Faraday Discuss. Chem. SOC., 1991, 91, 173-182 Transition-state Control of Product Rotational Distributions in H + RH -+ H, + R Reactions (RH = HCI, HBr, HI, CH4, C2H6, C,H,) James J. Valentini,” Pamela M. Aker,? Geoffrey. J. GermannS and Young-Duk Huh Department of Chemistry, Columbia University, New York, NY 10027, USA Measurements of the rotational state distributions for the H2 product of the H + RH -+ H2 + R reactions (RH = HC1, HBr, HI, CH4, C2H6, C3H8) at a collision energy of 1.6 eV are reported. For the reactions with the hydrogen halides we also have carried out quasiclassical trajectory calculations for conditions that mimic those of the experiments. We find that the rotational state distributions are quite characteristic and distinguishing in these systems. The combination of experiments and calculations allows us to provide some compelling explanation of how the structure and dynamics in the transition state are coupled to the product rotational state distributions.Not surpris- ingly, mere measurement of the rotational state distributions is insufficient to establish this connection, as illustrated by the results of the state-to-state experiments with the alkanes as reactants. These reactions give anomalous rotational state distributions, showing rotational excitation that actually increases with increasing product vibrational energy, rather than decreasing, as has been observed for all other reactions whose rotational and vibrational state distributions we know have been measured. State-to-state dynamics experiments do not provide the capability for ‘direct’ probing of the transition state in chemical reactions.In fact, in such experiments the transition state is effectively treated as a ‘black box’, into which reactants flow and from which products emerge, but into which we cannot peer. The hope of course is that the multitude of couplings of particular reactant quantum states with specific product quantum states revealed in such an experiment will provide a picture of what transpires in the black box. Ideally this revelation will be detailed enough to allow unambiguous interpretation, although it is quite difficult to realize this ideal. Even if this ideal is realized, the indirect nature of this type of transition-state probing has interpretation as a key element. Such interpretation usually takes the form of some theoretical description or model.Despite these limitations imposed on interrogating the transition state through the indirect route of state-to-state dynamics measurements, it is possible to use this indirect route to gather a large amount of significant information about the transition state. This is particularly true when individual rotational states of the reactants and products are detected. While the information so obtained is less easily interpreted than that provided by some of the direct probes of transition-state structure and dynamics reported elsewhere in this Discussion, this indirect information is much more easily obtained and can be obtained for a wider variety of reactions. This contribution reports a combination of state-to-state dynamical observation coupled with both theoretical calculations and model descriptions to provide an indirect, but nonetheless very detailed, look at how product rotational distributions are controlled by transition-state structure and dynamics in one particular class of reactions.These ?Present address: Department of Chemistry, University of Wisconsin, Milwaukee, WI 53201, USA. $ Present address: IBM, 650 Harry Road, San Jose, CA 95120, USA. 173174 Control of Product Rotational Distributions are the hydrogen-atom abstraction reactions, H + RH + H2 + R, where RH is HCl, HBr, HI, CH4, C2H6 or C3Hs. The experiments are carried out using reactants at ambient temperature, so individual quantum states of the reactants are not prepared.However, the reactions are studied at high collision energy, typically 1.6 eV, so that the reactant internal (thermal) energy is only a very small part of the total energy, and reactant orbital angular momentum dominates the reactant rotational angular momentum. Thus, further state preparation would probably provide little additional insight at a rather substantial increase in technical complexity. However, the