on the excited surface would produce similar effects. Indeed, this similarity between molecular photodissociation dynamics on the excited surface and molecular scattering was noted by Wilson and co-workers as early as 1969.33 Inelastic scattering experiments can lead to accurate information about the PES, in particular about those regions that are probed by the scattering process and that are the most sensitive to the ensuring dynamics, which in this case were regions in the vicinity of the conical intersection of the adiabatic 3Q0 and the ‘Q1 PES’s of CD31. Morokuma et aL20 has also pointed out in their classical trajectory calculations that the final CH3 rotational distribution for the I* channel is extremely sensitive to the nature of the PES at the conical intersection. It then appears that the AK # 0 scattering observed in our experiments might be a consequence of the coupling terms between the 3Qo and the ‘QI diabatic PES’s through the sin(3~)dependence at their intersection. The amount of scattering into the AK = f 3 n channels should therefore provide an accurate measure of the magnitude of these off-diagonal elements. This can be seen more clearly by an expansion of the excited potential in the body-fixed frame in terms of the spherical harmonics: (3) Here V(R) is the excited dissociative PES,R is the set of all nuclear coordinates, j and AK are the summation variables with AK = 0, f 3 , f 6 , ..., s j = 0, 1, 2, 3, ..., and AK is restricted to 3t3n by the C3 symmetry of the PES, C ~ A K are the all
important expansion coefficients which characterize the strength of the nth order scattering into the different AK channels, and &k(e,X) are spherical harmonics defined with the C3 axis of CD31 as the body-fixed Z axis and with 8 and as the polar and azimuthal angles of the vector connecting the CD3 center of mass with the departing I atom, respectively. Since the coupling terms have a sin(3~)dependence in Morokuma’s ab initio PES’q2Othese terms will be present for n > 0, and only the n = 1 terms are expected to be important. The n = 0 terms will yield the normal helicity conserving, zero-order AK = 0 scattering, while the n = 1 terms will give first-order scattering with AK = f 3 . Since the optical excitation step is primarily parallel and AK = K(CD3) - K(CD3I), for (K(CD3I)I = 1 only IK(CD3)I = 1, 2 , 4 are expected to occur, with the zero-order IK(CD3)I = 1 term being dominant. The zero-order terms therefore reflect scattering from a independent diabatic PES (Cjo) and the n = 1 terms reflect scattering due to the off-diagonal terms which couple the 3Q0 and the ‘QI PES’s (Cjf3). These latter terms are then clearly related to the populations in the (K(CD3)) = 2 and 4 levels for rotational quantum numbers N IIKI. More specifically, the ratio of the IKyI = 1 to the IKl f 1 populations are a measure of the relative strength of the off-diagonal terms which couple the diabatic surfaces that correlate to the Z(2P1,2)and the 1(*P3/2)spin-orbit states. These populations ratios therefore represent a quantitative experimental measurement of the nonadiabatic coupling between the 3 Q and ~ ‘QI surfaces at the conical intersection and is the fist such observation in the product rotational energy level distribution of a chemical reaction. This is significant since the strength of the nonadiabatic coupling can now be determined independently of the I:Z* ratio. Though it must be emphasized that while the off-diagonal elements can be used to calculate the ZZ* ratio, the relative CD3 IKl f 1 to IK/ = 1 level populations for a given N do not in general have a direct oneto-one correlation with this ratio. Indeed, the fact that the CD3 INK) level populations resulting from AK f 0 scattering during the “half collision” on the PES correlating to I* product is sensitive to the off-diagonal elements, which couple the 3Qo and ’QI diabatic surfaces, is purely a manifestation of the bending away from C3, symmetry in the region of the conical intersection. Once the C3, symmetry of the “half-collision” is broken the generation of torques parallel to the C3 axis of CD3 is no longer forbidden and scattering between CD3 levels with different K occurs subject to the constraint of C3 symmetry on the PES,eq 3. The index J in eq 3 is related to the scattering into levels with different rotational quantum numbers N . This is particularly important for the zero-order terms, since they give the variation of the excited PES’s with 8, the polar angle. The steepness of this dependence gives the amount of torque experienced by the CD3 during the dissociation process and the corresponding changes in the relative orbital angular momentum necessary to balance