Faraday Discuss. Chem. SOC., 1991,91, 73-78 Exchange Reactions of Hydrogen Atoms with SiD,: An Inversion Mechanism? Benjamin Katz Department of Chemistry, Ben Gurion University, Beersheba, Israel Jeunghee Park, Sunita Satyapa1,t Shintaro Tasaki, Arun Chattopadhyay, Whikun Yi and Richard Bersohn Department of Chemistry, Columbia University, New York, NY 10027, USA The reaction H + SiD4 -+ D + SiH3D is found to have a much lower threshold than the corresponding exchange reaction of H with CD4. The D atom carries away most of the initial translational energy of the H atom. When the H-atom velocity distribution is anisotropic, the D-atom velocity distribu- tion is anisotropic in the same sense. The exchange cross-sections for the reaction H + SiH3D are about one half of those for SiD,.All this evidence leads to the conclusion that the mechanism of the exchange is an inversion. Isotope-exchange reactions are interesting because of the near symmetry between reactants and products. The potential surface is symmetric, which reduces somewhat the labour of its construction. Reactions in which hydrogen-atom isotopes are substituted are of particular interest, again because the construction of a potential surface is made less formidable. The H+D, (or HD) reaction is of course the centrepiece of all hydrogen-atom exchange reactions. In addition to all of its other simplifications it has the advantage that abstraction and exchange are the same reactions. For all other hydrides there are always two possibilities, exchange and abstraction RD+H -+ RH+D ( 1 ) RD+H ---* R+HD (2) The exchange reactions H + MD4 -+ MHD3 + D are interesting from several points of view.First of all, at least part of an a6 initio potential surface has been constructed for the CH5 system'.' and this could, in principle, be done also for the SiH, system. Secondly, there already exist experimental data on isotopic variants of the CH5 system, namely T+ CH4 and T+ CD, .3 At thermal energies only abstraction could be observed. At a relative kinetic energy of 65 kcal mol-', the ratio of the cross-section for abstraction to that for exchange was 16 for T+CD, and 3 for T+CH,. At Euclear recoil energies (keV) the ratio was 0.8. The threshold energy for abstraction was 10 * 2 kcal mol-' and that for exchange was 35* 10 kcal mol-'. In the H+CD, reaction we have found by laser-induced fluorescence (LIF) weak D-atom signals at relative kinetic energies of 57 and 73 kcal mol-I.These experiments will be discussed in a later report. Bunker and c o ~ o r k e r s ~ , ~ devised a potential for the CH5 system which fitted the known bond energies and force constants. Using this potential they calculated and averaged over numerous classical trajectories for a number of values of relative kinetic energy. They found that the experimental cross-section ratios at the relative energy of 65 kcal mol-' could not be fitted unless more than three atoms were involved in the t Present address: Vassar College, Poughkeepsie, NY. 7374 Exchange Reactions of Silanes- Inversion ? exchange reaction. Inversion is therefore suggested.In contrast all exchange reactions of hydrogen isotopes so far observed in optically active molecules CHXYZ, where X, Y and Z are not hydrogen atoms, take place with retention of configuration. Because preliminary experiments produced only weak D-atom signals in the exchange reaction with CD,, we decided to try SiD, instead. It has longer bond lengths ( 1 . 4 8 ~ ~ . 1.08 A) and weaker bonds (92 vs. 99 kcal mol-*).6 The frequencies of SiH4 and CH, can be fitted using a central force model with a stretching force constant and two bending force constants.' In units of lo5 dyn cm-' the stretching force constant diminishes from 2.66 to 1.96 in going from CH, to SiH,. The bending force constants diminish from 0.60 to 0.22 and from -0.79 to -0.35 in the same units.In short, silane is a much looser and floppier molecule than the rigid methane. Because the hydrogen atoms are so much farther apart, during a collision with a fast atom, it should be much easier to change the shape of silane than methane. Experimental Our basic experiment is to generate H atoms by dissociating a suitable precursor with a pulsed laser and probing the H-atom reactant and the D-atom product by laser-induced fluorescence. The target molecule, in this case H2S, was dissociated by an excimer laser to produce H atoms of fairly well known energy. At a short time later, typically 70- 100 ns the probe laser was fired, producing 121.6 nm light which excited the hydrogen atoms. This technique has been described in previous papers from this lab~ratory.'