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The interaction of atomic hydrogen with Ni, Pd, and Pt clusters
CHEMICAL PHYSICS LETTERS
Volume 5 1, number 1
THE INTERACTION
R.P. MESSMER**,
OF ATOMIC
HYDROGEN
WITH
I October 1977
Ni, Pd, AND Pt CLUSTERS*
D.R. SALAHUSZ
GeneralEiectric Corporate Research and Development, Schenectady, New York 12301. USA
and
.
K.H. JOHNSON
and C.Y. YANGZS
Department of MaterialsScience and Engineering,MassachusettsInstitute of Technology. ambridge, Massachusetts02139. USA Received 9 March 1977 Revised manuscript received 3 June 1977
EIectronic structures of small Ni, Pd. and Pt clusters containing atomic hydrogen have been calculated by the SCF Xp: SW method, including relativistic effects. Hydrogen-metal bonding is dominated by d-orbitak for Pd and Pt and s-orbitals for Ni, consistent with photoemission spectra for hydrogen chemisorbed on and dissolved in these metals. The results, in conjunction with the concept of orbital electroncgativity, suggest why hydrogen solubility and catalytic reactivity vary among these metals.
The interaction of hydrogen with group-VIII transition metals such as Ni, Pd, and pt is of fundamental importance in the understanding of (1) the dissocia-
tive chemisorption of hydrogen on the surfaces of these metals [ 1] , (2) the catalytic activity of small particIes and clusters of these metals [2] , and (3) the solubtity of atomic hydrogen in these metals [3]. In a previous paper 141, it has been shown that the electronic structures of small globular Cu, Ni, Pd, and Pt clusters,
as calculated by the self-consistent-field X-alpha scattered-wave (SCF Xor SW) method [S] , mimic many of the characteristics of the corresponding bulk crystal&e band structures, while hating ad-
ditional features arising from the kite cluster size and the presence of “surface” atoms. In a more recent paper [6], it has been shown that low-coordination transition-metal
sites, such as those of a cluster or
* Research at M.I.T. sponsored by the Office of Naval Research and, in part, by the National Science Foundation, Grant No. DMR 74-15224. ** Visiting Scientist, M.I.T. $ Present address: Department of Chemistry, University of Montreal, Quebec, Canada. $* Present address: NASA Ames Research Center, Moffet Field, California, USA. 84
“stepped” surface, have local features of electronic structure which explain why such sites activate Hz dissociation and catalyze Hz-D, exchange [7] _ In the present communication, we report the results of SCF Xa! SW studies for the electronic struc-
ture of four-atom tetrahedral and six-atom octahedral Ni, Pd, and Pt clusters containing atomic hydrogen at the tetrahedral and octahedral interstitial sites. This work includes the first application of the relativistic Xac SW formalism developed by Yang and Rabii [8] to metal clusters. The cluster configurations chosen for study have the advantage that they are large enough to represent the local effects on electronic band structure of embedding hydrogen atoms in a surface or bulk interstitial environment, yet small enough to permit the resolution of individual metal-hydrogen bonding orbitals. As will be shown, the results are in good agreement with photoemission studies of the bulk interstitial compound &PdH [9] , and with re-
cently measured photoemission spectra for hydrogen chemisorbed on the (I 11) surfaces of crystalline Ni, Pd, and Pt [IO]. Moreover, the computed electronic structures, in conjunction with the concept of orbital electronegativity [I 1,121, suggest that in those metals where hydrogen solubility is high [3], absorption and
Volume51, number1
CHEMICAL
PHYSICS
chemisorption are closely linked and can be described by essentially identical theoretical models. This is supported by the observation that the photoemission spectrum for hydrogen dissolved in bulk palladium [9] is very similar to that for hydrogen chemisorbed on palladium [lo] , as will be discussed below. Molecular-orbital calculations were carried out for the representative nickel, palladium, and platinum clusters using both the standard nonrelativistic version of the SCF Xar SW method [S] and the recently developed relativistic version [S] _ In both cases the metal-metal internuclear distances were constrained to be equal to those for the corresponding crystalline metals and the muffin-tin approximation was employed, as has been shown to be adequate for metal clusters in ref. [4] _The resulting nonrelativistic orbital energies for the tetrahedral clusters with and without interstitial atomic hydrogen are shown in fig. 1. Also shown, for comparison, is the SCF Xa lsorbital energy for the isolated hydrogen atom*. The electronic energy levels are labeled according to the principal parsial-wave (s, p, d) character of the associated molecular orbit& and the highest occupied orbital in each cluster is indicated by the “Fermi level” (Ed). Since these clusters are intended to simulate the local interstitial bonding configurations of isolated hydrogen atoms embedded in an otherwise perfect bulk or surface lattice, the energy levels of the clus-
ters containing hydrogen have been shifted with respect to those of the corresponding hydrogen-free c!usters so that the respective Fermi levels line up. This approximation is based on the assumption that hydrogen chemisorption or absorption in the dilute limit does not severely perturb the chemical potential of the metallic host and is supported by the observation from photoemission data that the work functions of crystalline nickel, palladium, and platinum change by no more than i- 0.2 eV with hydrogen chemisorption [9] _ The electronic structure of each metal cluster shown in fig. 1 is characterized by a manifold of closely spaced d-levels bracketed by s,p- or s,p,d-hy* In the
SCF Xa method, the Is orbital energy of the hydrogen atom corresponds approximately to the electronegativity $(I + A), where I is the ionization potential and A is the
electron affinity. The transition-state procedure (see ref. (51) leads to relaxed orbital energies corresponding to I and A separately.
