DYNAMICS OF THE REACTION S ( 1 D ) + HD , H 2 , AND D 2 : ISOTOPIC BRANCHING RATIOS AND TRANSLATIONAL ENERGY RELEASE

Doppler profiles of H and D atoms from the reaction S(tD) with HD and a mixture of H and Dz have been measured by a laser-induced fluorescence technique with a vacuum ultraviolet laser. An isotopic channel branching ratio of q, (SD + H)/, (SH + D) is measured to be 0.9 + 0.1 in the reaction of S(ID) + HD at average collision energy Ecol 1.2 kcal/mol. In S(D) + HD, Dz, and Hz, the translational energies released are almost the same, 4.6 _+ 0.5 kcal/mol for H and D production channels. The measured branching ratio and translational energy release suggest that the reaction proceeds via a long-lived complex formed by insertion.


INTRODUCTION
An atom-diatomic molecular reactive scattering is one of the fundamental elementary chemical reactions. Among them, the system for an atom, S and O, in the electronically excited singlet state, S(1D) + H2(l') --> SH(2/7) + H(2S), AH =-6.4 kcal/mol (1) O(1D) + H2(1Z) ---> OH(Z/-/) + H(2S), AH -43.6 kcal/mol (2) has drawn much attention for many years because this system provides several particularly interesting features in the study of reaction dynamics. This system is characterized by a deep potential minimum corresponding to H20 or H2S on its XA surface that is directly associated to the reagents. Given these features, numerous experimental and theoretical studies have been performed to understand the dynamics of the reaction particularly for the O(D) + H2 system, Previous measurements on internal energy distributions and the angular distributions of the OH products largely support an insertion mechanism for this reaction. [3][4][5] Of particular importance among the measurements is the isotopic branching [H]/[D] ratio, which denotes the channel branching ratio (OD + H)/ q,(OH + D) from the reaction of O(1D) with HD. A measurement using a laserinduced fluorescence (LIF) detection of H/D atoms with vacuum ultraviolet (VUV) laser light at a low collision energy (Eco 2.4--3.4 kcal/mol) reported the ratio of 1.13 + 0.086 or 1.4 + 0.3. Theoretical ratio q,(OD + H)/,t,(OH + D) varies from 1.1 2.3, depending onwhat surface is used 8,9 because the ratio is very sensitive to the shape of the surface. Extensive theoretical studies and the recent measurements of the vibrational energy distribution of the OH product predict a very short-lived complex because of its large exoergicity.
On the other hand, detailed dynamics of the S(D) + H2 reaction are still ambiguous. Since the S(D) + H 2 reaction has much smaller exorgicity than O(D) + H2, comparison of these two isoelectronic reactions reveals a different detailed dynamics. In this paper, we report the reactions of S(D) with H, D2, or HD at a low collision energy using a vacuum-UV LIF technique which enables the measurement of the Doppler profiles of H and D spectra so that the average kinetic energies of the products can be calculated: S(1D) + HD SD + H, AH =-6.0 kcal/mol SH + D. AH =-5.6 kcal/mol (3) EXPERIMENT The experimental setup used is shown in Figure 1. CS2 and HD (H2, D2) gas flowed into a reaction cell. The cell, 60 60 60 mm, was pumped by a rotary pump and a liquid nitrogen trap. The pressures of CS2 and HD in the reaction cell were typically 5 and 60 mTorr, respectively. ArF excimer laser light at 193 nm (--2 mJ/pulse, 10 Hz) dissociated CS2 and produced translationally hot S (D) atoms. 200 ns after the firing the photolysis laser pulse, a probe vacuum-UV laser was fired to detect H and D atoms produced from the reaction. The two laser beams of the photolysis and probe were perpendicularly crossed with each other. The probe light for H and D atoms around 121.6 nm was generated by four-wave mixing using a 2w 60 scheme in a Kr gas cell with two tunable dye lasers pumped by a XeC1 excimer laser (308 nm, 240 mJ/pulse). The output of the vacuum-UV light going through the reaction cell was monitored with a vacuum-UV monochromator and a solar-blind photomultiplier. The laser induced fluorescence was observed by another solar-blind photomultiplier at right angles to both the photolysis and probe laser beams passing through a LiF window and a band-pass filter (Acton Research, , 120 nm, A 12 nm). The delay (200 ns) between the photolysis and probe light pulses was controlled with a time jitter of about 10 ns. Since the beam diameter of the photolysis laser was large enough, within a 200 ns delay the reactions were presumed to proceed In the experiments for the spatial distribution of the H atom velocity, the output of the photolysis laser was polarized with a pile-of-plates polarizer. Doppler profiles were measured in the two configurations of Ea//kp and Ed 2_ kp, where Ea is the polarization vector of the linearly polarized dissociation laser light and :p is the propagation direction of the probe laser. The dye laser for the dumping light 032 was installed with an intracavity etalon so that the spectral width was narrowed. In order to test the spectral resolution of our system, the Doppler spectra of the product D atoms were measured with Ar (2 Torr) added. While the theoretical thermal Doppler width is as narrow as 0.65 cm-1, the measured full width at half maximum was 0.92 cm that was expected for a D atom with T 300 K, considering that the splitting of the upper electronic states AE(2P1/2 2P3/2) is 0.37 cm -1 and the spectral width of the probe laser light is 0.34 cm-. Spectral width was broadened by a factor of 1.4 for the D atomic line at 300 K. Spectral broadening due to these terms is not large for the product H and D atoms from S(D) + H2, D2 and HD because H and D atoms have typical Doppler widths of 3 and 2 cm-1, respectively. The translational energy data were corrected for this broadening and the change was less than 5%.

