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A tunnelling model for activated adsorption at metal surfaces
Journal of Electron Spectroscopy and Related Phenomena, 45 (1987) 207-213 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
A TUNNELLING
S. HOLLOWAY,
MODEL
FOR ACTIVATED
D. HALSTEAD
AND
ADSORPTION
AT METAL
207
SURFACES.
A. HODGSON
The Donnan Laboratories, University of Liverpool, Grove Street, P.O. Box 147, Liverpool, L69 38X, U.K.
SUMMARY
A tunnelling mechanism is presented for the dependence of the initial sticking coefficient for a light gas as a function of its primary energy. A model calculation is presented for the adsorption of Hz and D2 on a metal surface. The sticking coefficient exhibits a strong dependence on both the primary beam energy and the degree of H2 vibrational excitation. The results are discussed in the light of recent molecular beam scattering results for N2 and CH4.
INTRODUCTION
With the advent of detailed molecular beam scattering experiments, the number of gas/surface systems exhibiting an activation barrier to adsorption are ever increasing. In terms of the kinetic behaviour for the reaction Az(gas)+metal -+ 2A(ads)+metal the effects of such a barrier are well known, (i) the initial sticking coefficient S, shows an abrupt increase as a function of translational energy of the molecules and (ii) the A2 desorption flux often has an angular distribution P($) - cos%+ [I]. With the notable exception of Nz/W(llO) [2], it has been observed that the principle effect of changing the initial angle of incidence is to simpl;- rescale the primary energy dependence of S, to the kinetic energy normal to the surface, E*=Et COs’8i (so called normal energy scaling) [3]. These observations appear to support the model first suggested by Lennard Jones [4], that the activation barrier to adsorption is inherently one-dimensional in nature and that it is located in the entrance channel of the reaction pathway (fig. 1) 131. Recently, Karikorpi et al [5] suggested a model for activated adsorption of H2 which extended this picture to include variations in the barrier with the impact parameter within the surface unit cell of the substrate. While this model was able to trivially account for both observations, (i) and (ii) above, it also proposed a technique for probing the topology of the reactive potential energy (hyper)surface @‘ES). The H2 diffraction intensities will contain detailed information concerning the spatial location of the barrier particularly in the energetic region where the sticking coefficient abruptly increases. By inverting such data, it should be possible to map out the PES in some detail. To extend our knowledge of entrance channel effects, a second technique would be
0368-2048/87/$03.50
0 1987 Elsevier Science Publishers B.V.
208
to measure both S, and P(t3f) and their dependencies on the internal states of the molecule. This forms the subject of this paper. The particular problem addressed here is the degree to which vibrational excitation in the incident molecule couples to the “reaction coordinate” in the language of transition state theory [6]. A model PES will be presented for the Hz/metal system based on an ab initio calculation 171~which displays the essential topological features for dissociative adsorption reaction. A quantum mechanical calculation for the ensuing dynamics will show that for subbarrier initial translational energies, there exists a significant probability for tunnelling through the barrier along the vibrational coordinate [8]. The consequences of this effect on both the adsorbed and scattered particles will be presented. MODEL
II
I
a)
H-H seDaration: x
3)
Section along x’-x”
Fig. 1 (a) Here is shown a schematic contour plot for the Hz/metal PES. The entrance channel (marked as HZ) is of the form given by eqs. 1 and 2, whereas the exit channel (marked as W) shows a sharp linear decrease as described in the text. A section across the PES at constant z along x’-x” is also shown (b), detailing the ground and first vibrational wavefunctions (not to scale) for the harmonic oscillator. Assume that a diatomic molecule is incident normally on a metal surface in its rotational ground state, with kinetic energy EL and in vibrational state v. The entrance channel PES is primarily derived from the electronic state of the system that asymptotically correlates with the (Hz/Metal) diabatic state. In the neighbourhood of the lowest bound states this can be simply modelled by an harmonic potential in the direction of the bond x; V,(x) = 1/zpo2x2,
(1)
the vibrational frequency w taken from gas-phase spectroscopy. As the molecule nears the surface it experiences a strong repulsive force in the centre of mass direction z, arising from the Pauli exclusion principle, which may be approximated by, V*(z) = V, emti,
(2)
where constants V, and h can be related to the surface electron density 191.Within an adiabatic picture this state will be distorted as it correlates to either the dissociatively
209