1 October 1977
LETTERS
I
N:‘J
Nl&
H
Pd.,H
Pd.3
H
P’4
Pt4H
H
-0.1 t 5p-
-
sp-
-
-
= = __I*
*I’ : ’ -’ -06
i
=
=
dsp-. : : :
*._!
,-
: ’ 8’ ’
\_,
Fig. 1. Nonrelativistic SCF Xa orbital energies of tetrahedral group-VIII transition-metal clusters with and without interstitial atomic hydrogen.
brid levels. This is similar to the results obtained for larger Ni, Pd, and Pt clusters, as described in ref. [4], and analogous to the overlap of the “d-band” by the “s,p-like conduction band” in the respective bulk crystalline metals [13]. In each cluster, the Fermi level (eF) passes through the top of the d-band, just as in the bulk transition metals [ 131. Although the calculated d-band width of each metal cluster is less than that of the corresponding bulk metal, the relative trends of increasing band width and downward shift of the energy levels from Ni4 to Pd, to Ptl are virtually identical to the corresponding trends for Ia@@ ByeI, pailadium, and platinum clusters [4] a&&$+xalline metals. Furthermore, the electronr ._-;.,Y ic structures of t&Pdd and Pt4 clusters are more nearly alike than those of the Ni4 and Pd, or Ni, and Pt4 clusters, consistent with the band structures of the bulk crystalline metals. The deepest energy levels shown in fig. 1 for Pd, and Pt4 respectively, associated with cluster orbitals having the al representation of the T, point group and roughly analogous to the Bloch band-structure states having the Fl representa-
tion of the crystal space group, are predominantly dlike with a small amount of s,p-hybridization. In contrast, the deepest energy level for the Ni4 cluster shown in fig. 1, also’associated with an al molecular
orbital and r, Bloch state, is predominantly s-like, but with significant d-orbital hybridization and some p-like character. The partial-wave decomposition of the cluster orbitals having al symmetry is summarized in table 1. These differences between the electronic 85
CHEhlICAL PHYSICS LETTERS
Volume 5 1, number 1
Table 1
Partial-wave decomposition or”the metal-atom contributions to al molecular-orbital charge distributions of tetrahedral clusters with and without interstitial atomic hydrogen. The orbital energies correspond to lowest levels shown in fig. 1 Cluster
N;‘4 NbH Pd4 Pd4 H pt4 R4H
Orbital energy (-E in Rydberg units)
Fractional partial-wave character s
P
d
0.580
0.63
0.11 0.18
0.26
0.724 0.628 0.758 0.681
0.47 0.05 0.15 0.04
0.03 0.10 0.03
0.35 0.92 0.75 0.93
0.821
0.12
0.09
0.79
of nickel aggregates and the electronic structures of palladium and platinum aggregates are crucial to understanding the differences in the photoemission spectra for hydrogen chemisorbed on these metals i9-j , as well as the differences among these metals with respect to hydrogen solubility [? ] and catalytic reactivity [ 1,2] _ SCF Xa atomic- and molecular-orbital energy eigenvalues, because of their equivalenci: to derivatives of total energy with respect to occupation numbers [S ] , can be rigorously identified with differential “orbital electronegativities” 111,123 which are an extension of Mulliken’s concept of electronegativity [ 141, originally defined as the average of the ionization potential and electron affinity of an isolated atom, to individual atomic and molecular orbit&. Thus the relative positions of the SCF X& orbital energies for the Ni4, Pd4, and Pt4 clusters (as well as for larger clusters 141) with respect to the SCF Xa! Is-orbital energy for atomic hydrogen, as shown in fig. 1, are a measure of the differences in orbital electronegativity and chemical potential between these metal aggregates and atomic hydrogen. The covalent bonding of atomic hydrogen at the cluster interstices is governed principally by the proximity in energy (or electronegativity) and concomitant overlap of the symmetry-conserving [ 15 ] al orbitals near the bottom of the Ni4, Pd,, and Pt4 d-bands with the H IS orbital_ The main result is the splitting off of a hydrogen-metal bonding energy level of al orbital symmetry from the bottom of the d-band of each cluster, accompanied by much smaller level shifts within the d-manifolds, as indicated in fig. 1 structure
86
1 October 1977
