J. Phys. Chem. 1995,99, 13571-13581
13571
ARTICLES Product State-Resolved Stereodynamics of the Reaction O(lD)
+ CH4 - OH + CH3
M. Brouard, H. M. Lambert, J. Short, and J. P. Simons” Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ,U.K. Received: February 27, 1995;In Final Form: April 3, 1999
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Polarized, Doppler-resolved laser induced fluorescence spectroscopy has been employed to study the product state-resolved stereodynamics of the velocity aligned, hot atom reaction O(’D) C& OH(2n,/2,v=0,N=5) CH, at a mean collision energy of 39 kJ mol-’. A forward simulation technique is used to extract product A-doublet level specific differential cross sections and center-of-mass (CM) rotational alignments from experimentally determined Doppler-resolved profiles. The results and analysis reveal (i) near conservation of kinetic energy in the channel leading to vibrationless OH products and hence high intemal excitation in the CH3 coproducts; (ii) indistinguishable differential (k,k’) cross sections for the two A-doublet components, both of which display pronounced forward and backward peaks, slightly weighted toward the backward hemisphere, and establish the intermediacy of a long-lived collision complex, and (iii) contrasting CM rotational alignments for the two A-doublet components, with a near isotropic angular distribution of j’ for OH II(A”) but a preferential j’ Ik’ polarization for the A’ level. The results are compared with previous investigations of the OH(v=4,N=8) channel of the O(ID) CH4 reaction and similar studies by Hall et al. [J. Chem. Phys. 1994,101,20331 of the H 0 2 OH 0 reaction. It is suggested that the form of the measured differential cross sections in part reflects angular momentum conservation constraints imposed by low rotational excitation in both the observed OH fragment and its CH3 partner. The k, k’, j’ distributions, on the other hand, provide more detailed insight into the nuclear motions in the transition-state region and evidence for electronic nonadiabaticity in the exit channel.
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1. Introduction In the past few years a powerful new strategy has been developed to probe the stereodynamics of bimolecular collisions. It exploits the “directionality” of polarized, molecular photodissociation to generate velocity-aligned atomic or molecular reagents, and the quantum state specificity of tunable, polarized Doppler-resolved laser probing, to reveal both scalarstate distributions and vectorial correlations (angular momentum alignments, differential cross sections) among the secondary, bimolecular collision products. The two sets of dynamical signatures are derived through analysis of the integrated spectral intensities and Doppler-resolved line shapes of the scattered products, recorded via laser-induced fluorescence or ionisation ( L E or REMPI) detection.’*2 The new strategy extends and complements the longestablished methods of crossed beam scattering by substituting frequency-resolved optical detection for time resolved mass spectroscopic detection, thereby permitting the resolution of individual state-resolved product channels. Fourier transform i n ~ e r s i o d -of~ appropriate combinations of individual Dopplerresolved spectral contours, recorded under alternative excitationdetection geometries and polarizations, is used to project threedimensional velocity and angular momentum distributions for both reactive and inelastically scattered collision product^.^-^ The product velocity distributions and the rotational angular momentum vector correlations are, of course, experimentally determined in a laboratory (LAB) reference frame so the problem of transformation into the center-of-mass (CM) collision frame still has to be addressed. In general, this transformation ~~~
E Abstract
~~
~
published in Advance ACS Abstracts, July 15, 1995.