adsorbed, 2H/Metal [71, or molecularly adsorbed, H$+/Metal [lOI state. If we assume that the initial translational energy is insufficient to allow the H2 to sample this region of configuration space, then such distortions will not affect the dynamics significantly. Thus we do not explicitly address “classical over the barrier” activation here, but consider those processes which are classically forbidden and will form the low energy tail of S,. The form of the activation barrier in the adsorbed state is determined by the steeply descending potential in the x-direction and to model the barrier, results of an ab initio total energy calculation for H2 interacting with a Cu cluster have been used [7]. These calculations indicate that the crossing seam is approximately linear, subtending an angle of -52’ with the x-axis with a minimum barrier of -1.4eV. This is schematically shown in fig. 1. In this preliminary study, we will treat the z-motion classically and the x-motion quantum mechanically. This mixed treatment is motivated by the fact that the xmotion is governed by the effective mass, p=M~/2, whereas the z-motion is determined by the molecular mass Mrr,al=2M~. Calculations are currently in progress where the Schrbdinger equation is explicitly solved for the time evolution of a 2dimensional wavepacket Y(z,x;t) over the model PES described above [ll]. This will provide a detailed check of the approximations used in this present work. For a given value of EL eq. 2 gives a value of the classical turning point in the z-direction, z,, = h-l ln(EI/V,). (31 It is quite clear that the maximum tunnelling will occur in this region of space since not only is it here that the barrier is at its lowest, but more importantly at zturn, the molecule is stationary. In this region, the tunnelling rate may be approximated by the golden rule expression for transitions from the v th vibrational state in the entrance channel to a small range of final states about AE in the 2I-I continuum 1121, cv2 R (v) - F c
(4)
I-4)” 1vf4*. f
For convenience, the interaction potential V is taken as being a constant. Essentially the problem is reduced to one of evaluating Franck-Condon overlaps between an initial vibrational state $v and final states vf, where f characterizes a continuum state of a diffusing chemisorbed hydrogen. Typically vf will be given by an Airy function in x. Since the F’ES decays steeply in the in the final state, this motivates the use of the multidimensional reflection approximation form for the wavefunction vf - 6(x-x,), a method which has been used with some success in molecular predissociation studies [121. Eq. 4 may then be trivially integrated, (5)
R(v) - I $, (x,) I 2. Before S, can be evaluated, it remains to estimate the length of time that the H2 molecule spends in the tunnelling region. Let us assume that a region of space exists, AZ, about zturn, where tunnelling is favourable. From eq. 2 it is straightforward
to show that the traversal time over this region is,
A2 - EL-‘/~.
210
Thus for a direct scattering encounter, the sticking probability is given by, S,(v) = Ar R(v)
(6)
All that remains is to relate xs to EJ, and this is done using the linear seam approximation discussed above; xs = a ztum + B. with constants a and B chosen to reproduce the barrier region of the theoretical PES [7]. When used in conjunction with eqs. 6 and 3, this gives the final expression for S,(v,EJ. RESULTS Fig. 2 shows the variation of S, as a function of the primary energy, EL for H;! and D2 molecules in their ground vibrational state, v=O, interacting with a metal surface having an activation barrier of 1.4eV. The general shape of the curves arises from the increased tunnelling which occurs as El increases, which affects a decrease in xs (see fig.la). There is a significant isotope effect which arises as a consequence of the
-5o! 0.00
0.20
0.40
0.60
0.80
1.00
Translational energy (eV) Fig. 2 The translational energy dependence of the initial sticking coefficient for H2 and D2 scattering from a surface having an activation barrier of 1.4eV. Results are presented for molecules in their ground vibrational state which would correspond to a room temperature supersonic beam. Typically, experimental observations for S, cover a range of approximately six orders of magnitude (see fig. 4). reduced spatial extent of the v=O wavefunction for the heavier particle. With the advent of state selection of reactants it is interesting to investigate the dependence of S, on the degree of initial vibrational excitation of the molecule. From gas phase scattering data for systems such as Br+Cl(v)+HBr(all v’)+Cl [13], it is well known that rate constants for vibrationally excited reactants can increase by orders of magnitude over ground state values and it is interesting to investigate if such results persist for surfaces reactions. Results for H2 are shown in fig. 3. In the asymptotic region of xy (I” (xJ > $6 (x,), and thus the ratio of S,(v)/S,(v=O), will be greater than unity. The gradual decay in the quotient with increasing El occurs since higher
211
translational energies bring the molecules nearer to the activation barrier. This trend is a quite general result and does not depend crucially upon the exact details of the PES. Results for D2 adsorption follow the same general pattern as Hz and are not included here.
