Famday Discuss. Chem. SOC., 1991, 91, 259-269 Hydrogen Exchange Reaction H + D, in Crossed Beams L. Schnieder, K. Seekamp-Rahn, F. Liedeker, H. Steuwe and K. H. Welge* Fakultat fur Physik, Universitat Bielefeld, 4800 Bielefeld 1, Germany Despite its fundamental importance as the prototypical bimolecular reaction, the hydrogen exchange reaction still remains a challenging and open prob- lem, both experimentally and theoretically. Theory has now developed to a stage much superior to that of experiment. Nowhere is this more true than, for example, in the determination of differential scattering cross- sections, state-to-state specific with respect to the vibrational and rotational degrees of freedom of the molecular products. In this paper we describe a new experimental approach to such measurements, and present first results from crossed-beam studies of the H + D2 reaction (at relative translational energies of I .29 and 0.54 eV)t using the novel technique of hydrogen Rydberg atom time-of-flight spectroscopy to monitor the velocity and angular distribu- tions of the D atom product. As the most fundamental system of elementary chemical kinetics, the hydrogen exchange reaction and its isotopic variants and H+D2 --* HD+D (Id have been a subject of much theoretical and experimental research.However, although begun more than 60 years ago with the fundamental work of London,’ the theoretical investigation of this reaction has only recently reached the point at which the problem has been treated quantitatively in three dimensions by exact quantum-mechanical2 and also quasi-classical trajectory calculations3 for the case in which the energy necessary to overcome the activation barrier (ca.0.42 eV for the linear H3 ~ o m p l e x ) ~ is provided as kinetic energy of the collision partners. The results are multiply differential cross- sections that are quantum-state specific with respect to the internal (vibration and rotation) degrees of freedom of the product molecules, as a function of the collision energy in the electronvolt range. The experimental investigation, also begun more than 60 years ago (by Farkas)’ is, in comparison, much less advanced. Significant progress has been achieved in recent years by studies with laser-based techniques under bulk conditions by Wolfrum,6 Valen- tini’ and Zare.s These experiments have yielded detailed, i.e.quantum-state specific, reaction rate constants (or total cross-sections) for reactions wirh kinetically hot H( D) atoms at energies in the range of 1 eV (produced photolytically by photodissociation of hydrogen iodide molecules). Most recently, experiments have also been reported involv- ing internally hot molecular reactant^.^ -7 i eV= 1.602 18 x lo-.” J. 259260 H + D2 Exchange in Crossed Beams Measurements of the dependence of the quantum-state specific total cross-sections, by Nieh and Valentini," on the relative translational energy appear to show pronounced structures. These have been interpreted in terms of quantum resonances of the transition complex and have attracted particular attention. However, these observations have not been corroborated by the theoretical calculations," which, although they do indeed predict energy-dependent resonance-like structures, suggest that such features will appear in a pronounced fashion only in the multiply differential state selective cross- sections.The calculations indicate that when measurements are made under the integral bulk conditions the structures are smoothed and averaged out. This has been confirmed by detailed experiments by Kliner et aL12 Cross-beam experiments which, in principle, can be expected to yield the most detailed quantum-state specific differential cross-sections have been carried out since 196313 with reaction ( l b ) . Most notable in this regard are recent investigations of this system by Gotting et aZ.,14 Buntin et all5 and by Continetti and Lee16 with kinetically hot reactants ( i e .with fast atoms). Common to all crossed-beam experiments is the detection of the HD product molecules by mass spectroscopy and analysis of their velocity (speed and angle) distribution by time-of-flight (TOF) spectroscopy. One important requirement for such experiments is that the collision conditions be energeti- cally monochromatic. Gotting et ~ 2 . ' ~ have produced fast D atoms by adiabatic expansion of gas from an electric discharge in deuterium, Buntin et all5 have employed the photodissociation of D2S at 193 nm, and Continetti and Lee16 have used DI photolysis at 248 nm. However, the goal of quantum-state specific differential cross-section measurement has not been achieved.It appears that with these experiments the conven- tional crossed-beam TOF technique has reached its practical limits of sensitivity and energy resolution. In this paper we present a new experimental approach to investigating the hydrogen exchange reaction in a crossed-beam configuration. The technique is based on a new kind of TOF spectroscopy for hydrogen atoms which we have developed previously for the investigation of photodissociation processes and which is distinguished by high sensitivity and kinetic energy resolution. 17-22 In its present state the TOF technique itself has a resolution of the order of A E / E = 0.003, i.e. 3 meV for H atoms with 1 eV of kinetic energy. In the experiments presented in this paper the overall resolution achieved was much lower because of the less accurately defined kinematics of the collision conditions.Nevertheless the studies indicate that the technique has sufficient potential to achieve rotational state resolution of the HD product molecules. In these first experiments we have concentrated upon reaction ( 1 c). We have chosen this reaction instead of reaction (16) for the simple reason that the precursor HI was available for the generation of fast reactant H atoms and because the main purpose of the work was to study the feasibility of the technique. Reaction (1 6) could, of course, be studied with the present technique equally well, and such experiments will be done. In this paper we describe the technique in some detail and report the first results so obtained.Experimental Fig. 1 shows schematically the experimental set-up, consisting essentially of a vacuum chamber separated into two parts: the photolysis chamber, where fast hydrogen atoms are generated, and the reaction-detection chamber. In the photolysis chamber a pulsed beam of HI in Ar cooled by adiabatic expansion and with its axis 15 mm away from the separating wall is crossed perpendicularly by a pulsed photolysis laser beam of 1 mm diameter (pulse duration ca. 5 ns). Atoms from the intersection volume enter the reaction-detection chamber through an orifice (ca. 2 mm diameter) and cross a pulsed D2 beam at a distance of 15 mm behind the wall. D atoms generated in the reactionL. Schnieder et al. 261 H I / A r I l a s e r p r o b e , Laser (121 6nm) 0 \ Fig.1 Schematic view of the experimental geometry. Two parallel pulsed molecular beams (HI-Ar and DZ, respectively) are crossed by pulsed lasers for dissociation ( A = 266 nm) and D-atom excitation ( A = 121.6 and ca. 365 nm) zone are selectively excited by two-photon absorption with tunable (VUV and UV)-laser light (ca. 15 ns pulse duration). In the first step atoms are excited from the ground state, D( Is), to the first excited state, D(2p), at the Lyman-a wavelength (121.6 nm), and from there to either ionization [reaction (2a)l or to high Rydberg D*(n) states [reaction ( 2 b ) ] , i e . D(ls)+VUV -+ D(2p)+UV -+ D'+e- (2a 1 -+ D(2p)+UV --+ D*(n) (2b) The velocity distribution of the nascent D(1s) atoms is then obtained by a TOF measurement of the ions or the Rydberg atoms, since momentum and kinetic energy remain practically unchanged in the excitation process.We have developed and employed first the D+ TOF technique, and subsequently also the D*( n ) TOF technique. In photofragment spectroscopy experiments we have achieved 17-20 an energy resolution of A E / E ~ 0 . 