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Molecular levels for a CO molecule chemisorbed at various angles on a Ni(100) surface
Volume 58. number1
MOLECULAR
CHEM KAL
PIlYSICS LETIERS
LEVELS FOR A CO MOLECULE
CHEMWORBED
1 September1978
AT VARIOUS
ANGLFS
ON A Pii(ltl0) SURFACE Ame ROS6N Depcvtmentof Physics, clhnlmersUniversityof Technology. GGteborg.Sweden Received30 May 1978
Molecuiarclustertheory has been used to examine the effect on the molecularlevelswhen a CO moleculeis chemisorbed at variousangleson a Ni(100) surface.CalcuIationswere fust performedfor a linearNi-CO clusterin C-v symmetry for differentnickel-carbon distances2.5 < h < 4.5 au keepingthe carbon-o.uygen distanceR (C-O) equal to the free motecuIarvalueR (C-O) = 2.13 au_The symmetry requirementwas then droppedfor h = 3.5 au and the CO moleculeuas bent 20”. 40” and 60” relativeto the surfacenom&. The splittingof the CO molecularl;r level was found to be O-1,0.3 and 0.7 eV for the correspondingaqIes. The 40 level was almost unchangedwith the anglewhile the 5u was about 0.3 eV more bound for the 60” anglecomparedto the verticalposition.
The chemisorption of the CO molecule on a NiflCJO) surface has been the subject of many experimental as well as theoretical investigations in recent years. A primary objective in these works has been to determine the bonding geometry of the CO molecule and the binding energies for the chemisorbed CO molecuiar levels. Experimental angle-resoIved photoelectron spectroscopy
experiments by Ahyn et al. [l] combined with theoretical calculations by Davenport [2] have given the identification of the different CO molecular levels. That analysis cont%-medalso that the CO molecule is bonded to the surface with the carbon end down and with the molecular axis normal to the surface with an accuracy of So. EELS experiments recently performed by Andersson 131 have been interpreted in terms of CO terminally bonded to a nickel atom in the surface i-e_ a top position. Andersson and Pendry [4] found further in a LEED experiment that for the Ni(lOO) c (2 X 2) CO structure the top position is most probable with a vertical carbon-oxygen layer distance of (0.95 1: 0.10) A. This means that the CO molecule is tipped over at an angle of 34” t 10” with respect to the surface normal ifthe carbon-oxygen distance is equal to the Ni(CO)4 value of 1.15 A. There is therefore scme ambiguity between the angle-resolved photoelectron experiments and the LEED investigations concerning the CO bond length and the N&CO bond angle.
The variation of the one-electron &ergies, binding
energies, and charge distribution-with.T+e height of the CO molecule above the surface h& recently been calcuiate&for the hollow-, top- and bhdge:bonding geometr& using the Hartree-Fock-Slater model [S] _ The calculations_w>e performed for the Ni&O cluster for hollow bonding iIz_C4, symmetry, the N&Cd and Ni&O clusters for top-bonding m-C,, and C4, symmetry and for the Ni2C0 cluster for bridge-bonding in C2, symmetry. The CO molecule was in those calculations assumed to be chemisorbed with the molecular axis perpendicular to the surface thus keeping the above-mentioned symmetries. About the same behaviour was found in the earlier analysis for the CO 3o, 40, Sa and 1s molecular levels when the calculations were performed in top-bonding geometry for the NiCO and Ni&O clusters. In this work cluster calculations were performed for the Ni-CO cluster at various bond angles with the aim of exploring the influence on the molecular levels. The approach used is based upon *he local density HartreeFock-Slater @FS) molecular orbital approximation ushg variational methods with an exchange parameter a = 0.70 [6-8]. The HFS and overlap matrix elements are evaluated by using a numerical integration scheme 191 with numerical basis sets consisting of symmetrized free atomic orbitals [g-10]. Muffin-tin approximations 95
Volume 58, number 1
CHEMIC_AL PHYSICS LJZTTERS
-1 September 1978
[l f ] to the molecular potential are avoided so that asphericalsystems can be treated accurately with basis function and potential of rather general form_ The calculations performed in this work are based upon the selfconsistontcharge (SCC) [S] method which means that a Mull&en population analysis is performed of the basis functions to determine orbital charges for the construction of the molecular potential. DetaiIs of the computational procedure have been presented previouslY [81Models for CO bonded on a Ni(100) surface in topposition are shown in fig. 1. The effect on the moiecuIar levels has been analyzed by varying the a&e Q! from 0” to 60” thus breaking the C,, symmetry_ Ground state valence IeveIs for the NiCO cluster and for the free CO mole&e calcuIated in the HFS SCC scheme are shown in fig. 2. The free molecuIar 1eveJ.s for aR(C-0) distance of2.13 au are presented to the right. This bond length was then used and the variation of the molecular levels as a function of height above the nickel surface was varied in the range 2.5 au < h < 4.5 au_ The levels are labeled with the free CO notation and the Ni-CO notation in parentheses. 2000 points were used in the numerical integration of the Hartree-FockSlater and overlap matrix elements- For a bond distance ofh = 3-S au which is about the vaIue found for free carbonyis, the level ordering is 5a, la, 40 and 30 with increasing binding energy. This ordering is also in agreement with the result of the angle-resolved photoe_mission expe%iments [l] . The level ordering of chemisorb-
0 C Ni
Ni FE- 1. Model for CO bonded on a Ni(100) surface in top &xition (i.e. linear bond) in C, symmetry. Model for CO bonded at various angk 4 on a Ni(100) surface. To the left is shown the plan and to the ri&t the election of the CO mofeade from ihe surface.
