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Relaxation dynamics of vibrationally highly excited H2 molecules on a Cu surface
L391
Surface Science 217 (1989) L391-L396 North-Holland, Amsterdam
SURFACE
SCIENCE
LETTERS
RELAXATION DYNAMICS OF VIBRATIONALLY H, MOLECULES ON A Cu SURFACE M. CACCIATORE,
HIGHLY
EXCITED
M. CAPITELLI
Centro Studio Chimica dei Plasmi, Dipartimento 70126 Bari, Italy
di Chimica,
Universitri di Bari, Via Amendola
173,
and G.D. BILLING Chemistry Loboratory ZZZ, H.C. Outed 21000 Copenhagen, Denmark
Institute,
University
of Copenhagen,
Received 2 March 1989; accepted for publication 7 April 1989
Relaxation dynamics of vibrationally highly excited Ha molecules on a Cu surface has been calculated by using an highly accurate potential energy surface. The results show an increase of dissociation probability as a function of vibrational quantum level and a practical absence of vibrational deactivation at low kinetic energies of impinging molecules.
Vibrational relaxation and dissociation of highly vibrationally excited hydrogen molecules Hz(u) on metallic surfaces is a field of increasing interest due to the importance of this process in creating non-equilibrium H2 vibrational distributions for the production of negative ion beams (H-) [l]. Dissociation of Hz(u) on metallic surfaces is also of importance due to the obvious connection to the reverse process where H2( u) is formed by recombination of atomic hydrogen on the surface [2-41. Here we report theoretical results obtained by using a highly accurate potential energy surface and a realistic dynamical model for these processes. We have used a semi-classical theory developed for atom/molecule surface scattering [5], in which the effect of phonon-excitation, surface temperature and electron-hole pair excitation is taken into account by an effective potential. However, in the present calculations the latter process is neglected. Thus the Hamiltonian which governs the molecule-surface dynamics can be written as [5]: f&f=
c
(2~-~(P,?+f’..+&f)+
V,,k>
i=1,2
0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L392
iU. Cacciatore et al. / Highly excited H2 on a Cu surface
where V,,(r) is the H-H interaction approximated by a Morse potential, xi the x-coordinate of H atom i and P,, the corresponding momentum. T, is the surface temperature and t the interaction time. Eint is the energy transferred to the surface phonons and V,,, an effective potential, which may be expressed as [5]: V,n=
V,({xiY
.YiY zi})
+
CvP’(xi7 k
Yi,
Zi)Vk(t,
T,),
(2)
where V, is the “static” interaction between the pure H atoms and the surface, i.e. with the surface atoms in their equilibrium positions. Vi’) is the first derivative of the potential with respect the phonon mode k and nk a time and surface temperature dependent coefficient which contains information upon the phonon excitation/deexcitation processes induced by the collision [5]. Hamilton’s equations of motion are integrated, using the Hamiltonian (1) for a number of initial values of the kinetic and vibrational energy of the H, molecule. The only variables which have to be selected randomly are the phase angles corresponding to the vibrational and rotational momenta and the aiming point (within a unit cell) upon the surface. Thus the quantities reported below converge to within 10% accuracy with about 30 trajectories for each initial condition. Full dynamical calculations have been carried out on the GRAY/l at the CINECA/Bologna. The interaction potential was obtained as an analytical fit to recent ab initio CI calculations on the H,-Cu (cluster) system [6]. The analytical fit reproduces the ab initio data to within about lo-30%. (Details will be given elsewere.) Fig. 1 shows the H,-Cu interaction for H, placed perpendicular to the surface at a four-fold site as a function of z and r. The figure shows a repulsive interaction for r values around the equilibrium distance. But as soon as the H-H bond length increases to beyond about 1 A a barrier or actually two barriers appear. Passing the first barrier would leave the H, molecule in a stretched surface bound configuration and the second in a subsurface state. A light molecule such as H, will have a large probability to tunnel through the barrier and enter into a surface bound state. Since the barrier height decreases with the bond length the probability for this event will increase with increasing vibrational energy. Fig. 2 shows a calculation of the tunnelling probability for H, interacting at the four-fold site. We see that there is a strong dependence of the dissociation probability through tunnelling with the vibrational quantum number. In a classical mechanical treatment of the collision the probabilities for reaching the surface bound configuration will of course be zero below the barrier. But since it is a dynamical barrier it may be surpassed if H, is in a vibrationally excited state and due to the vibration eventually reaches a stretched configuration in which the barrier is lowered and hence may be passed. In this process the H, molecule may dissociate at the surface and, as
M. Cacciatore et ai. / Highiy excited H2 on a Cu surface
L393
Fig. 1. H,-Cu interaction potential with H, placed perpendicular to the surface at the four-fold site as a function of molecule-surface distance (z) and H-H bond distance ( T~_~). Unit E = 100 kJ/mol.