the CD3 rotation. It is this correlation between the CD3 rotation and its relative orbital motion with the I atom about the original CD31center of mass which must necessarily bias angularly resolved final state distributions against products in states with velocity components perpendicular to the direction of polarization of the photolysis laser as was stated earlier. Our rotational state distributions are also in reasonable agreement with recent experiments where the methyl radical n(N,K) distribution was measured following the 266 nm photofragmentation of methyl iodide, in particular those of Chandler and co-worker~,~*~ and Nibler and co-workers.” However, since the initial parent quantum state was not selected
x
x
N,K Rotational Level Populations of CD3 in these experiments and the parent states were only characterized by the molecular beam temperature, which was used as an adjustable fitting parameter in some case^,^.^ it is difficult to make direct comparisons regarding the complete n(N,K) distributions. The experiments of Nibler et al. are, however, an exception." They correlated their CH3, K-resolved n(N,K) distribution with the measured CH31 energy level populations in their molecular beam. Although Nibler et al. studied the photofragmentation of CH31, it is worthwhile comparing their K(CH3I) to K(CH3) correlations. In their experiments they found an average change in the helicity quantum number between the parent and the methyl fragment of -1.1. However, they assumed that the CH3 radical experiences three collisions before detection, but that the first collision was not effective in changing K. Since our experiments are conducted in a vacuum of Torr and products are detected within 10 ns of being born, the CD3 products should not have experienced any collisions and are thus truly nascent. Nonetheless, we observe an average change of 1.2 quanta of K in going from the initially selected J = K = 1 parent energy level to N = 4 and 5 levels of the CD3 fragment and -0.7 overall (see Figure 4). It is therefore quite probable that the AK = f 3 propensity was observed by Nibler et al. but was not interpreted as such due to the possibility of post photofragmentation collisions and thus non-nascent product rotational distributions. In the experiments of Chandler and co-workers, they assumed that a CD3I temperature of 15 K gave the best fit to their experimental n(N,K) distributions, as was stated above, while still being consistent with the assumption of AK = 0 scattering.8 They also reported that CD3I temperatures of 10 and 20 K were inconsistent with their experimental distributions and helicity conservation, yet Nibler et aL1' reported that a temperature of 21 K gave essentially exact agreement with Chandler's et al. reported distributions. If Nibler et al. are correct, it is therefore possible that the AK = &3 propensity was also observed in the experiments of Chandler et al. but was not discovered because of their fitting procedure. In any event, Chandler et al. reported the average rotational energy gained by para, v" = 0 CD3 from para CD31(15 K) was -75 cm-' as compared to -70 cm-' in our experiments, and both are therefore in good agreement considering the very different experimental conditions.* Loo et al.Io reported an average CD3 rotational energy of 109 cm-I. They also claimed to have a 15 K CD31beam with an average rotational energy of 16 cm-', therefore making the CD3 rotational energy gain -94 cm-I, which is too high. This is not surprising since the average rotational energy of Loo et al. was obtained from a K = 0 enhanced Boltzmann distribution which is sensitive to all rotational levels and in particular to the high-energy K = 0 levels. We note that Chandler et aL8 recalculated the average rotational energy of Loo et al., including the K = 0 enhancement, and obtained a value of -94 cm-' which is in better agreement with ours and Chandler's experiments and which gives a CD3 rotational energy gain of -78 cm-l. Including the AK = f 3 propensity in the analysis of previous experiments (e.g., enhancing the N = 4, K = 3 populations in Loo et al. distribution's) and higher N levels (e.g., N > 6) in our analysis, which should increase our average rotational energy by a few wave numbers, would bring our results into better agreement with both experiments. Finally, it is clear that the N = K distributions observed by Powis and Black in their effusive beam experiments'* should be partly influenced by the AK = f 3 propensity in addition to having CD3I molecules with significant populations in high K levels which experience AK = 0 scattering which is after all the dominant mechanism for CD3 rotational excitation.