~~ The 121.6 nm Lyman (Y light was generated by four-wave mixing in two different ways.In the early experiments this was done by frequency tripling, that is, by mixing three 364.8 nm photons in Kr to give a fourth wave at 121.6 nm. One exploits in this way the near resonance with the Kr absorption at 123.6 nm. Later a still more efficient method was used involving the mixing of two 212.56 nm photons and an 845 nm photon, both dye lasers having been pumped by the same XeCl excimer laser. The 212.56nm light is obtained by frequency-doubling 424.1 1 nm light in a barium metaborate crystal which was cut at such an angle that 212nm light entering normal to one face would have the maximum probability of being doubled. The energy of two 212.56 nm photons is exactly resonant with a g + g transition to the 5p[O1/2] state of Kr; by use of both resonances much more intense VUV is generated at the expense of added experimental complexity.Silane is transparent at both 248 and 193 nm and furthermore it was explicitly shown that no D-atom signals appeared when SiD, was irradiated in the absence of H2S. SiH3D was synthesized by reacting LiAlH, with SiC13D (obtained from Merck Isotopes) in ether." Just before an experiment the deuterated silane was frozen in liquid nitrogen and pumped on to remove any hydrogen which might have formed by reaction with traces of water. The results are all obtained from the LIF excitation curves of H and D atoms. Their peaks conveniently are 21 cm-' apart, far enough so the curves do not overlap and near enough so that the laser parameters remain constant during the sweep from one resonance to the other.The results are categorized as follows: (1) cross-section of H with SiD,, (2) cross-section s f H with SiH3D, (3) average kinetic energy of the D product and (4) alignment of the D-atom velocity when the H-atom velocity is aligned. Cross-sections for H + SiD, ---* SiDJH + D The rate constant k for the above reaction can be extracted from the rate equation: d(D)/dt = k(SiD,)(H) (3)B. Katz et al. 75 - 5 0 5 detuning wavenumber/ cm- ' - 4 - 2 0 2 4 detuning wavenumber/cm-' 2 4 Fig. 1 H-atom and D-atom fluorescence excitation spectra taken 100 ns after dissociation of H2S with polarized 193 nm light in the presence of SiD4. The heavy (light) lines are spectra taken with the E vector perpendicular (parallel) to the probe laser beam.The curves have been normalized to equal maximum amplitude whose solution at short times is (D)/(H) = k(SiD,)t (4) Fig. 1 shows typical LIF excitation curves for an H reactant and a D product. The H curve is nearly unchanged in times of the order of 500 ns whereas the much weaker D signal increases linearly with time. In eqn. (4) c is the time between the pump (dissociat- ing) and the probe pulses. In general a second-order rate constant is an average ( U(T( u ) ) , that is the product of the relative speed of the reactants times the cross-section averaged over the distribution of relative speeds. When one of the reactants is produced by a photodissociation and is much faster than the other, the distribution in relative transla- tional energies is much sharper than with thermal reactions.One can show' that the average relative translational energy is given by: and the mean-square fluctuation in Erel is76 Exchange Reactions of Silanes- Inversion ? Table 1 Relative translational energies and cross-sections for reactions of H atoms with deuterated silanes parent wavelength of average relative cross-section molecule dissociation/nm energyleV /A2 silane H2S 193.3 2.08 f 0.05 0.36 f 0.03 SiD4 H2S 193.3 2.07 f 0.05 0.17 f 0.03 SiH3D pi,j is the reduced mass of particles i andj, HX is the H-atom precursor and M is the species with which the H atom reacts. P is the momentum gained by the photodissoci- ation and is equal and opposite for the two fragments.The H atoms used in these experiments were generated by photodissociation of H2S" at 193.3 nm. At this wavelength only 63% of the SH radicals are in the v = 0 state, with a corresponding H-atom relative speed of 2.09 x lo6 cm s-l. The other SH