KINETIC
ENERGY
leV)
Fig. 2. The tunneiling probability through the first barrier for Hz interacting in the four-fold site as a function of the vibrational state (0) and the impact kinetic energy.
L394
IU. Cacciatore et al. / Highly excited Hz on a Cu surface
c
Z(A) % 7.
%
6.
5.
4,
b
3
2
1
0
I 0.
1.
I
I
2.
3.
I
1 .
_
4.
3.
I ^
b.
X(i)
Fig. 3. A dissociative trajectory where one H atom is absorbed and the other reflected from the surface. The Cartesian (x, y) axes define the crystal plane, z being the axis normal to the surface. The two arrows show the direction of the z-component of the momentum for the two H atoms in the final configuration. The initial vibrational state of the hydrogen molecule is u = 8 and kinetic energy E, = 0.2 eV. The approaching angle between the H, centre of mass distance and the surface normal is 0 = 45 O. T, = 300 K.
shown in fig. 3, one atom may be adsorbed once the other leaves the surface. In this case the binding energy is transformed into kinetic energy of the two atoms and it may, as shown on fig. 3, enter into the motion perpendicular to the surface with enough momentum away from the surface to be able to escape the attractive well. Table 1 shows the dissociation probability for H, collisions with a Cu surface as a function of initial internal vibrational excitation and kinetic energy. We see that the dissociation probability increases with the vibrational excitation such that the kinetic energy threshold is lowered considerably with the vibrational energy. The table also shows that the rotational-vibrational quenching of the H, molecule leaving the surface is modest if not absent. Also the energy transfer to the phonons is small due to the small mass of the H atom compared with the Cu mass. By considering the reverse trajectories we can then conclude that the atom recombination through a direct mechanism will produce vibrationally excited
L395
M. Cacciatore et al. / Highly excited H2 on a Cu surface
Table 1 Dissociation probabilities and energy accommodation for H,(u,j) colliding with a Cu(100) surface as a function of vibrational and rotational angular momenta u and i and initial kinetic energy ”
WI
pD
a)
0
t
b)
.,
J
b)
Ei,, b*c)(ev)
j
%,
5
0
1.0 2.0
0.0 0.70
5 5
091 1
0.016 0.026
6
0
0.2 0.4 0.6 1.0
0.0 0.0 0.0 0.62
6 6 6 6
OJ 031 1 1
0.0024 0.0060 0.0095 0.014
8
0
0.05 0.2
0.0 1.0
g(7)
0
0.001
10
0
0.05 0.1
0.95 1.0
a) Dissociation probability. b, Average values for reflected trajectories. ‘) Energy transferred to surface phonons.
H,. However when the H, is formed by an indirect mechanism, where one or both H atoms moves along the surface recombines and then desorbs, we expect production of H, in low u states [4]. But H, production through a desorption mechanism takes place on a longer time scale and it may therefore not be possible to follow these processes numerically. Previous calculations by Gelb and Cardillo [7] on H,-Cu use a potential energy surface which is very different from the present. One difference is that it has a repulsive H, and H-Cu interaction at small z distances. Also in the work of De Pristo et al. [S] a purely repulsive H,-Cu interaction resembling our r - r, curve on fig. 1 is used. Such potentials are only realistic for the study of the lower vibrational levels of H,, translational or rotational accommodation at small kinetic energies and not for reactive (dissociative) trajectories. There is recent experimental evidence for the production by hydrogen recombination on a tungsten covered Fe surface giving H2( u) with u up to about 9 [2] and up to u = 5 [3]. The present work seems to suggest that such a recombination process can occur through a direct mechanism. In ref. [2] it is noticed that the energy of the u = 9 state is larger than the available kinetic energy of an H atom in the experiment. Our calculations show that the “missing” energy comes from the potential energy difference of the surface bound H atoms, which according to fig. 1 may be absorbed with a binding energy around 1 eV, and the binding energy of an H, molecule. This energy minus the negligible phonon excitation energy is released when the H, molecule is formed. If the absorbed H atom is bound more strongly to the
L396
M. Cacciatore et al. / High& excited H2 on a Cu surface
surface it is likely that the H, molecule formed at the surface will not be able to leave the surface due to the dynamical build up of a barrier as the distance r decreases during the vibration or because the binding energy of H, plus the kinetic energy of the incoming atom is less than the binding energy of the H surface interaction. Therefore this may offer the explanation why u > 10 is not observed in the experiment. However, this discussion may be premature since one should bear in mind that the H,-Cu interaction could be very different from the Hz-Fe/W interaction. Financial support of this research by Progetto Finalizzato of the Italian CNR is acknowledged.