individual ro-vibrational states of the H2 product are detected, using coherent anti-Stokes Raman scattering (CARS) spectroscopy under single-collision or near-single-collision conditions. State-to-state dynamics experiments and complementary quasiclassical trajectory calculations seem to indicate that the way in which the transition-state structure and dynamics control the rotational distributions is relatively simple and fairly clear in the case of the H-atom abstraction reactions with the hydrogen halides.However, for the H-atom reactions with the alkanes the connection between the transition-state charac- teristics and the H2 product rotational state distributions is apparently more complicated and more difficult to understand, although the important theoretical calculations that will probably allow their interpretation have not been carried out yet. Experiment The experimental approach used here has been described in detail in a previous report of some of these results,’ so only a brief review will be provided. The experiments use HI as a photolytic precursor for the H-atom reactant. The HI precursor and the RH reactant are flowed through a reaction cell at ambient temperature and a few Torr pressure, with the pressure maintained by a mechanical vacuum pump.The apparatus employs a Quanta-Ray Nd : YAG laser, the 523 nm second-harmonic output of which is split into three parts. One part pumps a Quanta-Ray PDL-2 pulsed dye laser, that provides typically 5 mJ pulses to be used as the tunable Stokes frequency, w,, for the CARS process. Some of the remaining 532 nm light is doubled to provide ca. 15 mJ of the 266 nm light (cod) that photolyses HI to make the H-atom reactant. The last part of the 532 nm light, ca. 20 mJ of each laser pulse, is used directly for the pump frequency, wp, in the CARS process. The wp, w, and wd beams are collinearly combined using dichroic mirrors and focused into the reaction cell, where they are precisely overlapped spatially and have coincident foci.Delay lines provide the temporal control necessary to keep the up and w, pulses temporally overlapped, and delayed with respect to the arrival of the @d pulse at the cell by ca. 4 ns. The HI precursor and RH reactant are flowed through the reaction cell at a rate sufficient to ensure renewal of the gas in the sampled volume between laser shots at the 10 Hz repetition rate of the Nd: YAG laser. The CARS beams generate a signal beam at the anti-Stokes frequency, was= 20, - w, = up + ( wp - 0,) = up + w,, where w, is the Raman transition frequency of the molecules being probed.2 The intensity of this signal is proportional to the difference in population between the two particular ro-vibrational states (v’,j’ and v’+ 1,j’) of the H2 product that are connected by the specific Q-branch Raman transition being probed.Thus, by scanning o, and measuring the signal intensity of was an intensity vs. frequency spectrum is obtained that can be analysed to give the H2 product state population distributions. Results and Discussion Fig. 1 and 2 show the rotational state distributions of the H2 product of the H + HCl and H + HI reactions at 1.6 eV collision energy. The rotational distributions are quiteJ. J. Valentini et al. 175 160 120 s .- - 80 a a a 4 0 0 0 10 J ’ 20 16 12 a 4 0 0 10 J’ Fig. 1 Rotational state distribution for the H2 product of the H + HCI reaction at 1.6 eV collision energy. The populations in even-j‘ states have been multiplied by a factor of three to smooth out the even-j‘-odd-j intensity alternation associated with the different nuclear spin degeneracies of the even-j’ (degeneracy = 1) and the odd-j’ (degeneracy = 3) rotational states.The solid lines are linear surprisal analysis best fits’ to the experimental measurements, with the rotational surprisal parameters (6,) 3.7 (a) and 7.4 (b) 16 12 s .