0022-365419512099- 13571$09.0010
is achieved through forward calculation: LAB speed-dependent vector correlations and distributions, or altematively, the experimental Doppler-resolved contours from which they were derived, are optimally recovered from trial CM differential cross sections. This approach, developed by Aoiz et ale6and based upon the bipolar moment formalism of Dixon’O is the one employed here. Altemative analytical procedures have been developed and exploited by Zare and co-worker~”-’~ and by Hall and c o - ~ o r k e r sto’ ~whose excellent discussions the reader is commended. The present work continues the exploration of the stereodynamics of a key atmospheric rea~tion:’~ O(’D)
+ CH, - OH(vS4,N) + CH, AHo = -182 kJ mol-’ (1)
the kinematics of which maximize the sensitivity of the Doppler profilesAaboratory speed distributions of the scattered products to the nature of the state specific differential cross section~.~-’1-’3 The current study focuses on a channel generating OH fragments with low rotational angular momenta, namely OH(2113/2; v=O,N=5). There are many reasons for this choice: earlier studies by Weisenfeld and co-workersI6have reported bimodal rotational state distributions in the OH generated by reaction of O(lD) with paraffinic hydrocarbons and proposed the intermediacy of long and short-lived collision complexes, respectively generating “cold” and “excited” product quantumstate distributions. The intermediacy of a long-lived complex for the channel generating OH(v=O,N=S) should be reflected in the shape of the corresponding differential cross section. 0 1995 American Chemical Society
13572 J. Phys. Chem., Vol. 99, No. 37, 1995
A second aspect concems the incidence of electronic orbital alignment, reflected in the II(A’)/n(A”) A-doublet population ratios. OH fragments produced with N = 5 have sufficient rotational angular momentum to allow a significant degree of electronic orbital alignment, in or perpendicular to the rotation plane” but not so much as to reduce the satellite features, associated with the operation of Hund’s case-a coupling, to very low relative intensities. Doppler profile measurements of pairs of main and satellite features (associated with Aj = 0 or f l ) allow the separate and direct determination of the differential cross sections and rotational alignments in each, separately resolved A-doublet state. In an earlier study of the channel generating OH(v=4,N=8), the A-doublet levels were assumed to behave identically’ but a recent stereodynamical investigation of the reaction
H
+ O,-OH(v,N) + 0
by Hall and co-workers14 has thrown the validity of this assumption into doubt. The results of the new investigations provide remarkable insights into the “intramolecular” dynamics of the state-specific transition-state complex and the correlation between the electronic orbital and rotational angular momenta in the products of the bimolecular reaction (1). They also indicate the need for due caution in drawing quantitative inferences on the transition-state dynamics based solely on asymptotic product quantum-state distributions between near degenerate final states. These and other matters are more fully addressed in section 6. 2. Experimental Section
O(’D) atoms were produced by photolysis of Nz0 at 193 nm with an ArF excimer laser (Lambda-Physik Lextra 50). The central portion of the photolysis laser beam was collimated with a telescope using quartz lenses and passed through a MgF2 Senarmont polarizer producing two spatially separated and linearly polarized beams. The ordinary ray was selected by an iris after the two beams had diverged over a distance of 1.5 m and passed into the reaction cell. The alignment of the incident polarized laser radiation could be changed from horizontal to vertical by rotating the polarizer through 90”. Pulse energies measured at the cell entrance window were typically 2-3 mJ. The reaction product OH was probed state-specifically with Doppler resolution by means of LIF in the Av = 0 sequence of the A2C+-X2n3/2 band system using a tunable dye laser (Lambda Physik FL3002E) which was pumped by an XeCl excimer laser (Lambda Physik EMG201MSC). The fundamental of the dye laser was produced by operating with a sulforhodamine dye solution and subsequently frequencydoubled with a KD*P crystal (Lambda Physik FL30). A UG-5 filter placed after the SHG crystal passed the W laser radiation while effectively blocking that of the fundamental. With an intracavity etalon in place, a bandwidth of approximately 0.08 cm-’ was achieved. The dye laser radiation was linearly polarized with the aid of a polarizer placed between the oscillator and the amplifier and by the action of the doubling crystal. The fluorescence was collected and collimated by anfl1.3 quartz lens suspended vertically inside the reaction cell and reimaged on the photocathode of a photomultiplier (EM1 9813QB) by a matching lens outside the cell. A broad-band W filter (UG-11) was inserted between the lenses to reduce the amount of scattered light from the lasers reaching the detector. The photolysis and probe laser beams were directed into the reaction cell in three different configurations of propagation axes