by the orbital energies for the Ni4H, I’daH, and Pt4H clusters and the connecting dashed lines. The metallic 4s-like component of this al orbital is largely responsible for the bonding of hydrogen to the nickel aggregate, as indicated by the partial-wave decomposition for the al orbital of lowest energy in table 1. However, the contribution of the 3d-like component to the bonding is not negligible, amounting to 35% of the Ni4-H al bonding orbital charge. This result is inconsistent with the claims of other workers [16, 171 who, on the basis of theoretical studies of the interaction of hydrogen with only one or two nickel atoms, find that the Ni 3d orbit& remain essentially localized and atomic-like and therefore conclude that these orbitals do not contribute to the chemisorption of hydrogen on nickel. The rehybridization of 4s- and 3d-like orbital components upon interaction of hydrogen with the Nia cluster is evident in the somewhat different mixtures of “s” and “d” partial-wave components for Ni4 and Ni,H shown in table 1. In contrast to the results for nickel, the metal d-orbital components almost exclusively dominate the bonding of hydrogen to palladium and platinum aggregates, the contributions of Pd 5s- and Pt 6s-like components amounting to only 15% and 12% for Pd,H and Pt4H respectively. These results underscore the danger of making general conclusions about the dominance of s-orbit& over d-orbitals in determining the chemisorption and catalytic reactivity of hydrogen on transition metals exclusively on the basis of theoretical studies of first-row transition metals, as has recently been done by some workers in the published literature 116,171. The present findings are essentially unaltered for hydrogen interacting with larger nickel, palladium, and platinum aggregates having octahedral configurations. For example, the partial-wave decompositions of the aIg orbitals responsible for the bonding of hydrogen at the octahedral interstices of sixatom clusters, as summarized in table 2, are very similar to the results shown in table 1. In order to determine the effects of special relativity on the electronic structures of these transitionmetal aggregates and hydrogen bonded thereon, particularly for palladium and platinum clusters where such effects are expected to be most important, we have calculated the relativistic corrections to the results shown in fig. 1 using the relativistic version of the Xcu scattered-wave method recently developed by
CHEMICAL
Volume 5 1, number 1
PHYSICS
Table 2 partial-wave decomposition of the metal-atom contributions to alg molecular-orbital charge distributions of octahedral clusters with and without interstitial atomic hydrogen Cluster
Orbital energy <-e in Rydberg units)
S
Nis
0.653
NisH
0.981
Pd6 PdBH R6
QH
Fractional partial-wave character P
d
0.67
0.15
0.42
0.28
0.646 0.952
0.09 0.23
0.06 0.20
0.18 0.31 0.85 0.57
0.706 i -024
0.07 0.19
0.06 0.18
0.86 0.62
Yang and Rabii [8] . These results, which include the relativistic energy-level shifts and spin-orbit splittings, are shown in fig. 2. The manifolds of energy levels in fig. 2, including the splitting off of a hydrogenmetal bonding orbital from the bottom of each dband, are qualitatively similar to the nonrelativistic results of fig. 1. The principal effect of relativity is to widen the Pt4 d-band and to lower its center of gravity with respect to the H Is orbital energy. The latter result implies a relativistic increase in the effective group orbital electronegativity of the platinum aggregate, makiig it somewhat of an electron acceptor with respect to hydrogen, rather than an electron donor as implied by the respective positions of the nonreIativistic Pt4 energies and H 1 s level in fig. 1. This finding is consistent with the slight decrease in Nb
N&H
H
Pd4
P4H
Pts
H
Pt,,H
L October
LETTERS
1977
the work function of platinum upon hydrogen chemisorption observed in photoemission measurements [lo], whereas the slight increases in work function observed for hydrogen chemisorption on nickel and palladium are explicable in terms of the relative positions of the corresponding energy levels in figs. 1 and 2. The relativistic effects on the electronic structures of I’d4 and PdaH are qualitatively similar to those for Pt4 and Pt,H,
respectively,
although they are too the chemistry and the interpretation of photoemission data. The relativistic contributions to the electronic structure of Ni, and small
to significantly
NiaH
are negligible.