- U 2 8 a 4 a 0 16 12 32 24 16 8 0 0 10 20 0 10 20 J’ J’ 0 0 10 20 0 4 8 12 J’ J’ Fig. 2 Rotational state distribution for the H2 product of the H + HI reaction at 1.6 eV collision energy. The solid lines are simple smoothe curves drawn through the data to aid the eye. As with the data in Fig. 1 the even-j’ populations have been multiplied by three176 Control of Product Rotational Distributions characteristic.The 1.42 eV exoergic H + HI -+ H2 + I reaction produces H2 over a broad range of rotational states, with a distribution that is highly dependent on the vibrational state of the product (fairly high rotational states in the lower vibrational states) while the nearly thermoneutral (AH = -0.04 eV) H + HCl -+ H2 + Cl reaction yields H2 product in low rotational states only. The H + HBr -+ H2 + Br reaction, which is intermediate between the H + HI and H + HCl reactions thermochemically (AH = -0.72 eV) produces rotational state distributions (not shown here) that not surprisingly are intermediate between those observed in the H + HI and H + HCl reactions. One characteristic of these three reactions that makes for an interesting comparison is that they differ energeti- cally, and therefore in their potential-energy surfaces, but are kinematically effectively identical, having reactant reduced masses, preactants, of 0.97,0.99 and 0.99, for HCl, HBr and HI, respectively.Although the trend observed in the rotational state distributions among these three reactions appears simply to track the thermochemistry of the reactions, the individual rotational state distributions are not so simple. Each of these reactions has a potential- energy surface with a collinear minimum-energy path, yet only for the H + HCl reaction are the rotational distributions peaked at the low j ’ typical of collinearly dominated reactions. The reason is that although the minimum-energy path is collinear, for the 1.6 eV collision energy at which the reactions are studied the H + HI reaction, and to a lesser extent the H + HBr reaction, are not dominated by collinear transition-state geometries, rather non-collinear transition-state geometries are dominant.Based on an examination of just the experimental observations this would be nothing more than a supposition. However, quasiclassical trajectory (QCT) calculations show, to the extent that such calculations can, that the rotational state distributions we observe for the H + HI, H + HBr and H + HCl reactions are a direct reflection of the transition- state structure. The QCT calculations are carried out on approximate potential-energy s~rfaces,~ and the calculations are themselves only an approximation to the ‘true’ quantum dynamics of the system, so the QCT results can be used as an interpretation of the experimental results only if they can be corroborated.The required corroboration is provided by a comparison of the rotational state distributions predicted by the calculations, with those actually observed e~perimentally.~ Such a comparison is presented in Fig. 3 and 4. The plotted QCT results are actually a combination of the results obtained in calculations at 1.6 and 0.68 eV. This is necessary because the photolysis of HI at 266nm that we use to generate the H-atom reactant produces both H + I(2P3/2) and H + I(2P1/2) fragment channels, with the former, dominant channel giving the nominal 1.6 eV collision energy, while the latter, minor channel yields collisions of 0.68 eV. For comparison with the experimental measurements the trajectory results at the two energies are combined in a ratio that reflects the [H + I(2P3/2)]/[H + I( 2P1/2)] photolysis branching ratio as well as the difference in reactive cross-sections at the two energie~.~ The QCT and experimental data in Fig.3 and 4 are scaled such that both give the same total reaction cross-section, so the figures actually compare ro-vibrational distribu- tions, not simply rotational distributions. Because of this, and because the QCT vibra- tional distributions are not in quite as close accord with experiment as are the rotational distributions, the agreement between the experimental and calculated rotational distribu- tions is actually slightly better than that indicated by the comparison shown in the figures.Nonetheless, this comparison reveals the fidelity of the description of the rotational dynamics provided by the QCT approach. Given the accurate description of the H + HI, H + HBr and H+ HCl reactions pro- vided by the QCT results, we can use the calculations to provide a ‘direct’ probe of the transition-state structure and dynamics. The transition state is certainly more accessible computationally than experimentally, and