0 1 with the ion TOF technique and A E / E =0.003 with the Rydberg TOF technique.2"22 The drift path length, given by the distance between the (VUV and UV)-laser beams and a fine-mesh metal grid, was 24.3 cm in these experiments. In the case of ion TOF measurement the drift region was maintained, as much as possible, free of electric fields. Ions arriving at the grid are accelerated beyond the grid and detected by a multiplier. In the more recent variant Rydberg atoms are field-ionized upon passing through the grid, and ions (or electrons) are detected by the multiplier.The detector can be rotated around the (VUV and UV)-laser beam axis through angles ranging from OLAB = 5" to 6 L A B = -135", with @LAB = 0" defined by the reactant H-beam direction. The application of the Rydberg TOF technique depends crucially on the radiative lifetime of the Rydberg levels, since the radiative lifetime T,,d must be long compared with the flight time T. According to the two-photon selection rules, levels with orbital angular momentum quantum numbers Z = O and 2 can be excited under field-free conditions. Following the excitation scheme (2b) levels with Z=2 are most probably populated. Even for rather high principal quantum numbers such as 80 the radiative lifetime only reaches 268 ps [Fig.2(a)], a value which is comparable with the flight times occurring in the present measurements (see below). In order to achieve longer262 H+D, Exchange in Crossed Beams I I ' I 1 10 30 50 70 90 n -80 -60 -40 -20 0 20 40 60 80 "1 - n2 Fig. 2 (a) Lifetime of excited states in atomic hydrogen as a function of the principal quantum number, n, for angular momentum I = 0,2 and n = I - 1. ( b ) Lifetime of parabolic states as functions of the parabolic quantum number n, - n2 for different values of the principal quantum number, n, and magnetic quantum number rn = 0 lifetimes the excitation has been carried out with a DC electric field (of the order of 10 V cm-') applied to the excitation region. In the field, parabolic states are prepared with lifetimes shown in Fig.2 ( b ) . We have tested the effects of this measure, which was originally introduced as a means of removing ions from the excitation volume, by observing flight-time distributions as a function of the principal quantum number of the Rydberg level: no significant change of the TOF distribution was observed when levels ranging from n = 30 to n = 90 were excited. The explanation for these surprisingly high lifetimes is the production of Rydberg atoms in high orbital angular momentum states, I, produced adiabatically as the atoms leave the electric field. Resu 1 t s We have carried out experiments at various H atom kinetic energies with photolysis light at 266, 193 and 280 nm using, respectively, the fourth harmonic of the Nd : YAG laser, the radiation of an ArF laser (oscillator-amplifier arrangement), and tunable light from a frequency-doubled dye laser.Here we report results obtained at 266 nm. At thisL. Schnieder et al. 263 3.0 2.5 2 . 0 % > u- 1.5 1 . 0 0 . 5 0 2.68 ,/ 6 / - 193 nm 4 - H + D,( v = 0 I HD (V=O) +D O142eV - 3.0 - 2 . 5 - 2.0 2 q!! \ - 1.5 - 1 . 0 - 0 . 5 - 0 Fig. 3 Energy diagram for the reaction H + D2 with different energy scales for total energy and relative translational energy. Indicated are the experimental values for the relative translational energy and the accessible vibrational states of the HD molecule laser delay/ps Fig. 4 Plot of the time dependence of the H-atom density at the intersection volume obtained by varying the delay between the dissociation laser (193 nm in this case) and the probe lasers for H-atom detection.Results are shown for two different orientations of the polarization vector of the dissociation laser laser relative to the direction of detection for two different velocity groups