96
Fig. 2. SCC ground state oneelectron eigenvalues (in eV) for whence levek of the CO-Ni cluster iu topposition. To the Ieft are shown the variation of the molecuhr levels as a function of the cabon-nickel
distance h. In the middle
is shown
the effect of varying the carbon-oxygen distance R (C-0) at tixed h = 35 au. To the right in the figure are shown the molecuku levels when the CO mo!ecuIe is chemisorbed at various Q.
ed CO is therefore different compared with the free molecular data 1121. The theoretical ordering of the So and la level is however somewhat sensitive to the type of potential used as was found in the earlier Calculations [S] _ One may therefore conclude from the theoretical calculations that the free CO In level is shifted to less binding energy and close to the 50 chemisorbed level when the molecule is chemisorbed. Broddn et al_ [X3] suggested in a recent analysis of the photoemission experiments and a comparison with carbonyl data that the carbon-oxygen distance should be increased to 2.17 au compared with 2.13 au for the
Volume~58, number 1
CHEMICAL
PHYSICS LETTERS
free CO. A calculation for h equal to 3.5 au has been made using a carbon-oxygen distance of 2.20 au and the result is shown in fig. 2 at the middle. The result withR(C-0) = 2.13 au has also been presented to the right for comparison_ The 40 level is unchanged while the Sa and Is levels are shifted about 03 and 0.4 eV upwards for the larger R (C-O) distance. The splitting Su-la is increased from 0.4 eV to 0.7 eV. These N&CO calculations were performed for C,, symmetry which means that the secular equation is partioned into the different symmetry blocks o, rr, 6. Bending the molecule means that the linear symmetry is lost and the calculations must be performed for a secular equation in which all the matrix elements are evaluated. In order to test the convergence of the result as a frrnction of the number of integration points two new calculations for linear Ni-CO were performed with 4000 points one enforcing the C,, symmetry and the other without symmetry. The results are given in fig. 2. It is only the levels close to the Fermienergy which are shifted less than 0.: eV while the 30,40, Scr and la levels are located at the same binding energy. 2000 points should therefore be enough but in order to be sure that the numerical uncertainties are small the following calculations were performed with 4000 points_ The linear symmetry is then dropped and the CO molecule is bent at 20”, 4.0” and 60” with the result shown in fig. 2. We notice how the splitting of the lrr level is increased to about 0.7 eV for an angle of 60”. The So level is shifted about 0.4 eV while the 40 level is unchanged. For an angle of 34O i 10” as proposed by Andersson and Pendry [4] the splitting is about 0.2 eV. Such a small splitting is indetectable in normal photoelectron experiments in which only the energy is measured. Allyn et al. [l] concluded from the angleresolved experiments that the CO molecule is standing up with an accuracy of about 5O. This conclusion was mainly based on a measurement of 4a level versus photon energy. That experiment showed resonance behaviour which is in agreement with the calculation of Davenport [2] for a CO molecule standing up. A tilted CO molecule should according to our calculations give two peaks separated by about 0.2 eV for the angle proposed by Andersson and Pendry. It is of course difficult to resolve those peaks and a splitting should therefore give a somewhat broader peak com-
1 September 1978
pared with the spectra for free molecules [12,14] _A smaller carbon-oxygen distance than the free molecular value shoufd correspond to a smaller tilting angle in the LEED analysis and be in better agreement with the photoelectron spectroscopy data. The author gratefully acknowledges the support by Professor I. Lindgren and discussions and comments on the manuscript by Dr.S. Andersson and Dr. J-W. Davenport. Financial support from the Swedish Natural Science Research Council is gratefully recognized. The calculations were performed at Gothenburg University Computing Centre and at Gessellschaft fur Schwerionenforschung (GSI) Darmstadt. Thanks should be given to Professor B. Fricke for arranging my visit at GSI.