RESULTS
The typical vacuum-UV LIF spectra of the H and D atoms produced from the reaction of S(ID) with HD are shown in Figure 2. The isotopic ratio [H]/[D] is calculated to be 0.9 + 0.1 for S(1D) + HD from the obtained spectra and listed in Table I Table I  With a linearly polarized photolysis laser at 193 nm, the measured Doppler profiles of the H(D) atoms were identical to each other for the two polarization configurations of ]d [[ kp and gd --[-lp. This indicates that the angular distributions of the H and D atoms are almost isotropic in the laboratory (LAB) frame although an anisotropic angular distribution is expected for the reactant S(1D) atoms produced from photodissociation of CS2 by the polarized 193 nm laser light. Therefore, we assumed an isotropic velocity distribution for the H and D atoms in the LAB frame. The average kinetic energies of the H and D atoms in the laboratory frame were calculated from Figure 2 with the second moment <vZ> of the observed Doppler profiles and then converted to the total kinetic energy released to the products in the center-of-mass (c.m.) frame <Et>. A second moment of the Doppler profiles of a product atom is given by the following equation: where g(v) is the normalized Doppler profile, v the frequency of the probe laser, and Vo the resonance center frequency.   where m(i) refers to a mass of the reactant and T is room temperature. <Ethan(S)> is the average translational energy in the LAB frame for the S(D) atoms which are produced in the photolysis of CS2 at 193 nm. The average kinetic energy of S(1D) from CS2 at 193 nm has been reported to be 4.8 kcal/mol by McCrary et al. 13 The estimated collision energies <Eco,> are 1.2, 1.3, and 1.1 kcal/mol for S(D) + HD, D2, and H 2. The average available energy is obtained by <EAvL> <Eco,> + AH as shown in Table II. In this calculation the heat of formation used for AH(SD) 34.61 kcal/mol, AH(SH) 34.10 kcal/mol AH(OD) 8 Table I, which is 0.9 +_ 0.1. Black and Jusinski 6 reported that the rate constant for the S(D) + H system is k 2.1 x 10 -l cm molec-ls -1 at 300 K. This large rate constant suggests that reactant attraction is rather strong and leads to a complex. When considering product branching ratios from a hot complex, Zamir and Levine 7 proposed the prediction of a statistical theory. The prior distribution of states in the products is of the form, P(Er, ER, EvIEAv0 (2J + 1) pv(Er) ,5 (EAw-Ev-ER-Ev)/p (EAw). (8) The density of translational states pv(Er) is given as usual by AvEr where A T -//22h3. P(EAw) is the total density of states and serves to normalize the prior distribution. In the present set of reactions A / HD, the rotational and vibrational levels of product hydrides are widely separated so that a summation over the discrete vibrational states is required for calculation of the state density. where J and v are the rotational and the vibrational quantum number, respectively.
ui, is the reduced mass of systems and j. In the calculation of EAW, the averaged collision energies <Eco,> are calculated from the data of the translational energy reported by McCrary et al. 13 Substituting the known spectroscopic data and EArL from calculated with the average value <Eco>, probably because the range of distribution of the collision energy is as small as 1 kcal/mol. Our experimental result, 0.9 + 0.1 for S(1D) + HD is in good agreement with the theoretical ratio, suggesting the formation of the complex. For comparison purpose, the isotopic branching ratio [H]/[D] is also calculated for O(D) + HD using eq. (9), which is 1.01. The reported experimental value was 1.5 + 0.2 for the same collision energy. This difference between the theoretical and experimental values suggests nonstatistical behavior of the H20* complex.

B. Kinetic Energy Release And Reaction Mechanism
The detailed dynamics of the reaction can be understood from the internal energy and the isotropic angular distribution of the products. The deep potential well followed by a steep increase in the potential energy along the reaction coordinate favors a long-lived complex and a statistical energy distribution among the degrees of freedom of the products. As shown in Table II,  H2 S decomposes much more slowly than H20*.
Most of the recent trajectory calculations predict a very short lifetime of the complex, shorter than one or two bending vibrational periods of the H2 O* complex. The short lifetime of the complex H20 would be expected because the system has a relatively small reduced mass upon which a large impulsive force is applied with large excess energy. Fitzcharles and Schatz presented a simple kinetic model for O(D) + HD as follows. The O(D) atom preferably approaches at right angles to the HD molecular axis and the insertion takes place. The bending mode in the HDO* complex is strongly excited. Before the vibrational energy in the bending mode is redistributed among other modes, a hard collision between the H and D atoms causes dissociation of the complex and the lighter H atom escapes the complex with higher probability. On the other hand, in the HSD* complex that has only 6.8-7.2 kcal/mol as the available energy, the bending mode is not strongly excited. Hence, the vibrational energy is randomized in the long-lived HSD* complex. Thus, the relative quantum yield of H and D is close to unity. Energy partitioning in dissociation of an energized molecule is discussed in the framework of the statistical theory by Zamir and Levine. 8 An average translational energy <Er> is given by, <ET> --vVV'x=0 m=a0 ET P(E, ER, EvlEAvL). (10) With suitable molecular constants, the average translational energies for the reactions of S(lD) + HD, H2, D2 are calculated using the average collision energies. The fraction <fit> of the translational energy over the available energy is shown in Table II The dissociation mechanisms are schematically shown in Figure 4. During a relatively long lifetime of a HSD* complex, the excess energy in this reaction is randomized almost completely and follows the statistical energy partition rule. However, in the HOD* complex, a hard collision between the H and D atoms induces separation of the H or D atoms from the oxygen atom. The intermediate H20* decomposes into OH + D or OD + H after this single bending vibration. An anisotropic angular distribution of the product OH was reported by Buss et al. in their molecular beam scattering experiment of O(1D) + H 2.