of H atoms264 H+D, Exchange in Crossed Beams time of flightlps I 1 ' 1 I I 1 II 30 35 40 45 50 55 time of flight/ps Fig. 5 D-Atom TOF spectra for ( a ) Ere, = 1.29 eV and ( b ) Ere, = 0.54 eV. The length of the drift path is 243.5 mm energy the HI dissociation yields atoms with kinetic energies in the laboratory frame of Eki,(H) = 1.59 and 0.66 eV associated with, respectively, the lower and upper spin-orbit states of the iodine atom. The D2 beam, obtained from a pulsed valve and collimated by a skimmer to 3 mm diameter at the intersection with the H-atom beam, had an average speed of ca.1950 ms-' with a speed distribution corresponding to a translational temperature of ca. 35 K and a rotational temperature of ca. 200 K. At this D2 beam kinetic energy the two laboratory energies of the H atoms correspond to relative kinetic energies in the centre-of-mass (CM) frame of Eg& = 1.29 and 0.54 eV. (For photolysis at 193 and 280 nm the corre- sponding CM collision energies are EL% = 2.68 and 1.93 eV and E$E = 1.11 eV.) The vibrational states of the HD product molecules that are thermodynamically accessible at these energies are indicated in Fig. 3, together with the potential barrier for reaction via the linear collision c~mplex.~L.Schnieder et al. 265 Fig. 6 Vector diagrams for ( a ) V, = 17 641 ms-' and ( b ) V, = 11 216 ms-' and right-angle intersec- tion of the two beams 1.50 1.25 1:OO 0.75 0.50 0.25 kinetic energy of D atoms/eV 0.65 0.50 0.35 0.20 kinetic energy of D atons/eV Fig. 7 D-Atom kinetic energy distributions obtained from the TOF spectra shown in Fig. 5. Indicated are the calculated D-atom kinetic energies in combination with product molecules in different quantum states266 H -k D2 Exchange in Crossed Beams Ere, = 1.29 eV 1.5 1.0 0.5 1.5 1.0 0.5 kinetic energy/eV Fig. 8 D-Atom kinetic energy distributions recorded under different laboratory scattering angles for ( a ) Erel = 1.29 eV and ( b ) Erel = 0.54 eV. The solid angle of detection was 0.0053 sr The H atoms produced in the HI photodissociation are rather well defined in kinetic energy; the uncertainty due to kinematic smearing is small in comparison with other effects limiting the resolution.Fig. 4 shows pulses of the H atoms as they pass the reaction-detection zone determined in its extensions by the width of the narrower of the VUV and UV laser beams (the respective diameters of which were 0.5 and 0.8 mm). As can be seen, depending on the polarization of the photolysis light (which was of wavelength 193 nm in this particular illustration), clean pulses of either fast or slower H atoms reach the reaction zone, the length of which (ca. 200 ns) is determined by, aside from the speed of the atoms, essentially the photolysis laser beam diameter, which was ca. 1.5 mm. Fig.5 shows TOF spectra measured at EgL = 1.29 and 0.54 eV. These raw-data signals are accumulated from 20 000 laser shots (10 Hz repetition rate). From these spectra the corresponding kinetic-energy distribution of the atoms is straightforwardly derived from the time-to-energy transformation. In order to obtain the energy distribu- tion (kinetic and internal) of the HD+ D products, the collision kinematics must be taken into account. From the Newton diagrams (Fig. 6) we see that only forward scattered D atoms can be observed. Fig. 7 gives the signals converted to D-atom kinetic energy. Indicated are the vibrational-rotational energies of the HD products. Obviously, the structure of the signal distribution reflects the distribution of the HD molecules inL. Schnieder et al.267 Ere, = 0.54 eV kinetic energy/eV Fig. 8 (continued) the vibrational states, i.e. v1 = 0, 1 and 2 at EP& = 1.29 eV and v1 = 0 at EgE = 0.54 eV. Qualitatively, it is seen that in the OLAB = 0" direction the rotation of the HD molecules is only relatively weakly excited. Since the vibrational structure is clearly resolved, a more detailed analysis of the rotational distribution should, in