Chimica Fine II
References [l] See: Proc. Third European Workshop on the Production and Application of Negative Ions, Eds. H. Hopman and W. van Amersfoort (FOM Institute for Atomic and Molecular Physics, Amsterdam, 1988); C. Gorse, M. CapiteIli, M. Bacal, J. Bretagne and A. Lagana, Chem. Phys. 117 (1987) 177. [2] R. HalI, I. Cadez, M. Laudran, F. Pichou and C. Shermamr, Phys. Rev. Letters 60 (1988) 337. [3] P.J. Eenshuistra, J.H.M. Botie, J. Los and H.J. Hopman, Phys. Rev. Letters 60 (1988) 340. [4] G.D. Kubiak, G.O. Sitz and R.N. Zare, J. Chem. Phys. 81 (1984) 6397; 83 (1985) 2538. [5] G.D. BiIling, Chem. Phys. 70 (1982) 223; 74 (1983) 143; G.D. BiIling and M. Cacciatore, Chem. Phys. Letters 113 (1985) 23; Chem. Phys. 103 (1986) 137; G.D. BiUing, Chem. Phys. 116 (1987) 269; Surface Sci. 203 (1988) 257. [6] P. Madhaven and J.L. Whitten, J. Chem. Phys. 77 (1982) 2673. [7] A. Gelb and M.J. CardiIIo, Surface Sci. 59 (1976) 128; 75 (1977) 197. [8] A.E. De Pristo, C.L. Lee and J.M. Hutson, Surface Sci. 169 (1986) 451.
Surface Science 217 (1989) L391-L396 North-Holland, Amsterdam
SURFACE
SCIENCE
LETTERS
RELAXATION DYNAMICS OF VIBRATIONALLY H, MOLECULES ON A Cu SURFACE M. CACCIATORE,
HIGHLY
EXCITED
M. CAPITELLI
Centro Studio Chimica dei Plasmi, Dipartimento 70126 Bari, Italy
di Chimica,
Universitri di Bari, Via Amendola
173,
and G.D. BILLING Chemistry Loboratory ZZZ, H.C. Outed 21000 Copenhagen, Denmark
Institute,
University
of Copenhagen,
Received 2 March 1989; accepted for publication 7 April 1989
Relaxation dynamics of vibrationally highly excited Ha molecules on a Cu surface has been calculated by using an highly accurate potential energy surface. The results show an increase of dissociation probability as a function of vibrational quantum level and a practical absence of vibrational deactivation at low kinetic energies of impinging molecules.