Hydrogen 654321“’
I
0.00
I
I
I
0.20 0.40 0.60 0.80 Translational energy (eV)
I
1.00
Fig. 3 The ratio of initial sticking coefficients as a function of translational energy for vibrationally state selected H2 molecules scattering from a surface having an activation barrier to adsorption of 1.4eV. For a given translational energy, the greater spatial extension of excited vibrational states results in an increased dissociation probability. EXPERIMENTAL SURVEY The growth of state-to-state scattering experiments at surfaces is prodigious [14]. While the majority of experimental [15] and theoretical work [16] has so far concentrated on rotational inelastic scattering, some studies of dissociative adsorption have appeared where vibrational problems have been addressed [17,18]. Of particular note are the studies of CH4 and CD, scattering from W 1191, and N2 from Fe surfaces [20] (fig. 4). These experiments employ beam-seeding techniques to explore wide ranges of translational energies while keeping the molecules in their vibrational ground state. The general shape of the v=O nitrogen results bear a strong resemblance to the theoretical curve shown in fig. 2. For the N2/Fe system, thermal beam experiments performed on cold substrates [21] have indicated that the PES is more complicated than our model suggests and that a molecular state occurs on the surface before any activation barrier is encountered. Although this would suggest that for low El our model would be neglecting an important reaction channel, these results do not invalidate our model at higher energies, where trapping into the precursor is unlikely. It is possible to map our model on to the methane experiments, by associating the degree of freedom, x, with a stretching mode of the CH4 molecule. This may be at least partially justified since the reaction occurring is essentially a bond scission, with H being abstracted from the CH4. The apparent linear relationship between S, and El for the methane data we believe, is an indication that the
212
theoretically predicted saturation effects have not yet set in, and to substantiate this claim, it would be necessary to extend the range of translational energies. Both the order of magnitude for the isotopic shift, and the divergence of the rates at lower EL are features which are well described by the model. For both systems preliminary experimental results obtained by heating the supersonic nozzle source 122,231, have been presented for beams containing a mixture of initial vibrational states. These data are well described by the model and form the basis for a separate study [24].
Methane/WC1101
N2/Fe(lll) -1 -
-1 -
cr? _32 P -5-
V? Z IJ
+l
I -7
I 0.0
1.0
2.0
CH4 CD4
-5
?