principle, be feasible. We refrain from doing this at present, however, since better results with resolved rotational structure are anticipated in the near future. Fig. 8 shows spectra measured at various scattering angles from eLAB=O to 75". Although rotational structure is not resolved, we observe qualitatively that the rotational excitation of the DH product molecules increases with the scattering angle.Fig. 9 shows the result of a measurement of the simple differential cross-section, i e . the total signal as a function of the scattering angle, integrated over the speed of the products and thus over all internal states of the HD products. In these measurements, made with the Rydberg TOF technique, the total resolution is limited principally by kinematic smearing effects and not by the TOF measurement itself, i.e. by contributions from the collision geometry (solid angles) and energetics as well as from the rotational energy spread in the D2 reagent beam. Unfortunately, the H + D2 reaction has not yet been treated theoretically to anything like the same detail as the D+ H, reaction, with the result that a quantitative evaluation of the experimental results is not possible at this time.However, the decrease of the differential reaction cross-section with the scattering angle is as one would expect, qualitatively, from comparisons with theory.23 Also, the relative shift of the rotational268 H+D, Exchange in Crossed Beams I I I 0 30 60 90 %A,/ O 0 30 60 90 k 4 B / " Fig. 9 Total D-atom flux as a function of laboratory scattering angle for ( a ) Ere, = 1.29 eV and ( b ) Ere, = 0.54 eV distribution of the HD product to higher rotational levels with increasing scattering angle agrees qualitatively with the theoretical predictions for the reaction D + H2.2 We thank the Deutsche Forschungsgemeinschaft for the support of this work. References 1 F. London, Z. Elektrochem., 1929, 35, 552.2 J. 2. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528. 3 N. C. Blais and D. G. Truhlar, J. Chem. Phys., 1988, 88, 5457. 4 D. G. Truhlar and C. J. Horowitz, J. Chem. Phys., 1978, 68, 2466. 5 A. Farkas, 2. Phys. Chem., Teil B, 1930, 10, 419. 6 T. Dreier and J. Wolfrum, Inr. J. Chem. Kine?., 1986, 18, 919. 7 D. P. Gerrity and J. J. Valentini, J. Chem. Phys., 1984, 81, 1298. 8 E. E. Marinero, C. T. Rettner and R. N. Zare, J. Chem. Phys., 1984, 80, 4142. 9 D. A. V. Miner and R. N. Zare, J. Chem. Phys., 1990,92, 2107. 10 J.-C. Nieh and J. J. Valentini, Phys. Rev. Let?., 1988, 60, 519. 11 J. 2. H. Zhang and W. H. Miller, Chem. Phys. Ler?., 1988, 153, 465.L. Schnieder et al. 269 12 D. A. V. Kliner, D. E. Adelman and R. N. Zare, to be published. 13 S. Datz and E. H. Taylor, J. Chem. Phys., 1963,39, 1896. 14 R. Gotting, H. R. Mayne and J. P. Toennies, J. Chem. Phys., 1986, 85, 6396. 15 S. A. Buntin, C. F. Giese and W. R. Gentry, J. Chem. Phys., 1987, 87, 1443. 16 R. E. Continetti, B. A. Balko and Y. T. Lee, J. Chem. Phys., 1990,93, 5719. 17 H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Faraday Discuss. Chem. SOC., 1986, 18 J. Biesner, L. Schnieder, J. Schmeer, G. Ahlers, Xiaoxiang Xie, K. H. Welge, M. N. R. Ashfold and 19 J. Biesner, L. Schnieder, G. Ahlers, Xiaoxiang Xie, K. H. Welge, M. N. R. Ashfold and R. N. Dixon, 20 Xiaoxiang Xie, L. Schnieder, H. Wallmeier, R. Boettner, K. H. Welge and M. N. R. Ashfold, J. Chem. 21. L. Schnieder, W. Meier, K. H. Welge, M. N. R. Ashfold and C. M. Western, J. Chem. Phys., 1990, 92, 22 M. N. R. Ashfold, R. N. Dixon, S. J. Irving, H.-M. Koeppe, W. Meier, J. R. Nightingale, L. Schnieder 23 N. C. Blais and D. G. Truhlar, Chem. Phys. Lett., 1989, 162, 503. S. A. Buntin, C. F. Giese and W. R. Gentry, Chem. Phys. Lett., 1990, 168, 517. 82, 99. R. N. Dixon, J. Chem. Phys., 1988,88, 3607. J. Chem. Phys., 1989,91, 2901. Phys., 1990, 92, 1608. 7027. and K. H. Welge, Philos. Trans. R. SOC. London, Ser. A, 1990, 332, 375. Paper 1/00751C; Received 18th February, 1991