affect
The most striking confirmation of these theoretical results are the photoemission spectra recently measured by Demuth [lo] for hydrogen chemisorbed on the (Ill) faces of nickel, palladium, and platinum, which are reproduced in fig. 3. For each metal, the data clearly show a chemisorption:induced photoemisI
cl6L
I
H20N
I
I
Ni (18)
,
,
hrr =212av
=+H++=
H
-a+
-0.3
l-
SPY-
sp{=
-
= SP{Z
-
=K=H=H= c) 3L H20NPt(lll)
spd,
hv = 2l.PaV
-
I
I
I
I
I
I
I2 IO B 6 4 2 ELECTRONBINDING ENEfi 2. SCF Xor orbital energies of tetrahedral group-VIII transition-metal clusters with and without interstitial atomic hydrogen, including relativistic corrections for the Pde, PdQH, Fig.
pt4, and Pt4H clusters.
SVI
Fig. 3. Photoemission energy distribution curves N(E) relative to the Fermi Ievel EF for cIean (solid curve) and near saturation coverages of hydrogen (dashed curve) for (a) Ni( 11 l), (b) Pd(l11) and (c) Pt( 111). Experimental results of ref. [IO] . 87
CHEMICAL
Volume 5 1, number 1
PHYSICS
don peak at an energy slightly higher than the metal d-band photoemission peaks, suggestive of a hydrogenmetal bonding state Or “resonance” split off from the manifold of d-orbitals as predicted in figs. 1 and 2. On the basis of the intensity and width of the chemisorption-induced photoemission structure as a function of incident photon energy, Demuth [lo] concludes that hydrogen chemisorption on Ni( 1 II) occurs primarily via the s-orbitals (with some d-orbital participation), whereas the metal d-orbitals dominate hydrogen chemisorption on Pd( 111) and Pt( 111). This interpretation is completely consistent with the partial-wave decomposition of the hydrogen-metal bonding orbitals of a1 and aIg symmetries described above and summarized respectively in tables 1 and 2. Furthermore, the chemisorption-induced spectral modification of d-band photoemission from Pd( 111) and Pt(ll1) surfaces [lo] (fig. 3) is explicable in terms of the calculated shifts of d-manifold energy levels in going from Pd, to Pd,H and from Pt4 to Pt4H (fig. 2). On the other hand, the uniform enhancement of the d-band photoemission from the Ni( 111) surface upon hydrogen chemisorption is consistent with the almost negligible shifts calculated for the d-orbital manifold in going from Ni4 to Ni4H. Note that the hydrogeninduced d-level shifts for Pt4H and Pd4H are significantly larger and in better agreement with experiment (fig. 3) for the relativistic limit (fig. 2) than in the
nonrelativistic limit (fig. l), showing the role of relativistic contributions to the electronic structure in elucidating certain details of the chemistry of heavy transition-metal aggregates_ It may seem inappropriate for one to interpret experimental results for hydrogen chemisolption on nickel, palladium, and platinum surfaces in terms of
ENERGY BELOW EF kV)
’
Fig. 4. Photoemission energy distribution curves for Pd (dashed curve) ant? a two-phase mixture of p-PdH and Pd (solid curve). 88
LETTERS
1 October 1977
a theoretical model which presumes hydrogen atoms in interstitial environments. However, it should be emphasized that the photoemission spectrum for the interstitial bulk hydride, /3-PdH [9] (reproduced in fig. 4), is qualitatively similar to that for hydrogen chemisorbed on palladium (fig. 3b), particularly in regard to the appearance of a hydrogen-induced “resonance” below the d-band. Moreover, recent cluster modets for hydrogen chemisorption on nickel surfaces also yield hydrogen bonding orbitals at energies below the d-manifold [ 18]_ Thus it has not been possible, thus far, to dinstinguish either experimentally or theoretically between hydrogen chemisorption and absorption in such transition metals. In regard to the well known fact that atomic hydrogen is more soluble in palladium than in nickel or platinum [3], the almost perfect tuning of the palladium cluster d-orbital