Brouard et al. and polarization directions. Case A involved coaxial but counterpropagating lasers with polarizations directed parallel to the vertical detector axis. Case B differed only in that the photolysis laser polarization was directed perpendicular while the probe laser polarization remained parallel to the detector axis. In case D the lasers propagated along separate axes which intersected in a mutually perpendicular arrangement with the detector axis while the laser polarizations were directed as in case B. The variation of both probe and photolysis laser energies was monitored and used to correct the LIF signal on a shot-by-shot basis. The laser monitor photodiode and the LIF photomultiplier signals were each processed by gated integrators (SRS 250) and digitized by a computer interface (SRS 245) using a homemade data acquisition program (a small constant detector background signal was subtracted from each channel prior to dividing the LIF signal by the two laser energy monitor signals). The number of shots was completed and then the average was computed and stored in computer memory. The CHq and N20 gases (research grade) were obtained from BOC and used without further purification. Each gas flow was controlled by a needle valve and adjusted to give an approximately 1:l mixture in a total cell pressure of 13.3 Pa at room temperature. At this total pressure and at the 180 ns delay between firing the photolysis and the probe lasers, less than 16% of the product OH molecules probed have suffered a hardsphere collision. At shorter delays (80 and 130 ns), the product OH LIF signal decreased due to the shorter reaction times but did not exhibit any increase in the spectral width or change of shape in the Doppler profile. This indicated that collisional relaxation processes in OH were not important at the 180 ns delay used in the experiments. The dye laser was scanned over four OH transitions probing the A-doublet levels of OH(X2&2,U=0,N=5), namely, RI1(5) (main), R21(5)(satellite), Q11(5)(main), and Q21(5) (satellite). The two “R’ lines probe the upper II(A’) A-doublet level while the two “Q’ lines probe the lower ll(A”) level. Note that the R21(5)satellite line arises from a transition with Aj = 0 and is actually Q branch in character. Similarly, for the Q21(5)satellite line Aj = - 1 and is P branch in character. Thus each A-doublet level may be probed by both Q and P/R type transitions which are conveniently separated by only 0.02 nm in the spectrum. Doppler profiles were obtained for each of the four OH transitions mentioned above in the three experimental configurations (cases A, B, and D) by scanning the dye laser with the intracavity etalon in place. The best signallnoise ratio was obtained after averaging the normalized signal over 30 or 45 laser shots per etalon step with laser repetition rates of 10 or 15 Hz. Lower resolution scans (laser bandwidth of 0.32 cm-I) in cases A and B geometries, were taken of pairs of main and satellite lines or main and main lines while averaging 90 laser shots per grating step. The low resolution scans were used to obtain the LAB frame rotational alignment parameter (A:’). Each scan at low or sub-Doppler resolution was repeated three to five times, and the average used in the subsequent analysis. The LIF signal was rigorously checked for linearity with respect to the dye laser pulse energy by scanning over the main and satellite lines of interest under relaxed conditions. A laser delay of 17 ps was sufficiently long to allow the Doppler widths to relax to that of a 300 K sample. The dye laser energy was lowered until the ratio of the integrated LIF intensities for the main and satellite lines agreed with the ratio of appropriate isotropic line strengths’* and alignment correction factors.I0 These correction factors refer to the small alignment created by absorption of linearly polarized laser light. Low-resolution
The Reaction O(lD)
+ CHq - OH + CH3
J. Phys. Chem., Vol. 99, No. 37, 1995 13573
scans of main and satellite lines and Doppler profiles of main lines were taken under these conditions. The weaker satellite lines, however, could be probed at higher dye laser energies and still remain unsaturated. The linear regime was established after repeated scans over the relaxed satellite lines demonstrated that the normalized LIF intensities and widths remained unchanged as the dye laser energy increased.