the trajectory calculations lend themselvesJ. J. Valentini et al. 177 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0 4 8 1 2 0 4 8 1 2 J ’ J’ Fig. 3 Comparison of experimental rotational state distributions (points with error bars, as in Fig. 1) with those derived from QCT calculations (-) for the H + HCl -D Hz + C1 reaction.The experimental results and the QCT results have been scaled to have equal total cross-sections. (a) u’=O, ( b ) v ’ = 1 0.06 - 0.04 - U 0 5 10 15 20 0.06 0.04 U 0.02 0.00 0 5 10 15 20 J ’ 0.10 0.08 0.06 0.04 0.02 0.00 0 5 10 15 0.02 p--T 0.00 0 5 10 J ’ Fig. 4 Comparison of experimental rotational state distributions (points with error bars, as in Fig. 2) with those derived from QCT calculations (-) for the H + HI + H2 + I reaction. The experimental results and the QCT results have been scaled to have equal total cross-sections. (a) u’=O, ( b ) o’= 1, ( c ) v ’ = 2 , ( d ) u ’ = 3178 Control of Product Rotational Distributions % o o o , , , , , , I 30 0 L - _ L _ L . L - 1 I I I 0 . 0 0.5 1.0 1.5 2 .0 2 . 5 3 . 0 3 . 5 impact parameter/ A Fig. 5 Scatter plot of H-H-I angle us. H+HI impact parameter for those trajectories that to reaction to produce H,+ I. X, trajectories at 1.6 eV collision energy; 0, at 0.68 eV led readily to quite revealing interpretative analysis. For example, scatter plots of the H-H-X angle vs. impact parameter for those trajectories that react reveal a fairly strong correlation between these two variables. Such a scatter plot, for the H + HI + H2 + I reaction, is shown in Fig. 5 . The observed correlation approximately follows the relation b = ( r H , + r ~ ~ ) s i n 8 ( 1 ) where 6 is the impact parameter and 8 is the H-H-X angle at the transition state. The distances rHX and rHH are, respectively, the saddle-point distance between the halogen atom X and the H atom bonded to it, and the saddle-point distance between the two H atoms.This implies that the reaction occurs for transition-state structures that orient the H of the hydrogen halide such that it is directly in the path of the incoming H atom. Put another way, it means that reaction is dominated by those trajectories in which the impact parameter between the H reactant and the H of the HX is near zero, not by those trajectories for which the nominal impact parameter, 6, defined in terms of the HX centre-of-mass, is near zero. At the high energies of these collisions the barrier height energetic constraints that favour collinear H - H -X transition-state geometries are relaxed, and replaced by geometric constraints that cause the impact parameter and input angle to be correlated such that the transition-state geometry favours H-H-X geometries that minimize rHH irrespective of the H-H-X angle.Because of the sin 8 weighting of the input angle 8, non-collinear H-H-X geometries are much more probable than nearly collinear geometries. This weighting and the correlation expressed in eqn. (1) dictate that the opacity function should be maximized at b#O if the barrier height energetic constraints that favour collinear transition-state geometries are sufficiently overcome by the collision energy. This condi- tion is satisfied for the H + HI and the H + HBr reactions at the 1.6 eV collision energy of our experiments and calculations, as the barrier height for 8 = 90" is only 0.1 eV for H + HI and 1.1 eV for H + HBr.3 The opacity functions of both these reactions show a maximum at 6 # 0 for 1.6 eV collision energy, as indicated in Fig.6. However, for the H + HCl reaction this condition is not satisfied, since the barrier height exceeds the collision energy for angles ca. 90", and Fig. 6 shows that the opacity function for this reaction has a maximum at 6=0, not b>O. At the 0.68 eV collision energy both the H + HCl and the H + HBr reaction opacity functions have maxima at 6 = 0, while the H+ HI reaction still has a peak at b # 0, but it is a much weaker maximum than atJ. J. Valentini et al. I I I 1 1 1 I - - 0.10 - 179 0.08 0.06 0.04 0.02 0.00 0.00 0.60 1.20 1.80 2.40 3.00 impact parameter/ A Fig. 6 Opacity functions for the H + HX - H2 + X reactions at 1.6 eV collision energy.(-) X = I, (- - -) X = Br, ( - * -) X = Cl 80 60 h 1 si 40 z v 20 0 20 16 12 8 4 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 0 0 . 