, I 3.0
-3
## -7
4.0
5.0
Translational energy (eV)
0.0
0.2
0.4
0.6
0.8
1.0
Translational energy (eV)
Fig. 4 Experimental results for the dissociatiative chemisorption reactions N2*2N [20], and CH4+H+CH3 [19]. Initial results for hydrogen adsorption on W(100) [WI showed a strong isotope dependence [S,(H$/S,(D$ -1.4141 in the opposite direction to that which would be expected on the basis of the present model. Similar findings have also been reported for the adsorption of hydrogen on various faces of Cu, based on the results of HD formation in Hz-D scattering experiments [26]. In more detailed studies by Madey [27], and Thomas and King [28] it was shown that within experimental accuracy, there was no measurable isotope effect for the W(100) surface. In the light of recent experimental developments, it would be of great interest to measure the primary energy dependence of the pure Hz and D2 dissociative adsorption reaction on a surface exhibiting a large activation barrier. In its present form, surface motion has not yet been included in the model. Although trivially, the shape of the activation barrier would be modified by such effects, from a dynamics point of view, it is probable that vibrational deactivation would mitigate a net decrease in any vibrational enhancement expected at OK. This would give rise to the slight substrate temperature dependence for S, which has been reported for the Nz/Fe system [20]. An investigation of such effects is currently in progress. CONCLUSIONS A theory for the dissociative adsorption of molecules at metal surfaces has been presented. It is based upon a quantum mechanical description of the tunnelling of the
213
molecule through an activation barrier in its vibrational coordinate. The consequences of the model have been quantitatively discussed by employing a model potential energy surface based upon a recent theoretical treatment for the Hz/Cu system. Results obtained for the dependence of the initial sticking coefficient on translational energy, isotopic composition and primary vibrational energy appear to be in good qualitative agreement with recently obtained data for the N2/Fe and CH,/W systems. ACKNOWLEDGEMENTS We would like to express thanks to Dan Auerbach, Bill Gadzuk, David King and Charlie Rettner and for useful discussions pertaining to this work. REFERENCES 1. J.A. Barker and D.J. Auerbach, Surface. Sci. Rept. 4,l (1985). 2. D.J. Auerbach, H.E. Pfniir, C.T. Rettner, J.E. Schlaegel, J. Lee and R.J. Madix, J. Chem. Phys. al,2525 (1984). 3. S. Holloway, J. Vat. Sci. Tech. A 5,476 (1987). 4. J.E. Lennard-Jones, Trans. Faraday Sot. 28,333 (1932). 5. M. Karikorpi, S. Holloway, N. Henriksen and J.K. Norskov, Surf. Sci. 179, L41 (1987). R.B. Bernstein “Chemical Dynamics via Molecular Beam and Laser 6. Techniques” (Oxford Univ. Press, Oxford, 1982). 7. J. Harris and S. Andersson, Phys. Rev. Lett. 55,1583 (1985). 8. For gas phase studies see T.F. George and W.H. Miller, J. Chem. Phys. 57,2458 (1972); at surfaces H. F. Winters, J. Chem. Phys. 64,3495 (1976). N. Esbjerg and J.K. Norskov, Phys. Rev. Lett. 45,807 (1980). 9. J.K. Norskov, A. Houmoller, P. Johansson and B.I. Lundqvist, Whys. Rev. 10. Lett. 76,257 (1981). 11. M. Hand and S. Holloway, to be published. 12. E.J. Heller and R.C. Brown, J. Chem. Phys. 79,3336 (1983). 13. D.J. Douglas, J.C. Polanyi and J.J. Sloan, J. Chem. Phys. 59,6679 (1973). 14. D.S. King and R.R. Cavanagh, in: New Laser and Optical Investigations of Chemistry and Structure at Interfaces, (Verlag Chemie, Berlin, 1985). 15. AC. Luntz, Physica Scripta 35,193 (1987). 16. J.C. Tully, J. Elec. Spect. (these proceedings). 17. D.J. Auerbach, J. Elec. Spect. (these proceedings). R.B. Gerber and A. Amirav, J. Whys. Chem. 90,4483 (1986). 18. C.T. Rettner, H.E. Pfniir and D.J. Auerbach, Phys. Rev. Lett. 54,2716 (1985). 19. 20. C. T. Rettner and H. Stein, Whys. Rev. Lett. in press. G. Ertl, S.B. Lee and M . Weiss, Surf. Sci. 114, 515 (1982). 21. C.T. Rettner, H.E. Pfniir and D.J. Auerbach, J. Chem. Phys. 84,4163 (1985). 22. C. T. Rettner and H. Stein, J. Chem. Phys. 87,770 (1987). 23. S. Holloway, A. Hodgson and D. Halstead, Phys. Rev. L&t. (sub. for 24. publication). P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 51,5352 (1969). 25. M. BaIooch, M.J. Cardillo, D.R. Miller and R.E. Stickney, Surf. Sci. 46,358 26. (1974). 27. T.E. Madey, Surf. Sci. 36,281 (1973). D.A. King and G. Thomas, Surf. Sci. 92,201 (1980). 28.