3. Data Analysis and Results The shape of the LIF Doppler profile of a product of a photoninitiated bimolecular reaction depends not only on its LAB speed distribution W(v’)d2, but also on the angular correlations between k, v’, and j’, where k is the reagent relative velocity vector, and v’ and j’ are the product LAB velocity and rotational angular momentum vectors, respectively. It has been shown6 that the Doppler line-shape function for photon-initiated bimolecular reaction products is well-approximated as
where vp refers to the projection of the LAB velocity onto the propagation direction of the probe laser and P2( ) is the second Legendre polynomial. The two terms go( v’) and g2( v’) are given by
where characterizes the anisotropy in the reagent velocity distribution produced in the photolysis step, and the LAB speeddependent terms /3(v’) are the bipolar moments describing the product vector correlations. The coefficients bo to b4 are angular momentum coupling and geometrical factor^'^,'^ which vary in magnitude and sign for different experimental arrangements of photolysis and probe lasers (cases A, B, or D) and for different initial and/or final rotational levels involved in the probe laser excitation step. It is thus possible to construct composite profiles, which depend solely on the LAB speed distribution or on the product of the LAB speed distribution and a single bipolar moment, from weighted sums and differences of Doppler profiles taken in the different geometries and probed in different branches. The weighting procedure in the construction of the composite profiles begins with normalization of each experimental Doppler profile to the value of the integral of eq 3 over up, which turns out to be the LAB speed-averaged value of go(v’). This normalization factor is the bracketed term in the following expression 6, relating the integrated LIF intensity I , to the population P , isotropic line strength S,and LAB frame rotational alignment A:’ of a given rotational level N 4N) OC P(N)
m w o + 5~4b,AbZ’l
(6)
where the rotational alignment
Ah2’ = 2/&9kj,( v‘))
(7)
is averaged over the speed. It is thus convenient to derive the rotational alignment from ratios of integrated L F intensities obtained in separate, lower resolution experiments in which it is necessary only to probe the same level with Q- and R-branch
TABLE 1: Construction of Composite Doppler Profiies by Weighting According to Experimental Geometry and Rotational Branch rotational profile Ia Ib IIa IIb IIIa IIIb
geometry ’/3(A
A-D
D-B
+ E + D)
branch -
Q
R
-q2R -qoR -q2R -qoR -q2R -qoR
429 qoQ qiQ qoQ q29 qoQ
resultin line-shape function
f = q29q$ - q 2 ~ q ox~=; udu‘
f j W ( v ’ ) ~ ’du’l(2u’) ~
fJpvyW(v’)d2 P2(X) du’l(2u’) 3/fpJpku,w(U‘)U’2 P2(X) du‘l(2u‘) 3/jjpJpk,’w(V’)u’2 d~’l(2~’) -31fpJp~u~W(~‘)~’2 P2(X) du‘l(2u’) 6/j,,J~~LyW(~‘)~‘2 P2(X) d ~ ’ l ( 2 ~ ‘ )
transitions and in case A and B geometries. In this way the alignment parameters Af’, for the n(A’) and lI(A’’) A-doublet levels were determined to be -0.04 f 0.04 and f0.02 f 0.03, respectively, by probing main and satellite lines. The large error limits were due to the uncertainty in the areas determined for the weaker satellite lines. In past any difference between A-doublet levels was ignored and the alignment parameter was obtained from ratios of intensities of the main branch lines only. Following this tradition, the alignment parameter would have been calculated to be -0.029 f 0.002. Given the alignment parameter(s) and the ratio of main line intensities, a A-doublet population ratio, lI(A‘)KI(A’’), of 1.32 f 0.09 was calculated using eq 6. Since the alignment parameters were so small, there was no significant difference in the ratio calculated with alignment parameters determined from main and satellite lines or from main lines only. The bo-b4 multipliers have been evaluated elsewhere and tabulated as linear functions of one of two factors (qo or q 2 ) which characterize the angular momentum coupling of a transition for the ideal geometry where the fluorescence is collected along a line.6.’0-’9Kim et al. l 4 have derived a simple correction term to be applied to certain of the purely geometrical factors used to evaluate the qi and b, multipliers,I0 which accounts for the collection of fluorescence over a given solid angle. For those experimental geometries in which the probe laser polarization is parallel to the detector axis (cases A, B, and D), the corrections to qo and to q 2 are small (11% and 52%, respectively) for our fll.3 collection optics. These q factors are independent of the experimental geometry for cases A, B, and D but depend on j’ at low rotational quantum numbers and approach a limiting value at higher j’. The rotational branch weighting factors, which are expressed in terms of qo and q2, and the experimental geometry weights used in the construction of composite Doppler profiles are listed in Table 1 along with the resulting lineshape functions. Note that profiles IIa and IIIa yieId the same information and may be averaged after accounting for the difference in sign. It is apparent from comparison of the Ia profile with the others (see Figures 1 and 2) that the signal-to-noise ratio ( S / N ) is much better when the composite profile is a “sum” rather than a “difference” profile. Consequently, the speed distribution is better determined than are the other bipolar moments. To take advantage of the enhanced S I N gained by summing profiles, all “difference” profiles were constructed in two steps. First, the positive and negative weighted profiles were added separately. The intermediate profiles were then renormalized and reweighted before taking their difference. The enhanced SM in these “difference” profiles was demonstrated by a sharper, cleaner appearance of the P2( ) functional form of the lineshape. Indeed, the integrated areas of those profiles with a P 2 ( ) dependence (see Table 1) were an order of magnitude closer to the expected value of zero when constructed by this two-step method as opposed to the simpler one-step addition of all of the individually weighted profiles.