electronegativities to the hydrogen &orbital electronegativity, as indicated in fig. 2 by the relative positions of the corresponding energy levels, suggests almost perfect covalency between palladium, in aggregate form, and atomic hydrogen. In contrast, nickel and platinum aggregates are respectively electropositive and electronegative with respect to hydrogen_ The strength of a heteronuclear chemical bond, as originally described by Pauling 1191, can be viewed as having covalent and ionic contributions in general. It is welI known that the solubility of an impurity in a metal generally decreases with increasing electronegativity difference between solute and solvent, other factors such as atomic size factor remaining constant [20]. Thus the attainment of nearly zero net orbital electronegativity difference between palladium aggregates and atomic hydrogen, thereby minimizing ionic contributions to the bonding and optimizing Pd(4d)-H( 1s) covalency, is consistent with the higher solubility of hydrogen in palladium, as compared with nickel and platinum_ The labile exchange of dissociatively chemisorbed hydrogen atoms between the surface and underlying interstices, making the metal a reservoir for atomic hydrogen, couid facilitate the reactivity of hydrogen with other chemisorbed molecules [6], offering a possible explanation of why palladium is an order of magnitude more active in catalyzing hydrogenation reactions than nickel or platinum [21] _ Although the metal-metal internuclear distances in the clusters have been constrained in the present studies to the
Volume 5 1, number 1
CHEMICAL PHYSICS LETTERS
values for the corresponding bulk crystalline metals, previous theoretical work on the cohesive energies of metal clusters has shown that the equilibrium internuclear distance decreases somewhat with decreasing number of atoms in the cluster [22] _ The latter fmding suggests that the size factor for small metal clusters is less favorable for interstitial hydrogen incorporation than larger particles or crystallites, thus providing a possible explanation of the observed reduction of hydrogen solubility with decreasing particle size [23]_ Finally, the SCF Xar SW values for the relative 4sand 3d-like partial-wave components of the Ni4-H aI bonding orbital have already been used by Schiinhammer 1241 to parameterize an Anderson-type hamiltonian for hydrogen chemisorption on nickel. From this, Schijnhammer has calculated the adsorbate Green’s function and the width of the chemisorptioninduced photoemission peak, yielding a result in excellent agreement with the measurements of Demuth
WI References [l] G-C. Bond, Catalysis by metals (Academic Press, New York, 1962). [2] J.R. Anderson, The structure of metallic catalysts (Academic Press, New York, 1975). [ 31 F.A. Lewis, The palladium/hydrogen system (Academic Press, New York, 1967). [4] R.P. Messmer, SK. Knudson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev. B13 (1976) 1396. [5] J.C. Slater and K.H. Johnson, Phys. Rev. B5 (1972) 844; K-H. Johnson, in: Advances in quantum chemistry, Vol. 7, ed. P.-O. LEwdin (Academic Press, New York, 1973) p_ 143; J-C. Slater, Quantum theory of molecules and solids, Vol. 4. The self-consistent field for molecules and solids (McGraw-Hill, New York, 1974); K.H. Johnson, in: Annual review of physical chemistry,
1 October 1977