Vibrational relaxation and dissociation of highly vibrationally excited hydrogen molecules Hz(u) on metallic surfaces is a field of increasing interest due to the importance of this process in creating non-equilibrium H2 vibrational distributions for the production of negative ion beams (H-) [l]. Dissociation of Hz(u) on metallic surfaces is also of importance due to the obvious connection to the reverse process where H2( u) is formed by recombination of atomic hydrogen on the surface [2-41. Here we report theoretical results obtained by using a highly accurate potential energy surface and a realistic dynamical model for these processes. We have used a semi-classical theory developed for atom/molecule surface scattering [5], in which the effect of phonon-excitation, surface temperature and electron-hole pair excitation is taken into account by an effective potential. However, in the present calculations the latter process is neglected. Thus the Hamiltonian which governs the molecule-surface dynamics can be written as [5]: f&f=
c
(2~-~(P,?+f’..+&f)+
V,,k>
i=1,2
0039-6028/89/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
L392
iU. Cacciatore et al. / Highly excited H2 on a Cu surface
where V,,(r) is the H-H interaction approximated by a Morse potential, xi the x-coordinate of H atom i and P,, the corresponding momentum. T, is the surface temperature and t the interaction time. Eint is the energy transferred to the surface phonons and V,,, an effective potential, which may be expressed as [5]: V,n=
V,({xiY
.YiY zi})
+
CvP’(xi7 k
Yi,
Zi)Vk(t,
T,),
(2)
where V, is the “static” interaction between the pure H atoms and the surface, i.e. with the surface atoms in their equilibrium positions. Vi’) is the first derivative of the potential with respect the phonon mode k and nk a time and surface temperature dependent coefficient which contains information upon the phonon excitation/deexcitation processes induced by the collision [5]. Hamilton’s equations of motion are integrated, using the Hamiltonian (1) for a number of initial values of the kinetic and vibrational energy of the H, molecule. The only variables which have to be selected randomly are the phase angles corresponding to the vibrational and rotational momenta and the aiming point (within a unit cell) upon the surface. Thus the quantities reported below converge to within 10% accuracy with about 30 trajectories for each initial condition. Full dynamical calculations have been carried out on the GRAY/l at the CINECA/Bologna. The interaction potential was obtained as an analytical fit to recent ab initio CI calculations on the H,-Cu (cluster) system [6]. The analytical fit reproduces the ab initio data to within about lo-30%. (Details will be given elsewere.) Fig. 1 shows the H,-Cu interaction for H, placed perpendicular to the surface at a four-fold site as a function of z and r. The figure shows a repulsive interaction for r values around the equilibrium distance. But as soon as the H-H bond length increases to beyond about 1 A a barrier or actually two barriers appear. Passing the first barrier would leave the H, molecule in a stretched surface bound configuration and the second in a subsurface state. A light molecule such as H, will have a large probability to tunnel through the barrier and enter into a surface bound state. Since the barrier height decreases with the bond length the probability for this event will increase with increasing vibrational energy. Fig. 2 shows a calculation of the tunnelling probability for H, interacting at the four-fold site. We see that there is a strong dependence of the dissociation probability through tunnelling with the vibrational quantum number. In a classical mechanical treatment of the collision the probabilities for reaching the surface bound configuration will of course be zero below the barrier. But since it is a dynamical barrier it may be surpassed if H, is in a vibrationally excited state and due to the vibration eventually reaches a stretched configuration in which the barrier is lowered and hence may be passed. In this process the H, molecule may dissociate at the surface and, as
M. Cacciatore et ai. / Highiy excited H2 on a Cu surface
L393
Fig. 1. H,-Cu interaction potential with H, placed perpendicular to the surface at the four-fold site as a function of molecule-surface distance (z) and H-H bond distance ( T~_~). Unit E = 100 kJ/mol.
KINETIC
ENERGY
leV)
Fig. 2. The tunneiling probability through the first barrier for Hz interacting in the four-fold site as a function of the vibrational state (0) and the impact kinetic energy.
L394
IU. Cacciatore et al. / Highly excited Hz on a Cu surface
c
Z(A) % 7.
%
6.
5.
4,
b
3
2
1
0
I 0.
1.
I
I
2.
3.
I
1 .
_
4.
3.
I ^
b.
X(i)
Fig. 3. A dissociative trajectory where one H atom is absorbed and the other reflected from the surface. The Cartesian (x, y) axes define the crystal plane, z being the axis normal to the surface. The two arrows show the direction of the z-component of the momentum for the two H atoms in the final configuration. The initial vibrational state of the hydrogen molecule is u = 8 and kinetic energy E, = 0.2 eV. The approaching angle between the H, centre of mass distance and the surface normal is 0 = 45 O. T, = 300 K.