2 0 . 4 0 . 6 ‘rot1 ( ‘tot - Evib) Erotl(Eto1- Evib) Fig. 7 Experimental rotational population distributions for the HD product of the H + CD4- HD+CD, reaction (-) and for the H2 product of the H+HCl- H2+C1 reaction (---). ( a ) u’=O, ( b ) u ’ = 1 1.6 eV collision energy. For the H + HI reaction at 1.6 eV collision energy the impact parameter at which P ( b ) is a maximum agrees well with what a simple geometrical model would predict in the absence of any energetic constraints on the transition-state geometry., The H+CH,, H+C2H, and H+C3H, reactions are all very similar to one another energetically, with A H = -0.06, -0.26 and -0.26 eV, respectively, and similar kinemati- cally as well, having preactants = 0.94, 0.97 and 0.98, respectively.All three are also very similar in both regards to the H + HCl reaction already discussed, which has AH = -0.04 eV and prLreactants = 0.97. However, the rotational state distributions of the molecular hydrogen products of the H + alkane reactions are characteristically different from and more complicated than the H2 rotational state distributions of the H + HCl rea~tion.~ This is shown by the data in Fig. 7. Our experiments on the hydrogen atom plus methane reaction were actually done with the methane isotopomer CD,. The small cross-section for this reaction (see below) makes it difficult to investigate the H + CH4 + H2 + CH3 reaction without interference180 Control of Product Rotational Distributions a v z 80 60 4 0 20 0 20 16 12 8 4 0 0 .0 0 . 4 0 . 8 0 . 0 0 . 4 0 . 8 ‘rot/(‘tot- E v i b ) E r o t / ( E t o t - Evib) Fig. 8 Experimental rotational population distributions for the H2( HD) product of three H+ alkane reactions. (-) CD4, (- - -) C2H6, ( a * .) C3H8. ( a ) u’ = 0, ( b ) u’ = 1 from the H+HI -+ H2+ I reaction that is also taking place as a consequence of the presence of unphotolysed HI precursor in the reaction cell. Thus, to allow a true comparison of rotational energy disposal in the two reactions, the rotational distributions of the HD product of the H + CD, reaction and the H2 product of the H + HCl reactions compared in Fig. 7 are plotted vs. rotational energy rather than rotational angular momentum.The product state distributions in this figure have been normalized such that the total cross-section is the same for both reactions, to allow an unbiased comparison of rotational distributions independent of total cross-section. (The experimental total reaction cross-section for the H+ HCl- H2+C1 reaction, 2 A2, is much larger than the cross-section for the H + CD, -+ HD + CD, reaction, 0.15 A2.) In v’ = 0 the alkane reaction yields product that is much colder rotationally than the HC1 reaction. One would be tempted to associate this difference readily with the higher barrier to reaction in the alkane reaction, Eb = 0.54 eV,6 as compared to that for the HCl reaction, 0.22 eV, and possibly a faster increase in the barrier height upon distortion away from the collinear minimum-energy path.The disparity in reaction cross-sections lends support to this supposition, but the rotational distribution in v’ = 1 certainly does not. The v’ = 1 rotational distribution of the HD from the H + CD4 reaction is actually hotter than that of the H2 from the H + HCl reaction. In fact, the v’= 1 HD product is hotter rotationally than the v’ = 0 product! This is an unusual result, as the normally observed behaviour, so common as to be generally regarded as universal, is that product rotational energy decreases as product vibrational energy increases. For the H + CD4 + HD + CD, reaction, product rotational excitation and product vibrational excitation are not negatively correlated, they are positively correlated.It is not just the H+CD, reaction that shows this behaviour; in fact the H-atom abstraction reactions of the heavier alkanes show it even more clearly. This is evident in the data presented in Fig. 8 for all three H +alkane reactions we have studied so far. The hydrogen-atom abstraction reactions of the ethane and propane have experimental total cross-sections (1.5 A’ for H + C2H6 and 2.9 A2 for H + C,H,) that are sufficiently large that interference from the reaction of H with the unphotolysed HI is not significant, so we used the perproto