A TUNNELLING
S. HOLLOWAY,
MODEL
FOR ACTIVATED
D. HALSTEAD
AND
ADSORPTION
AT METAL
207
SURFACES.
A. HODGSON
The Donnan Laboratories, University of Liverpool, Grove Street, P.O. Box 147, Liverpool, L69 38X, U.K.
SUMMARY
A tunnelling mechanism is presented for the dependence of the initial sticking coefficient for a light gas as a function of its primary energy. A model calculation is presented for the adsorption of Hz and D2 on a metal surface. The sticking coefficient exhibits a strong dependence on both the primary beam energy and the degree of H2 vibrational excitation. The results are discussed in the light of recent molecular beam scattering results for N2 and CH4.
INTRODUCTION
With the advent of detailed molecular beam scattering experiments, the number of gas/surface systems exhibiting an activation barrier to adsorption are ever increasing. In terms of the kinetic behaviour for the reaction Az(gas)+metal -+ 2A(ads)+metal the effects of such a barrier are well known, (i) the initial sticking coefficient S, shows an abrupt increase as a function of translational energy of the molecules and (ii) the A2 desorption flux often has an angular distribution P($) - cos%+ [I]. With the notable exception of Nz/W(llO) [2], it has been observed that the principle effect of changing the initial angle of incidence is to simpl;- rescale the primary energy dependence of S, to the kinetic energy normal to the surface, E*=Et COs’8i (so called normal energy scaling) [3]. These observations appear to support the model first suggested by Lennard Jones [4], that the activation barrier to adsorption is inherently one-dimensional in nature and that it is located in the entrance channel of the reaction pathway (fig. 1) 131. Recently, Karikorpi et al [5] suggested a model for activated adsorption of H2 which extended this picture to include variations in the barrier with the impact parameter within the surface unit cell of the substrate. While this model was able to trivially account for both observations, (i) and (ii) above, it also proposed a technique for probing the topology of the reactive potential energy (hyper)surface @‘ES). The H2 diffraction intensities will contain detailed information concerning the spatial location of the barrier particularly in the energetic region where the sticking coefficient abruptly increases. By inverting such data, it should be possible to map out the PES in some detail. To extend our knowledge of entrance channel effects, a second technique would be
0368-2048/87/$03.50
0 1987 Elsevier Science Publishers B.V.
208
to measure both S, and P(t3f) and their dependencies on the internal states of the molecule. This forms the subject of this paper. The particular problem addressed here is the degree to which vibrational excitation in the incident molecule couples to the “reaction coordinate” in the language of transition state theory [6]. A model PES will be presented for the Hz/metal system based on an ab initio calculation 171~which displays the essential topological features for dissociative adsorption reaction. A quantum mechanical calculation for the ensuing dynamics will show that for subbarrier initial translational energies, there exists a significant probability for tunnelling through the barrier along the vibrational coordinate [8]. The consequences of this effect on both the adsorbed and scattered particles will be presented. MODEL
II
I
a)
H-H seDaration: x
3)
Section along x’-x”
Fig. 1 (a) Here is shown a schematic contour plot for the Hz/metal PES. The entrance channel (marked as HZ) is of the form given by eqs. 1 and 2, whereas the exit channel (marked as W) shows a sharp linear decrease as described in the text. A section across the PES at constant z along x’-x” is also shown (b), detailing the ground and first vibrational wavefunctions (not to scale) for the harmonic oscillator. Assume that a diatomic molecule is incident normally on a metal surface in its rotational ground state, with kinetic energy EL and in vibrational state v. The entrance channel PES is primarily derived from the electronic state of the system that asymptotically correlates with the (Hz/Metal) diabatic state. In the neighbourhood of the lowest bound states this can be simply modelled by an harmonic potential in the direction of the bond x; V,(x) = 1/zpo2x2,
(1)
the vibrational frequency w taken from gas-phase spectroscopy. As the molecule nears the surface it experiences a strong repulsive force in the centre of mass direction z, arising from the Pauli exclusion principle, which may be approximated by, V*(z) = V, emti,
(2)
where constants V, and h can be related to the surface electron density 191.Within an adiabatic picture this state will be distorted as it correlates to either the dissociatively
209