radicals are in higher u states with lower speeds for their H-atom partners, but the average speed is 1.94 x lo6 cm s-l. The average relative energy under these conditions is listed in Table 1. The average relative energy was calculated from eqn. (5) and the uncertainties quoted are the square roots of the values calculated from eqn. (6). The rate constatnt for these H atoms was (0.70f0.07) x lo-'' molecule-' s-l. Dividing by the average speed we obtain a cross- section of 0.36 f 0.03 A'. We also found D signals when H2S was dissociated at 248 nm.Thus the potential barrier is less than 1 eV, the energy of these H atoms. Cross-sections for H + SiH3D -+ SiH4 + D The rate constant for the exchange of H with SiH3D under the same conditions as with SiD, is (0.33 f 0.03) x lo-'' molecule-' s-l. The corresponding cross-section is 0.17 f 0.03 A'. The main point is that the cross-section is more than one quarter of the corresponding cross-section for SiD,. Kinetic Energy of the Product D Atoms As described in the introduction, the kinetic energy is simply calculated from the second moment of the fluorescence excitation curve. How elastic is the exchange reaction? In other words, what fraction of the original kinetic energy of the reactant H atom is retained in the product D atom? At 193 nm we find that the average initial kinetic energy is 2.08 eV and the leaving D atom has a kinetic energy of 1.78 f 0.22 eV.Relatively little energy is left behind in the SiHD3 molecule. Alignment of D-Atom Velocities An H,D exchange reaction is very favourable for an angular distribution study because the laboratory and centre-of-mass velocities are negligibly different. Photodissociation with polarized light can generate an anisotropic velocity distribution of the reactant H atoms which has the form f(K,.> = 1 / 4 4 1 +PRP'(COS R , d (7) where Ou,E is the angle between the electric vector of the light wave and the velocity o of the H atom. PR is the anisotropy parameter for the alignment of the velocity of the reactant H. To obtain the distribution of velocity directions u' of the product D atoms, we must integrate over all initial directions of the reactant H atom using the addition theorem for Legendre polynomials with the result W'(C0S %,d = (P'(C0S @))P,(COS 0 u d (8)B.Katz et al. 77 The distribution function for the direction of the D-atom velocity is where pp = PR(P2(c0s 0)) is the product D anisotropy parameter and 0 is the angle between the velocity vectors t, and u'. The necessary conditions for anisotropy of the product D atom are that both the reactant velocity and the differential cross-section be anisotropic. By averaging over the distribution function of eqn. (7) or (9) one can show that the anisotropy parameters PR or pp can be extracted from the experimental fluorescence excitation curves (as shown in Fig.1): where 11 (I) means that the probing laser beam is parallel (perpendicular) to the E vector of the dissociating laser. For H2S at 193 nm the value -0.82 f 0.08 was obtained. When corrected for the 95% polarization of the light, this value agrees with the previously reported value of -0.96." For the SiD, exchange reaction the D atoms had an uncorrec- ted anisotropy parameter, pp = -0.72 f 0.35. Discussion What can we conclude about the mechanism of the reaction from the evidence? Does it take place by a direct substitution analogous to an s N 1 reaction in which the main players are the entering H atom and the Si and D atom of a Si-D bond? Or does it take place by an inversion analogous to an sN2 reaction in which the D atom departs from the side of the molecule opposite to the side which the H atom attacks? In the inversion every atom of the molecule plays a role.The angular dependence of the reaction cross-section implicit in the fact that ( P2( cos 0)) = 0.88 (+0.12 - 0.41) leads to a typical reactive scattering angle 0 = 16". The positive sign for the average means that the H and D velocity vectors are generally either parallel or antiparallel to each other. We believe that a direct localized attack of the H atom on an Si-D bond would cause the D atom to recoil at a fairly large angle, making ( P 2 ( 0 ) ) small or even negative. In an inversion both velocities are generally in the same direction. The fact that the typical angle is 16" rather than zero may be explained qualitatively by the