Vol. 26, eds. H. Eyring, C.J. Christensen and H.S. Johnston (Annual Reviews, Palo Alto, 1975) p. 39. [6] K.H. Johnson and A. Balars, to be published. [ 7 ] G.A. Somorjai, in: The physic& basis for heterogeneous catalysis, eds. E. Drauglis and R-1. Jaffee (Plenum Press, New York, 1975) p_ 395. [8] C-Y. Yang and S. Rabii, Phys. Rev. Al2 (1975) 362; C.Y. Yang, Chem. Phvs. Letters 41 (1976) 588 PI D.E. Eastman, J.K. Chshion and A.& Swiiendick, Phys. Rev. Letters 27 (1971) 35. 1101 I.E. Demuth, to be published; private communication. 1111J. Hinze, M.A. Whitehead and H.H. Jaffe, J. Am. Cbem. Sot. 85 (1963) 148. [I21 K.H. Johnson, Intern. J. Quantum Chem. 1 lS, to be published. [131 L-H. Bennett, ed., Electronic density of states. National Bureau of Standards Special Publication 323, Washington, D-C. (1971). 1141 R.S. hiulliken, J. Chem. Phys. 46 (1949) 497. [IS] R.G. Woodward and R. Hoffmann, Accounts Chem. Res. 1 (1968) 17; The conservation of orbital symmetry (Academic Press, New York, 1969). t161 A.B. Kunz, M.P. Guse and R.J. Blint, J. Phys. B8 (1975) L358; R.J. Blint, A.B. Kunz and M.P. Cuse, Chem. Phys. Letters 36 (1975) 19 1; A.B. Kunz, M.P. Guse and R.J. Blint, in: Elcctrocatalysis on non-metallic surfaces, ed. A-D. Franklin, Nationai Bureau of Standards Special Publication 455, Washington, D.C. (1976) p- 53. t171 CF. Melius, Chem. Phys. Letters 39 (1976) 287; CF. Melius, J-W. Moskowitz, A-P. Mortofa, h1.B. BaiUe and M.A. Ratner, Surface Sci. 59 (1976) 279. [ISI D.E. Ellis, H. Adachi and F-W. Averill, Surface Sci. 58 (1976) 497. [I91 L. Pauling, The nature of the chemical bond (Cornell Univ. Press, Ithaca, 1960) p. 80. 1201 W. Hume-Rothery, The structure of metals and alloys (Institute of ,MetaIs, London, 1936). 1211 G.C.A. Schuit and L-L. van Reijen, Advan. Catalysis 10 (1958) 242. 1221 3-G. Fripiat, K.T. Chow, M. Boudart, J-B. Diamond and K.H. Johnson, J. Mol. Catalysis 1 (1975) 59. [23] M. Boudart, private communication_ [24] K. Scho’nhammer, Solid State Commun. 22 (1977) 51.
89
Volume 5 1, number 1
THE INTERACTION
R.P. MESSMER**,
OF ATOMIC
HYDROGEN
WITH
I October 1977
Ni, Pd, AND Pt CLUSTERS*
D.R. SALAHUSZ
GeneralEiectric Corporate Research and Development, Schenectady, New York 12301. USA
and
.
K.H. JOHNSON
and C.Y. YANGZS
Department of MaterialsScience and Engineering,MassachusettsInstitute of Technology. ambridge, Massachusetts02139. USA Received 9 March 1977 Revised manuscript received 3 June 1977
EIectronic structures of small Ni, Pd. and Pt clusters containing atomic hydrogen have been calculated by the SCF Xp: SW method, including relativistic effects. Hydrogen-metal bonding is dominated by d-orbitak for Pd and Pt and s-orbitals for Ni, consistent with photoemission spectra for hydrogen chemisorbed on and dissolved in these metals. The results, in conjunction with the concept of orbital electroncgativity, suggest why hydrogen solubility and catalytic reactivity vary among these metals.
The interaction of hydrogen with group-VIII transition metals such as Ni, Pd, and pt is of fundamental importance in the understanding of (1) the dissocia-
tive chemisorption of hydrogen on the surfaces of these metals [ 1] , (2) the catalytic activity of small particIes and clusters of these metals [2] , and (3) the solubtity of atomic hydrogen in these metals [3]. In a previous paper 141, it has been shown that the electronic structures of small globular Cu, Ni, Pd, and Pt clusters,
as calculated by the self-consistent-field X-alpha scattered-wave (SCF Xor SW) method [S] , mimic many of the characteristics of the corresponding bulk crystal&e band structures, while hating ad-
ditional features arising from the kite cluster size and the presence of “surface” atoms. In a more recent paper [6], it has been shown that low-coordination transition-metal
sites, such as those of a cluster or
* Research at M.I.T. sponsored by the Office of Naval Research and, in part, by the National Science Foundation, Grant No. DMR 74-15224. ** Visiting Scientist, M.I.T. $ Present address: Department of Chemistry, University of Montreal, Quebec, Canada. $* Present address: NASA Ames Research Center, Moffet Field, California, USA. 84
“stepped” surface, have local features of electronic structure which explain why such sites activate Hz dissociation and catalyze Hz-D, exchange [7] _ In the present communication, we report the results of SCF Xa! SW studies for the electronic struc-