adsorbed, 2H/Metal [71, or molecularly adsorbed, H$+/Metal [lOI state. If we assume that the initial translational energy is insufficient to allow the H2 to sample this region of configuration space, then such distortions will not affect the dynamics significantly. Thus we do not explicitly address “classical over the barrier” activation here, but consider those processes which are classically forbidden and will form the low energy tail of S,. The form of the activation barrier in the adsorbed state is determined by the steeply descending potential in the x-direction and to model the barrier, results of an ab initio total energy calculation for H2 interacting with a Cu cluster have been used [7]. These calculations indicate that the crossing seam is approximately linear, subtending an angle of -52’ with the x-axis with a minimum barrier of -1.4eV. This is schematically shown in fig. 1. In this preliminary study, we will treat the z-motion classically and the x-motion quantum mechanically. This mixed treatment is motivated by the fact that the xmotion is governed by the effective mass, p=M~/2, whereas the z-motion is determined by the molecular mass Mrr,al=2M~. Calculations are currently in progress where the Schrbdinger equation is explicitly solved for the time evolution of a 2dimensional wavepacket Y(z,x;t) over the model PES described above [ll]. This will provide a detailed check of the approximations used in this present work. For a given value of EL eq. 2 gives a value of the classical turning point in the z-direction, z,, = h-l ln(EI/V,). (31 It is quite clear that the maximum tunnelling will occur in this region of space since not only is it here that the barrier is at its lowest, but more importantly at zturn, the molecule is stationary. In this region, the tunnelling rate may be approximated by the golden rule expression for transitions from the v th vibrational state in the entrance channel to a small range of final states about AE in the 2I-I continuum 1121, cv2 R (v) - F c
(4)
I-4)” 1vf4*. f
For convenience, the interaction potential V is taken as being a constant. Essentially the problem is reduced to one of evaluating Franck-Condon overlaps between an initial vibrational state $v and final states vf, where f characterizes a continuum state of a diffusing chemisorbed hydrogen. Typically vf will be given by an Airy function in x. Since the F’ES decays steeply in the in the final state, this motivates the use of the multidimensional reflection approximation form for the wavefunction vf - 6(x-x,), a method which has been used with some success in molecular predissociation studies [121. Eq. 4 may then be trivially integrated, (5)
R(v) - I $, (x,) I 2. Before S, can be evaluated, it remains to estimate the length of time that the H2 molecule spends in the tunnelling region. Let us assume that a region of space exists, AZ, about zturn, where tunnelling is favourable. From eq. 2 it is straightforward
to show that the traversal time over this region is,
A2 - EL-‘/~.
210
Thus for a direct scattering encounter, the sticking probability is given by, S,(v) = Ar R(v)
(6)
All that remains is to relate xs to EJ, and this is done using the linear seam approximation discussed above; xs = a ztum + B. with constants a and B chosen to reproduce the barrier region of the theoretical PES [7]. When used in conjunction with eqs. 6 and 3, this gives the final expression for S,(v,EJ. RESULTS Fig. 2 shows the variation of S, as a function of the primary energy, EL for H;! and D2 molecules in their ground vibrational state, v=O, interacting with a metal surface having an activation barrier of 1.4eV. The general shape of the curves arises from the increased tunnelling which occurs as El increases, which affects a decrease in xs (see fig.la). There is a significant isotope effect which arises as a consequence of the
-5o! 0.00
0.20
0.40
0.60
0.80
1.00
Translational energy (eV) Fig. 2 The translational energy dependence of the initial sticking coefficient for H2 and D2 scattering from a surface having an activation barrier of 1.4eV. Results are presented for molecules in their ground vibrational state which would correspond to a room temperature supersonic beam. Typically, experimental observations for S, cover a range of approximately six orders of magnitude (see fig. 4). reduced spatial extent of the v=O wavefunction for the heavier particle. With the advent of state selection of reactants it is interesting to investigate the dependence of S, on the degree of initial vibrational excitation of the molecule. From gas phase scattering data for systems such as Br+Cl(v)+HBr(all v’)+Cl [13], it is well known that rate constants for vibrationally excited reactants can increase by orders of magnitude over ground state values and it is interesting to investigate if such results persist for surfaces reactions. Results for H2 are shown in fig. 3. In the asymptotic region of xy (I” (xJ > $6 (x,), and thus the ratio of S,(v)/S,(v=O), will be greater than unity. The gradual decay in the quotient with increasing El occurs since higher
211
translational energies bring the molecules nearer to the activation barrier. This trend is a quite general result and does not depend crucially upon the exact details of the PES. Results for D2 adsorption follow the same general pattern as Hz and are not included here.