fact that the silane molecule is rotating prior to the collision and that the reacting H atom does not have to be incident exactly along the threefold axis.The inversion mechanism is nicely consistent with but not completely proven by the alignment of the D-atom velocity. Evidence against a direct attack of an H on a C-D bond is given by the ratios of the cross-sections of H with CD4 and CD3H. These would be in the ratio of four to one for a direct attack. However, the actual ratios show that the H atoms make the C-D bond more susceptible to attack. This is easily understood in the inversion model because the three non-reacting hydrogen atoms have to move quickly during the collision to reach the presumed trigonal-bipyramidal transition state. If these three atoms are heavier with more inertia, it will take longer for the atoms to reach the transition state.In the meantime the attacking H atom may just bounce away. The fact that half of the incident H-atom energy is retained in the exiting D atom is also an argument for inversion. During an inversion bond angles have to change but only two bond distances are changed, the new one and the one which is broken. When these two bonds are opposite each other as in an inversion, the most efficient transfer of momentum and energy will take place. Indeed because the D atom has twice the mass of the H atom and half of its velocity, the momentum of the leaving D atom is about the same as that of the entering H atom.78 Exchange Reactions of Silanes-Inversion ? On the basis of the above evidence the inversion mechanism seems to be the most natural explanation.Trajectory calculations which fit the many data given here should be helpful in obtaining a potential which will discriminate between inversion and direct attack mechanisms. The following simple model gives an overall picture of the reactive collisions between a hydrogen atom and silane. The forces between a hydrogen atom, all of whose electrostatic moments are zero, and silane, whose lowest non-zero moment is an octupole moment, are very short range. Therefore the fast incident H atom can be thought of as attacking a nearly stationary silane which is not reoriented before the collision. The collisions can be divided into three types, those for which the H, D and Si atoms are nearly collinear, those for which the H atom is directed to or near to the Si atom, i.e.opposite to an Si-D bond, and those collisions with a substantial impact parameter relative to the Si atom. The first type are well suited to transfer energy from the incident H atom to the weaker Si-D bond, forming HD molecules with low rotational energy. The second type result in the exchange reaction and the third type cause non-reactive inelastic processes in which rotations and bending vibrations of the silane are excited. This model can certainly be tested by probing the HD molecules formed by abstraction. Finally, we give some more chemical explanations of the mechanism. The force constants previously quoted show that silane offers considerable resistance to bond- length changes but very little to bond-angle changes.The inversion mechanism involves bond angle changes but no bond length changes of the non-reacting silicon-hydrogen bonds. It therefore should have a lower barrier to reaction than other mechanisms. Also because the high-frequency stretches (except for those of the newly made and newly broken bonds) are unaffected by the reaction, less vibrational energy should be released in the molecular product. The briefest explanation for the large difference in barriers to exchange between CH4 and SiD, is that the Si atom, being a second-row element requires much less energy to expand its valence shell, becoming pentavalent or even hexavalent. But even this explanation implies an inversion mechanism. The counter argument is that the Si-D bond being much weaker than the C-D bond is much more readily exchangeable.We conclude that at the energies used here exchange takes place by inversion. This research was supported by the U.S. National Science Foundation and the Petroleum Research Fund. Note added in proof: Maitre and Pellissier (Chem. Phys. Lett., 1990, 166, 49) used an ab initio study to show that SiH5 is not a stable radical but rather dissociates spon- taneously into H + SiH,. 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