ture of four-atom tetrahedral and six-atom octahedral Ni, Pd, and Pt clusters containing atomic hydrogen at the tetrahedral and octahedral interstitial sites. This work includes the first application of the relativistic Xac SW formalism developed by Yang and Rabii [8] to metal clusters. The cluster configurations chosen for study have the advantage that they are large enough to represent the local effects on electronic band structure of embedding hydrogen atoms in a surface or bulk interstitial environment, yet small enough to permit the resolution of individual metal-hydrogen bonding orbitals. As will be shown, the results are in good agreement with photoemission studies of the bulk interstitial compound &PdH [9] , and with re-
cently measured photoemission spectra for hydrogen chemisorbed on the (I 11) surfaces of crystalline Ni, Pd, and Pt [IO]. Moreover, the computed electronic structures, in conjunction with the concept of orbital electronegativity [I 1,121, suggest that in those metals where hydrogen solubility is high [3], absorption and
Volume51, number1
CHEMICAL
PHYSICS
chemisorption are closely linked and can be described by essentially identical theoretical models. This is supported by the observation that the photoemission spectrum for hydrogen dissolved in bulk palladium [9] is very similar to that for hydrogen chemisorbed on palladium [lo] , as will be discussed below. Molecular-orbital calculations were carried out for the representative nickel, palladium, and platinum clusters using both the standard nonrelativistic version of the SCF Xar SW method [S] and the recently developed relativistic version [S] _ In both cases the metal-metal internuclear distances were constrained to be equal to those for the corresponding crystalline metals and the muffin-tin approximation was employed, as has been shown to be adequate for metal clusters in ref. [4] _The resulting nonrelativistic orbital energies for the tetrahedral clusters with and without interstitial atomic hydrogen are shown in fig. 1. Also shown, for comparison, is the SCF Xa lsorbital energy for the isolated hydrogen atom*. The electronic energy levels are labeled according to the principal parsial-wave (s, p, d) character of the associated molecular orbit& and the highest occupied orbital in each cluster is indicated by the “Fermi level” (Ed). Since these clusters are intended to simulate the local interstitial bonding configurations of isolated hydrogen atoms embedded in an otherwise perfect bulk or surface lattice, the energy levels of the clus-
ters containing hydrogen have been shifted with respect to those of the corresponding hydrogen-free c!usters so that the respective Fermi levels line up. This approximation is based on the assumption that hydrogen chemisorption or absorption in the dilute limit does not severely perturb the chemical potential of the metallic host and is supported by the observation from photoemission data that the work functions of crystalline nickel, palladium, and platinum change by no more than i- 0.2 eV with hydrogen chemisorption [9] _ The electronic structure of each metal cluster shown in fig. 1 is characterized by a manifold of closely spaced d-levels bracketed by s,p- or s,p,d-hy* In the
SCF Xa method, the Is orbital energy of the hydrogen atom corresponds approximately to the electronegativity $(I + A), where I is the ionization potential and A is the
electron affinity. The transition-state procedure (see ref. (51) leads to relaxed orbital energies corresponding to I and A separately.
1 October 1977
LETTERS
I
N:‘J
Nl&
H
Pd.,H
Pd.3
H
P’4
Pt4H
H
-0.1 t 5p-
-
sp-
-
-
= = __I*
*I’ : ’ -’ -06
i
=
=
dsp-. : : :
*._!
,-
: ’ 8’ ’
\_,
Fig. 1. Nonrelativistic SCF Xa orbital energies of tetrahedral group-VIII transition-metal clusters with and without interstitial atomic hydrogen.