Brouard et al.
13574 J. Phys. Chem., Vol. 99, No. 37, 1995
0.6
A
A
0.0 -
-0.6 1 0.7
I
Sh'ft 5
0.7
0.0
~
(CrTI-')
0.6
e 0.0
-0.6 1 -0.7
I
'2.0 sk'ft (cm-'j
0.7
2500 v ' (rrl /s)
50CO
I
cu
> >
I
A
i
W
3 I
\\
2500
v
(ITl/Sj
C
Figure 1. Experimental composite Doppler profiles Ia (left column) and (IIa-IIIa)/2 (right column) for each A-doublet level, together with the speed distributions (bottom left) and bipolar moments /3/3kL., (bottom right) obtained from the Fourier inversion of the functions fitted to the Doppler profiles (solid curves in top and middle rows). The residuals from the fits, displayed above the profiles, are plotted on a vertical scale of -0.3 to +0.3.
The composite Doppler profiles were deconvoluted from the laser line shape in a nonlinear least-squares fitting procedure and then inverted using a Fourier transform technique to obtain the speed-dependentbipolar moments; both the fitting procedure and the Fourier inversion step have been described in detail elsewhere.6 Figures 1 and 2 provide a compact summary of
all the experimental data. Four types of composite Doppler profiles are displayed, types Ia and IIa in Figure 1 and types Ib and IIIb in Figure 2, for each A-doublet level, n(A') and n (A"), together with the best fits and residuals, the corresponding bipolar moments, and the speed distribution. Error bars ( f l u ) shown for the bipolar moments and the speed distribution were
- + e m
The Reaction O('D)
0.3
+ CHq
CH3
OH
J. Phys. Chem., Vol. 99,No. 37, 1995 13575
0.7
0.0 -
-0.3 -
I
~
0.0
0.7
0.7
shift ( c m - ' )
I 0.7
0'3
-0.3
I
i
I
I
0.7
- 0.7
0.5
0.1
A
> .-
W
n
> .-.
I
u
0
-+
>
a
0
L)
-+-,
*
0.l
0 AI
_ _ _ _
A
-0.3
0 U a, Y
-O.'I
I'
Figure 2. Experimental composite Doppler profiles Ib (left column) and IIIb (right column) for each A-doublet level, together with the bipolar moments By" (bottom left) and @tu" (bottom right) obtained from the Fourier inversion of the functions fitted to the Doppler profiles (solid curves in top row). The residuals from the fits, displayed above the profiles, are plotted on a vertical scale of -0.3 to +0.3.
determined from consideration of the uncertainties derived from the fit, the uncertainties in the value of At' used in the normalization of each Doppler profile, and an uncertainty of f O . O 1 cm-' in the laser line width. Since the speed-dependent bipolar moments were obtained by dividing the inverted profiles by the speed distribution, the small uncertainties associated with the speed distribution were also taken into account when estimating the error bars for the bipolar moments.
4. Differential Cross Sections and Laboratory Speed Distributions The LAB speed distribution W(v')d2 and the LAB speeddependent bipolar "mm Pkv'(d),which describe the angular correlation between the reagent and product LAB velocity vectors, are both "images" of the center of mass differential cross section. In a triatomic collision system, it is possible to
Brouard et al.