Hydrogen 654321“’
I
0.00
I
I
I
0.20 0.40 0.60 0.80 Translational energy (eV)
I
1.00
Fig. 3 The ratio of initial sticking coefficients as a function of translational energy for vibrationally state selected H2 molecules scattering from a surface having an activation barrier to adsorption of 1.4eV. For a given translational energy, the greater spatial extension of excited vibrational states results in an increased dissociation probability. EXPERIMENTAL SURVEY The growth of state-to-state scattering experiments at surfaces is prodigious [14]. While the majority of experimental [15] and theoretical work [16] has so far concentrated on rotational inelastic scattering, some studies of dissociative adsorption have appeared where vibrational problems have been addressed [17,18]. Of particular note are the studies of CH4 and CD, scattering from W 1191, and N2 from Fe surfaces [20] (fig. 4). These experiments employ beam-seeding techniques to explore wide ranges of translational energies while keeping the molecules in their vibrational ground state. The general shape of the v=O nitrogen results bear a strong resemblance to the theoretical curve shown in fig. 2. For the N2/Fe system, thermal beam experiments performed on cold substrates [21] have indicated that the PES is more complicated than our model suggests and that a molecular state occurs on the surface before any activation barrier is encountered. Although this would suggest that for low El our model would be neglecting an important reaction channel, these results do not invalidate our model at higher energies, where trapping into the precursor is unlikely. It is possible to map our model on to the methane experiments, by associating the degree of freedom, x, with a stretching mode of the CH4 molecule. This may be at least partially justified since the reaction occurring is essentially a bond scission, with H being abstracted from the CH4. The apparent linear relationship between S, and El for the methane data we believe, is an indication that the
212
theoretically predicted saturation effects have not yet set in, and to substantiate this claim, it would be necessary to extend the range of translational energies. Both the order of magnitude for the isotopic shift, and the divergence of the rates at lower EL are features which are well described by the model. For both systems preliminary experimental results obtained by heating the supersonic nozzle source 122,231, have been presented for beams containing a mixture of initial vibrational states. These data are well described by the model and form the basis for a separate study [24].
Methane/WC1101
N2/Fe(lll) -1 -
-1 -
cr? _32 P -5-
V? Z IJ
+l
I -7
I 0.0
1.0
2.0
CH4 CD4
-5
?