References CL. AUyn, T. Gustafkson and E-W. Phunmer, Chem. Phys. Letters 47 (1977) 127. J-W. Davenport, Phys. Rev. Letters 36 (1976) 945; The&, University of Pennsylvania <1976), unpublished_ S. Andersson, Solid State Commun. 21 (1977) 75. S. Andersson and J.B. Pendry, Surface Sci. 71(1978) 75. D-E. Ellis, EJ_ Baerends, H. Ada&i and F-W. Ave_m, Surface Sci. 64 (1977) 649; A. Ros&, E.J. Baerends and D-E. Ellis, Proceedings of the 3rd International Conference on Solid Surfaces, Vienna (1977); to be published. I61 EJ. Baerends, DB_ EBis and P. Ros, Chem. Phys. 2 (1973) 41. 171 E-3. Baerends and P_ Ros, Chem. Phys- 2 <1973) 52. 181 A. Rodn, D.E. EIiis, H. Ada&i and F.W. Averill, J. Chem.Phys. 65 (1976) 3629. tg1 D-E- Ellis and G-S. Painter, Phys. Rev. B2 (1970) 2887. IlO1 F-W. Averill and DE Ellis. J_ Chem. Phys- 59 (1973) 6412. [ll] J-C- Skter and K-H. Johnson, Phys. Rev. B5 (1972) 844; K-H. Johnson and F.C. Smith Jr., Phys. Rev. BS (1972) 831. [12] D-W. Turner, C. Baker, A.D. Baker and CR. BrundIe, Molecular photoelectron spectroscopy (Wiley, New York, 1970). [ 131 G. Brodgn, G. Pirug and HP. Bonzel, Chem. Phys Letters 51 (1977) 250. [ 141 E-W. Plummer, T. Gustafsson, W. Gudat and D.E. Eastuxn. Phys. Rev. A15 (1977) 2339_
97
MOLECULAR
CHEM KAL
PIlYSICS LETIERS
LEVELS FOR A CO MOLECULE
CHEMWORBED
1 September1978
AT VARIOUS
ANGLFS
ON A Pii(ltl0) SURFACE Ame ROS6N Depcvtmentof Physics, clhnlmersUniversityof Technology. GGteborg.Sweden Received30 May 1978
Molecuiarclustertheory has been used to examine the effect on the molecularlevelswhen a CO moleculeis chemisorbed at variousangleson a Ni(100) surface.CalcuIationswere fust performedfor a linearNi-CO clusterin C-v symmetry for differentnickel-carbon distances2.5 < h < 4.5 au keepingthe carbon-o.uygen distanceR (C-O) equal to the free motecuIarvalueR (C-O) = 2.13 au_The symmetry requirementwas then droppedfor h = 3.5 au and the CO moleculeuas bent 20”. 40” and 60” relativeto the surfacenom&. The splittingof the CO molecularl;r level was found to be O-1,0.3 and 0.7 eV for the correspondingaqIes. The 40 level was almost unchangedwith the anglewhile the 5u was about 0.3 eV more bound for the 60” anglecomparedto the verticalposition.
The chemisorption of the CO molecule on a NiflCJO) surface has been the subject of many experimental as well as theoretical investigations in recent years. A primary objective in these works has been to determine the bonding geometry of the CO molecule and the binding energies for the chemisorbed CO molecuiar levels. Experimental angle-resoIved photoelectron spectroscopy
experiments by Ahyn et al. [l] combined with theoretical calculations by Davenport [2] have given the identification of the different CO molecular levels. That analysis cont%-medalso that the CO molecule is bonded to the surface with the carbon end down and with the molecular axis normal to the surface with an accuracy of So. EELS experiments recently performed by Andersson 131 have been interpreted in terms of CO terminally bonded to a nickel atom in the surface i-e_ a top position. Andersson and Pendry [4] found further in a LEED experiment that for the Ni(lOO) c (2 X 2) CO structure the top position is most probable with a vertical carbon-oxygen layer distance of (0.95 1: 0.10) A. This means that the CO molecule is tipped over at an angle of 34” t 10” with respect to the surface normal ifthe carbon-oxygen distance is equal to the Ni(CO)4 value of 1.15 A. There is therefore scme ambiguity between the angle-resolved photoelectron experiments and the LEED investigations concerning the CO bond length and the N&CO bond angle.