shown in fig. 3, one atom may be adsorbed once the other leaves the surface. In this case the binding energy is transformed into kinetic energy of the two atoms and it may, as shown on fig. 3, enter into the motion perpendicular to the surface with enough momentum away from the surface to be able to escape the attractive well. Table 1 shows the dissociation probability for H, collisions with a Cu surface as a function of initial internal vibrational excitation and kinetic energy. We see that the dissociation probability increases with the vibrational excitation such that the kinetic energy threshold is lowered considerably with the vibrational energy. The table also shows that the rotational-vibrational quenching of the H, molecule leaving the surface is modest if not absent. Also the energy transfer to the phonons is small due to the small mass of the H atom compared with the Cu mass. By considering the reverse trajectories we can then conclude that the atom recombination through a direct mechanism will produce vibrationally excited
L395
M. Cacciatore et al. / Highly excited H2 on a Cu surface
Table 1 Dissociation probabilities and energy accommodation for H,(u,j) colliding with a Cu(100) surface as a function of vibrational and rotational angular momenta u and i and initial kinetic energy ”
WI
pD
a)
0
t
b)
.,
J
b)
Ei,, b*c)(ev)
j
%,
5
0
1.0 2.0
0.0 0.70
5 5
091 1
0.016 0.026
6
0
0.2 0.4 0.6 1.0
0.0 0.0 0.0 0.62
6 6 6 6
OJ 031 1 1
0.0024 0.0060 0.0095 0.014
8
0
0.05 0.2
0.0 1.0
g(7)
0
0.001
10
0
0.05 0.1
0.95 1.0
a) Dissociation probability. b, Average values for reflected trajectories. ‘) Energy transferred to surface phonons.
H,. However when the H, is formed by an indirect mechanism, where one or both H atoms moves along the surface recombines and then desorbs, we expect production of H, in low u states [4]. But H, production through a desorption mechanism takes place on a longer time scale and it may therefore not be possible to follow these processes numerically. Previous calculations by Gelb and Cardillo [7] on H,-Cu use a potential energy surface which is very different from the present. One difference is that it has a repulsive H, and H-Cu interaction at small z distances. Also in the work of De Pristo et al. [S] a purely repulsive H,-Cu interaction resembling our r - r, curve on fig. 1 is used. Such potentials are only realistic for the study of the lower vibrational levels of H,, translational or rotational accommodation at small kinetic energies and not for reactive (dissociative) trajectories. There is recent experimental evidence for the production by hydrogen recombination on a tungsten covered Fe surface giving H2( u) with u up to about 9 [2] and up to u = 5 [3]. The present work seems to suggest that such a recombination process can occur through a direct mechanism. In ref. [2] it is noticed that the energy of the u = 9 state is larger than the available kinetic energy of an H atom in the experiment. Our calculations show that the “missing” energy comes from the potential energy difference of the surface bound H atoms, which according to fig. 1 may be absorbed with a binding energy around 1 eV, and the binding energy of an H, molecule. This energy minus the negligible phonon excitation energy is released when the H, molecule is formed. If the absorbed H atom is bound more strongly to the
L396
M. Cacciatore et al. / High& excited H2 on a Cu surface
surface it is likely that the H, molecule formed at the surface will not be able to leave the surface due to the dynamical build up of a barrier as the distance r decreases during the vibration or because the binding energy of H, plus the kinetic energy of the incoming atom is less than the binding energy of the H surface interaction. Therefore this may offer the explanation why u > 10 is not observed in the experiment. However, this discussion may be premature since one should bear in mind that the H,-Cu interaction could be very different from the Hz-Fe/W interaction. Financial support of this research by Progetto Finalizzato of the Italian CNR is acknowledged.
Chimica Fine II
References [l] See: Proc. Third European Workshop on the Production and Application of Negative Ions, Eds. H. Hopman and W. van Amersfoort (FOM Institute for Atomic and Molecular Physics, Amsterdam, 1988); C. Gorse, M. CapiteIli, M. Bacal, J. Bretagne and A. Lagana, Chem. Phys. 117 (1987) 177. [2] R. HalI, I. Cadez, M. Laudran, F. Pichou and C. Shermamr, Phys. Rev. Letters 60 (1988) 337. [3] P.J. Eenshuistra, J.H.M. Botie, J. Los and H.J. Hopman, Phys. Rev. Letters 60 (1988) 340. [4] G.D. Kubiak, G.O. Sitz and R.N. Zare, J. Chem. Phys. 81 (1984) 6397; 83 (1985) 2538. [5] G.D. BiIling, Chem. Phys. 70 (1982) 223; 74 (1983) 143; G.D. BiIling and M. Cacciatore, Chem. Phys. Letters 113 (1985) 23; Chem. Phys. 103 (1986) 137; G.D. BiUing, Chem. Phys. 116 (1987) 269; Surface Sci. 203 (1988) 257. [6] P. Madhaven and J.L. Whitten, J. Chem. Phys. 77 (1982) 2673. [7] A. Gelb and M.J. CardiIIo, Surface Sci. 59 (1976) 128; 75 (1977) 197. [8] A.E. De Pristo, C.L. Lee and J.M. Hutson, Surface Sci. 169 (1986) 451.