13576 J. Phys. Chem., Vol. 99, No. 37, 1995
effect a direct inversion from the LAB to the CM frame since the energy budget can be determined exactly; when the bimolecular product is monitored state selectively (assuming no intemal excitation in the atomic coproduct), it allows a direct determination of the products’ recoil speeds.6,’ Thus, characterization of the LAB speed distribution, W(V‘)U‘~, is sufficient to allow precise determination of the CM differential cross section, provided that the collision energy is well defined, or that the reaction excitation function shows little collision energy dependence. In this case, the second moment of the LAB velocity distribution, &,!( d), is redundant information. In a polyatomic system, however, such as the one under current study, the energy budget is unknown, because the molecular coproduct will, in general, be generated in a range of intemal states. For such a system, a knowledge of the LAB speed distribution alone is insufficient to allow determination of both the product kinetic energy release and the differential cross section. However, measurement of the second moment of the LAB velocity distribution provides additional information, which in conjunction with W(v’)d2,can be used to place limits on the mean and likely range of intemal energies in the (unobserved) coproduct. The analysis procedure adopted below is that of iterative forward simulation of W(d ) d 2and &,( v’) based upon trial CM differential cross sections and intemal energy disposals in the (unobserved) coproduct- expressed in terms of the mean translational exoergicity (e)-see below. These simulations assume that the excitation function for the reaction is a constant, which seems justified given the large reaction cross section in the present case. Furthermore, explicit allowance for a distribution over Q is not made in these simulations, but the evidence to be provided suggests that Q takes a rather narrow range of values. It should be bome in mind that the present measurements are OH quantum-state selective, and the narrow range of intemal states apparently populated in the CH3 coproduct does not imply, of course, that the OH state averaged rovibrational population distribution in CH3 is also narrow. The forward simulation programme developed by Aoiz et al.6 calculates the LAB speed distribution W(V ’ ) V ’ ~ , the speed dependent bipolar moment, /3kv,( d ) , and the composite Doppler profiles (type Ia and IIa), given the following input: a velocity distribution for each of the reagents O(’D) and CH4, the laser line shape, a trial value of the average kinetic energy release in the reaction (Q), and a trial CM differential cross section. The CM velocity distribution of O(’D) generated by the polarized photolysis of N20 at 193 nm is well-approximated by a Lorentzian function with center and full width at half maximum of about 2.9 and 1.8 km s-I, respectively, and an anisotropy parameter of 0.48 f 0.02.20 The velocity distribution of the reagent O(’D) is obtained by convolution of this CM distribution with the thermal motion of the N20 precursor molecule.6 The velocity distribution of CHq is isotropic and may be characterized by a 300 K Maxwell-Boltzmann function. Integration over v(0’D) and v ( C h ) is done approximately by constraining its direction to lie parallel to v(O’D).~This approximation, which ignores integration over the spherical polar angles between the two reactant velocity vectors, nevertheless successfully reproduces the distributions over the velocity of the CM and the reactant relative velocity. However, use of the approximation results in an overestimate of the Pj3kv, bipolar moment at low LAB velocities. The laser line shape was obtained by the Fourier transform inversion of a thermalized Doppler profile and deconvolution of the Gaussian “thermal” contribution. The mean kinetic energy release (Q) in the reaction is related to the mean intemal energy (Ei(CH3)) by energy conservation, as follows:
E,(CH,)
+
ET
= E
> J(C&)). The low contribution from sideways scattering implies a propensity for L I1 L’, i.e., a near coplanar collision. The rotational alignment of j’(OH), at least for the II(A’) channel, is directed preferentially, in the collision plane and, therefore, perpendicular to L‘. The tilt angle between L and L’, and thus the contribution from sideways, out-of-plane 6. Discussion scattering, is dictated by the magnitude of J’. Clearly j’(0H) The results presented in sections 4 and 5 provide many new is small, since N = 5; the same must also be true for j’(CH3), insights into the product state resolved stereodynamics of the notwithstanding its very high internal energy. (This result is reaction of O(’D) with methane. The very low mean kinetic not too surprising perhaps, since it is not easy to visualize a energy release, (Q) = f 4 . 5 f 5 kJ mol-’, establishes the dynamical mechanism for strong rotational excitation of the CH3 predominant conversion of the reaction exothermicity, AHo, into fragment as it separates from its OH partner). If J’