, I 3.0
-3
## -7
4.0
5.0
Translational energy (eV)
0.0
0.2
0.4
0.6
0.8
1.0
Translational energy (eV)
Fig. 4 Experimental results for the dissociatiative chemisorption reactions N2*2N [20], and CH4+H+CH3 [19]. Initial results for hydrogen adsorption on W(100) [WI showed a strong isotope dependence [S,(H$/S,(D$ -1.4141 in the opposite direction to that which would be expected on the basis of the present model. Similar findings have also been reported for the adsorption of hydrogen on various faces of Cu, based on the results of HD formation in Hz-D scattering experiments [26]. In more detailed studies by Madey [27], and Thomas and King [28] it was shown that within experimental accuracy, there was no measurable isotope effect for the W(100) surface. In the light of recent experimental developments, it would be of great interest to measure the primary energy dependence of the pure Hz and D2 dissociative adsorption reaction on a surface exhibiting a large activation barrier. In its present form, surface motion has not yet been included in the model. Although trivially, the shape of the activation barrier would be modified by such effects, from a dynamics point of view, it is probable that vibrational deactivation would mitigate a net decrease in any vibrational enhancement expected at OK. This would give rise to the slight substrate temperature dependence for S, which has been reported for the Nz/Fe system [20]. An investigation of such effects is currently in progress. CONCLUSIONS A theory for the dissociative adsorption of molecules at metal surfaces has been presented. It is based upon a quantum mechanical description of the tunnelling of the
213
molecule through an activation barrier in its vibrational coordinate. The consequences of the model have been quantitatively discussed by employing a model potential energy surface based upon a recent theoretical treatment for the Hz/Cu system. Results obtained for the dependence of the initial sticking coefficient on translational energy, isotopic composition and primary vibrational energy appear to be in good qualitative agreement with recently obtained data for the N2/Fe and CH,/W systems. ACKNOWLEDGEMENTS We would like to express thanks to Dan Auerbach, Bill Gadzuk, David King and Charlie Rettner and for useful discussions pertaining to this work. REFERENCES 1. J.A. Barker and D.J. Auerbach, Surface. Sci. Rept. 4,l (1985). 2. D.J. Auerbach, H.E. Pfniir, C.T. Rettner, J.E. Schlaegel, J. Lee and R.J. Madix, J. Chem. Phys. al,2525 (1984). 3. S. Holloway, J. Vat. Sci. Tech. A 5,476 (1987). 4. J.E. Lennard-Jones, Trans. Faraday Sot. 28,333 (1932). 5. M. Karikorpi, S. Holloway, N. Henriksen and J.K. Norskov, Surf. Sci. 179, L41 (1987). R.B. Bernstein “Chemical Dynamics via Molecular Beam and Laser 6. Techniques” (Oxford Univ. Press, Oxford, 1982). 7. J. Harris and S. Andersson, Phys. Rev. Lett. 55,1583 (1985). 8. For gas phase studies see T.F. George and W.H. Miller, J. Chem. Phys. 57,2458 (1972); at surfaces H. F. Winters, J. Chem. Phys. 64,3495 (1976). N. Esbjerg and J.K. Norskov, Phys. Rev. Lett. 45,807 (1980). 9. J.K. Norskov, A. Houmoller, P. Johansson and B.I. Lundqvist, Whys. Rev. 10. Lett. 76,257 (1981). 11. M. Hand and S. Holloway, to be published. 12. E.J. Heller and R.C. Brown, J. Chem. Phys. 79,3336 (1983). 13. D.J. Douglas, J.C. Polanyi and J.J. Sloan, J. Chem. Phys. 59,6679 (1973). 14. D.S. King and R.R. Cavanagh, in: New Laser and Optical Investigations of Chemistry and Structure at Interfaces, (Verlag Chemie, Berlin, 1985). 15. AC. Luntz, Physica Scripta 35,193 (1987). 16. J.C. Tully, J. Elec. Spect. (these proceedings). 17. D.J. Auerbach, J. Elec. Spect. (these proceedings). R.B. Gerber and A. Amirav, J. Whys. Chem. 90,4483 (1986). 18. C.T. Rettner, H.E. Pfniir and D.J. Auerbach, Phys. Rev. Lett. 54,2716 (1985). 19. 20. C. T. Rettner and H. Stein, Whys. Rev. Lett. in press. G. Ertl, S.B. Lee and M . Weiss, Surf. Sci. 114, 515 (1982). 21. C.T. Rettner, H.E. Pfniir and D.J. Auerbach, J. Chem. Phys. 84,4163 (1985). 22. C. T. Rettner and H. Stein, J. Chem. Phys. 87,770 (1987). 23. S. Holloway, A. Hodgson and D. Halstead, Phys. Rev. L&t. (sub. for 24. publication). P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 51,5352 (1969). 25. M. BaIooch, M.J. Cardillo, D.R. Miller and R.E. Stickney, Surf. Sci. 46,358 26. (1974). 27. T.E. Madey, Surf. Sci. 36,281 (1973). D.A. King and G. Thomas, Surf. Sci. 92,201 (1980). 28.