The variation of the one-electron &ergies, binding
energies, and charge distribution-with.T+e height of the CO molecule above the surface h& recently been calcuiate&for the hollow-, top- and bhdge:bonding geometr& using the Hartree-Fock-Slater model [S] _ The calculations_w>e performed for the Ni&O cluster for hollow bonding iIz_C4, symmetry, the N&Cd and Ni&O clusters for top-bonding m-C,, and C4, symmetry and for the Ni2C0 cluster for bridge-bonding in C2, symmetry. The CO molecule was in those calculations assumed to be chemisorbed with the molecular axis perpendicular to the surface thus keeping the above-mentioned symmetries. About the same behaviour was found in the earlier analysis for the CO 3o, 40, Sa and 1s molecular levels when the calculations were performed in top-bonding geometry for the NiCO and Ni&O clusters. In this work cluster calculations were performed for the Ni-CO cluster at various bond angles with the aim of exploring the influence on the molecular levels. The approach used is based upon *he local density HartreeFock-Slater @FS) molecular orbital approximation ushg variational methods with an exchange parameter a = 0.70 [6-8]. The HFS and overlap matrix elements are evaluated by using a numerical integration scheme 191 with numerical basis sets consisting of symmetrized free atomic orbitals [g-10]. Muffin-tin approximations 95
Volume 58, number 1
CHEMIC_AL PHYSICS LJZTTERS
-1 September 1978
[l f ] to the molecular potential are avoided so that asphericalsystems can be treated accurately with basis function and potential of rather general form_ The calculations performed in this work are based upon the selfconsistontcharge (SCC) [S] method which means that a Mull&en population analysis is performed of the basis functions to determine orbital charges for the construction of the molecular potential. DetaiIs of the computational procedure have been presented previouslY [81Models for CO bonded on a Ni(100) surface in topposition are shown in fig. 1. The effect on the moiecuIar levels has been analyzed by varying the a&e Q! from 0” to 60” thus breaking the C,, symmetry_ Ground state valence IeveIs for the NiCO cluster and for the free CO mole&e calcuIated in the HFS SCC scheme are shown in fig. 2. The free molecuIar 1eveJ.s for aR(C-0) distance of2.13 au are presented to the right. This bond length was then used and the variation of the molecular levels as a function of height above the nickel surface was varied in the range 2.5 au < h < 4.5 au_ The levels are labeled with the free CO notation and the Ni-CO notation in parentheses. 2000 points were used in the numerical integration of the Hartree-FockSlater and overlap matrix elements- For a bond distance ofh = 3-S au which is about the vaIue found for free carbonyis, the level ordering is 5a, la, 40 and 30 with increasing binding energy. This ordering is also in agreement with the result of the angle-resolved photoe_mission expe%iments [l] . The level ordering of chemisorb-
0 C Ni
Ni FE- 1. Model for CO bonded on a Ni(100) surface in top &xition (i.e. linear bond) in C, symmetry. Model for CO bonded at various angk 4 on a Ni(100) surface. To the left is shown the plan and to the ri&t the election of the CO mofeade from ihe surface.
96
Fig. 2. SCC ground state oneelectron eigenvalues (in eV) for whence levek of the CO-Ni cluster iu topposition. To the Ieft are shown the variation of the molecuhr levels as a function of the cabon-nickel
distance h. In the middle
is shown
the effect of varying the carbon-oxygen distance R (C-0) at tixed h = 35 au. To the right in the figure are shown the molecuku levels when the CO mo!ecuIe is chemisorbed at various Q.