J. Phys. Chem., Vol. 99, No. 13, 1995 4371
VI. Conclusion We have determined the CD3 n(N,K) rotational distributions produced from the 266 nm photofragmentation of IJKM) = 1 111) CD31. We believe this to be the first report of product state distributions from a IJKM) state-selectedmolecule, and although we did not characterize the CD3 M-state-selected angular distributions, experimental observation was demonstrated. The primary new result from our experiments is the AK = f 3 propensity which we believe occurs because of scattering at the conical intersection between the 3Qo and the 'Q1 surfaces. We provided the outline of a model, which will be developed in more detail el~ewhere,~ that allows us to relate the relative CD3 energy level population n(N,K) resulting from the firstorder, AK = f 3 scattering to the strength of the nonadiabatic coupling between the aforementioned surfaces. To the best of our knowledge, no quantitative measure of the off-diagonal terms which couple two diabatic surfaces during a chemical reaction has ever been observed in product rotational state distributions. We also confinned that the zero-order, AK = 0 scattering was the dominant mechanism during the dissociation, at least for reaction on the adiabatic PES correlating to the Z(*P1,2) channel. On this point we are in agreement with previous experiments in which the methyl radical rotational distributions were measured and are in excellent agreement with the pseudotriatomic 3-dimensional calculations of Guo.*'
Acknowledgment. We are extremely grateful to the NSF for the support provided to do this work through the Young Investigator program, Grant No. DMR-9257433. Support was also provided by the UCLA Academic Senate and by the UCLA Office of the Dean of Physical Sciences. The authors are indebted to Dr. D. Chandler for his help with simulating the CD3 rotational distributions, to Dr. A. D. Hammerich for bringing H. Guo's paper to our attention, and to her and Prof. R. Kosloff for the preprint of their paper and for permission to use their results. We would also like to thank Prof. R. D. Levine and Dr. T. Seideman for their constant support and encouragement and for proof reading the manuscript. We are particularly indebted to Dr. T. Seideman for many useful and insightful discussions. References and Notes (1) Engel, V.; Staemmler, V.; Vander Wal, R. L.; Crim, F. F.; Sension, R. J.; Hudson, B.; Andresen, P.; Hennig, S.; Weide, K.; Schinke, R. J. Phys. Chem. 1992, 96, 3201. (2) Docker, P. M.; Hodgson, A.; Simons, J. P. In Molecular Photodissociation Dynamics; Ashfold, M. N. R., Baggot, J. E., Eds.; Royal Society of Chemistry: London, 1987; p 115. (3) Kim, D. Y . ;Pipes, L. C.; Brandstater, N. R.; and Baugh, D. A. Manuscript in preparation. (4) Andresen, P.; Beushauser, Y.; Hausler, D.; Liitf, H. W.; Rothe, E. W. J. Chem. Phys. 1988, 83, 1429. Crim, F. F. Annu. Rev. Phys. Chem. 1993,44, 397 and references cited therein. Hausler, D. Thesis, Max-PlanckInstitut fur Shromungsforschung, Gottingen, Germany, 1985. (5) David, D.; Bar, I.; Rosenwaks, S. J . Chem. Phys. 1993, 99, 4218. David, D.; Bar, I.; Rosenwaks, S . J . Phys. Chem. 1993, 97, 11571. (6) Seideman, T. Preprint. (7) Balint-Kurti, G. G.; Shapiro, M. Chem. Phys. 1981, 61, 137. (8) Chandler, D. W.; Janssen, M. H. M.; Stolte, S.; Strickland, R. N.; Thoman, J. W., Jr.; Parker, D. H. J . Phys. Chem. 1990, 94, 4839. (9) Janssen, M. H. M.; Parker, D. H.; Sitz, G. 0.;Stolte, S . ; Chandler, D. W. J . Phys. Chem. 1991, 95, 8007. (10) Loo, R. Ogorzalek; Haem, H.-P.; Hall, G. E.; Houston, P. L. J . Chem. Phys. 1989, 90, 4222. (11) Zahedi, M.; Harrison, J. A,; Nibler, J. W. J . Chem. Phys. 1994, 100, 4043. (12) Powis, I.; Black, J. F. J . Phys. Chem. 1989, 93, 2461. (13) Gedanken, A,; Rowe, M. D. Chem. Phys. Lett. 1975,34,39. Hertz, Roben A,; Syage, J. A. J . Chem. Phys. 1994, 100, 9265.
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