isotopomers, rather than the very expensive perdeutero com- pounds. Thus, the comparison of the rotational distributions from the three alkane reactions also involves comparison of HD and H2 products, and here in Fig. 8, as inJ.J. Valentini et al. 181 Table 1 Rotational energy disposal in the H + RH(RD) + H,(HD) + R reactions H+HC1 H+CD4 H + CzH, H + C3Hs EavailleV 1.65 1.64 1.86 1.86 Emtl Eavail v ’ = O 0.21 *0.01 0.08*0.01 0.11 fO.01 0.12f0.01 v”1 0.08f0.01 0.11 f0.01 0.16f0.01 0.19f0.01 v’=O 0.21 f 0.01 0.08 0.01 0.1 1 f 0.01 0.12 f 0.01 v’= 1 0.12 f 0.01 0.15 f 0.01 0.22 f 0.01 0.27 f 0.01 Erotl (Eavail- Evib) Fig. 7, we also plot the rotational distributions vs. rotational energy rather than vus. rotational angular momentum. While the v’ = 0 rotational energy distributions for all three alkanes are very similar, the v‘ = 1 rotational energy distributions are very different and quite characteristic for each reaction. As the complexity of the alkane increases, the v’= 1 product becomes rotationally hotter. The one behaviour that all three reactions have in common is that the rotational energy in the v’ = 1 product is greater, for H + C2H6 and H + C3H8 much greater, than that in the v’ = 0 product, as indicated by the data in Table 1. (In all three reactions, as with the energetically nearly identical H + HCl reaction, the only product vibrational states observed are v f = 0 and v f = 1, and population in higher vibrational states must not be more than 5% of the total population.) Thus, all the H+alkane reactions we have investigated, and probably all H + alkane reactions in general, have an anomalous and surprising positive correlation of the rotational and vibrational excitation of the product. Although we can put forth purely speculative rationalizations of this behaviour, we cannot provide a compelling explanation of the connection of this behaviour with the structure and dynamics of the transition states involved in these reactiorrs.However, such a connection must obtain. Given the apparent success of QCT calculations in elucidating this connection in the H + HX reactions, we expect that similar calculations on the alkane reactions will explain what features of the H + alkane transition-state structure and dynamics are responsible for this unusual behaviour. Conclusion Rotational state distributions measured for the H2 product of the H + RH -+ H2+ R Reactions (RH = HCl, HBr, HI, CH4, C2H6, C,H8) provide a very detailed, if indirect, probe of the transition-state structure and dynamics in these atom-transfer reactions.However, the measurements certainly require that theoretical calculations be carried out and model descriptions be developed in order to determine how the transition state controls the rotational distribution in the reactions. This is positively illustrated by the apparent success of QCT calculations in providing a compelling interpretation of the results obtained in the H + HI, H + HBr and H + HCl state-to-state dynamics experiments. The difficulty of establishing the connection between the product rotational state distribu- tion and the transition-state properties in the absence of such interpreting calculations is illustrated by the state-to-state results we have obtained for the H+CH,, H+C,H6 and H + C3& reactions, for which we observe surprising and not yet explained rotational state distributions. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences Office of Energy Research, US Department of Energy.182 Control of Product Rotational Distributions References 1 P. M. Aker, G. J. Germann and J. J. Valentini, J. Chem. Phys., 1989, 90, 4795. 2 J. J. Valentini, in Spectrometric Techniques, ed. G. A. Vanasse, Academic Press, New York, 1985, vol. 3 M. Baer and I. Last, in Potential Energy Surfaces and Dynamics Calculations, ed. D. G. Truhlar, Plenum 4 P. M. Aker and J. J. Valentini, Isr. J. Chem., 1990, 30, 157. 5 G. J. Germann, Ph.D. Thesis, University of California, Irvine, 1990. 6 T. Joseph, R. Steckler and D. G. Truhlar, J. Chem. Phys., 1987, 87, 7036. 7 R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity, Oxford 4, ch. 1, pp. 1-62. Press, New York, 1981, ch. 21, pp- 519-534. University Press, London, 1987, pp. 260-276. Paper 0/05726F; Received 19th December, 1990