ed CO is therefore different compared with the free molecular data 1121. The theoretical ordering of the So and la level is however somewhat sensitive to the type of potential used as was found in the earlier Calculations [S] _ One may therefore conclude from the theoretical calculations that the free CO In level is shifted to less binding energy and close to the 50 chemisorbed level when the molecule is chemisorbed. Broddn et al_ [X3] suggested in a recent analysis of the photoemission experiments and a comparison with carbonyl data that the carbon-oxygen distance should be increased to 2.17 au compared with 2.13 au for the
Volume~58, number 1
CHEMICAL
PHYSICS LETTERS
free CO. A calculation for h equal to 3.5 au has been made using a carbon-oxygen distance of 2.20 au and the result is shown in fig. 2 at the middle. The result withR(C-0) = 2.13 au has also been presented to the right for comparison_ The 40 level is unchanged while the Sa and Is levels are shifted about 03 and 0.4 eV upwards for the larger R (C-O) distance. The splitting Su-la is increased from 0.4 eV to 0.7 eV. These N&CO calculations were performed for C,, symmetry which means that the secular equation is partioned into the different symmetry blocks o, rr, 6. Bending the molecule means that the linear symmetry is lost and the calculations must be performed for a secular equation in which all the matrix elements are evaluated. In order to test the convergence of the result as a frrnction of the number of integration points two new calculations for linear Ni-CO were performed with 4000 points one enforcing the C,, symmetry and the other without symmetry. The results are given in fig. 2. It is only the levels close to the Fermienergy which are shifted less than 0.: eV while the 30,40, Scr and la levels are located at the same binding energy. 2000 points should therefore be enough but in order to be sure that the numerical uncertainties are small the following calculations were performed with 4000 points_ The linear symmetry is then dropped and the CO molecule is bent at 20”, 4.0” and 60” with the result shown in fig. 2. We notice how the splitting of the lrr level is increased to about 0.7 eV for an angle of 60”. The So level is shifted about 0.4 eV while the 40 level is unchanged. For an angle of 34O i 10” as proposed by Andersson and Pendry [4] the splitting is about 0.2 eV. Such a small splitting is indetectable in normal photoelectron experiments in which only the energy is measured. Allyn et al. [l] concluded from the angleresolved experiments that the CO molecule is standing up with an accuracy of about 5O. This conclusion was mainly based on a measurement of 4a level versus photon energy. That experiment showed resonance behaviour which is in agreement with the calculation of Davenport [2] for a CO molecule standing up. A tilted CO molecule should according to our calculations give two peaks separated by about 0.2 eV for the angle proposed by Andersson and Pendry. It is of course difficult to resolve those peaks and a splitting should therefore give a somewhat broader peak com-
1 September 1978
pared with the spectra for free molecules [12,14] _A smaller carbon-oxygen distance than the free molecular value shoufd correspond to a smaller tilting angle in the LEED analysis and be in better agreement with the photoelectron spectroscopy data. The author gratefully acknowledges the support by Professor I. Lindgren and discussions and comments on the manuscript by Dr.S. Andersson and Dr. J-W. Davenport. Financial support from the Swedish Natural Science Research Council is gratefully recognized. The calculations were performed at Gothenburg University Computing Centre and at Gessellschaft fur Schwerionenforschung (GSI) Darmstadt. Thanks should be given to Professor B. Fricke for arranging my visit at GSI.
References CL. AUyn, T. Gustafkson and E-W. Phunmer, Chem. Phys. Letters 47 (1977) 127. J-W. Davenport, Phys. Rev. Letters 36 (1976) 945; The&, University of Pennsylvania <1976), unpublished_ S. Andersson, Solid State Commun. 21 (1977) 75. S. Andersson and J.B. Pendry, Surface Sci. 71(1978) 75. D-E. Ellis, EJ_ Baerends, H. Ada&i and F-W. Ave_m, Surface Sci. 64 (1977) 649; A. Ros&, E.J. Baerends and D-E. Ellis, Proceedings of the 3rd International Conference on Solid Surfaces, Vienna (1977); to be published. I61 EJ. Baerends, DB_ EBis and P. Ros, Chem. Phys. 2 (1973) 41. 171 E-3. Baerends and P_ Ros, Chem. Phys- 2 <1973) 52. 181 A. Rodn, D.E. EIiis, H. Ada&i and F.W. Averill, J. Chem.Phys. 65 (1976) 3629. tg1 D-E- Ellis and G-S. Painter, Phys. Rev. B2 (1970) 2887. IlO1 F-W. Averill and DE Ellis. J_ Chem. Phys- 59 (1973) 6412. [ll] J-C- Skter and K-H. Johnson, Phys. Rev. B5 (1972) 844; K-H. Johnson and F.C. Smith Jr., Phys. Rev. BS (1972) 831. [12] D-W. Turner, C. Baker, A.D. Baker and CR. BrundIe, Molecular photoelectron spectroscopy (Wiley, New York, 1970). [ 131 G. Brodgn, G. Pirug and HP. Bonzel, Chem. Phys Letters 51 (1977) 250. [ 141 E-W. Plummer, T. Gustafsson, W. Gudat and D.E. Eastuxn. Phys. Rev. A15 (1977) 2339_
97