brid levels. This is similar to the results obtained for larger Ni, Pd, and Pt clusters, as described in ref. [4], and analogous to the overlap of the “d-band” by the “s,p-like conduction band” in the respective bulk crystalline metals [13]. In each cluster, the Fermi level (eF) passes through the top of the d-band, just as in the bulk transition metals [ 131. Although the calculated d-band width of each metal cluster is less than that of the corresponding bulk metal, the relative trends of increasing band width and downward shift of the energy levels from Ni4 to Pd, to Ptl are virtually identical to the corresponding trends for Ia@@ ByeI, pailadium, and platinum clusters [4] a&&$+xalline metals. Furthermore, the electronr ._-;.,Y ic structures of t&Pdd and Pt4 clusters are more nearly alike than those of the Ni4 and Pd, or Ni, and Pt4 clusters, consistent with the band structures of the bulk crystalline metals. The deepest energy levels shown in fig. 1 for Pd, and Pt4 respectively, associated with cluster orbitals having the al representation of the T, point group and roughly analogous to the Bloch band-structure states having the Fl representa-
tion of the crystal space group, are predominantly dlike with a small amount of s,p-hybridization. In contrast, the deepest energy level for the Ni4 cluster shown in fig. 1, also’associated with an al molecular
orbital and r, Bloch state, is predominantly s-like, but with significant d-orbital hybridization and some p-like character. The partial-wave decomposition of the cluster orbitals having al symmetry is summarized in table 1. These differences between the electronic 85
CHEhlICAL PHYSICS LETTERS
Volume 5 1, number 1
Table 1
Partial-wave decomposition or”the metal-atom contributions to al molecular-orbital charge distributions of tetrahedral clusters with and without interstitial atomic hydrogen. The orbital energies correspond to lowest levels shown in fig. 1 Cluster
N;‘4 NbH Pd4 Pd4 H pt4 R4H
Orbital energy (-E in Rydberg units)
Fractional partial-wave character s
P
d
0.580
0.63
0.11 0.18
0.26
0.724 0.628 0.758 0.681
0.47 0.05 0.15 0.04
0.03 0.10 0.03
0.35 0.92 0.75 0.93
0.821
0.12
0.09
0.79
of nickel aggregates and the electronic structures of palladium and platinum aggregates are crucial to understanding the differences in the photoemission spectra for hydrogen chemisorbed on these metals i9-j , as well as the differences among these metals with respect to hydrogen solubility [? ] and catalytic reactivity [ 1,2] _ SCF Xa atomic- and molecular-orbital energy eigenvalues, because of their equivalenci: to derivatives of total energy with respect to occupation numbers [S ] , can be rigorously identified with differential “orbital electronegativities” 111,123 which are an extension of Mulliken’s concept of electronegativity [ 141, originally defined as the average of the ionization potential and electron affinity of an isolated atom, to individual atomic and molecular orbit&. Thus the relative positions of the SCF X& orbital energies for the Ni4, Pd4, and Pt4 clusters (as well as for larger clusters 141) with respect to the SCF Xa! Is-orbital energy for atomic hydrogen, as shown in fig. 1, are a measure of the differences in orbital electronegativity and chemical potential between these metal aggregates and atomic hydrogen. The covalent bonding of atomic hydrogen at the cluster interstices is governed principally by the proximity in energy (or electronegativity) and concomitant overlap of the symmetry-conserving [ 15 ] al orbitals near the bottom of the Ni4, Pd,, and Pt4 d-bands with the H IS orbital_ The main result is the splitting off of a hydrogen-metal bonding energy level of al orbital symmetry from the bottom of the d-band of each cluster, accompanied by much smaller level shifts within the d-manifolds, as indicated in fig. 1 structure
86
1 October 1977
by the orbital energies for the Ni4H, I’daH, and Pt4H clusters and the connecting dashed lines. The metallic 4s-like component of this al orbital is largely responsible for the bonding of hydrogen to the nickel aggregate, as indicated by the partial-wave decomposition for the al orbital of lowest energy in table 1. However, the contribution of the 3d-like component to the bonding is not negligible, amounting to 35% of the Ni4-H al bonding orbital charge. This result is inconsistent with the claims of other workers [16, 171 who, on the basis of theoretical studies of the interaction of hydrogen with only one or two nickel atoms, find that the Ni 3d orbit& remain essentially localized and atomic-like and therefore conclude that these orbitals do not contribute to the chemisorption of hydrogen on nickel. The rehybridization of 4s- and 3d-like orbital components upon interaction of hydrogen with the Nia cluster is evident in the somewhat different mixtures of “s” and “d” partial-wave components for Ni4 and Ni,H shown in table 1. In contrast to the results for nickel, the metal d-orbital components almost exclusively dominate the bonding of hydrogen to palladium and platinum aggregates, the contributions of Pd 5s- and Pt 6s-like components amounting to only 15% and 12% for Pd,H and Pt4H respectively. These results underscore the danger of making general conclusions about the dominance of s-orbit& over d-orbitals in determining the chemisorption and catalytic reactivity of hydrogen on transition metals exclusively on the basis of theoretical studies of first-row transition metals, as has recently been done by some workers in the published literature 116,171. The present findings are essentially unaltered for hydrogen interacting with larger nickel, palladium, and platinum aggregates having octahedral configurations. For example, the partial-wave decompositions of the aIg orbitals responsible for the bonding of hydrogen at the octahedral interstices of sixatom clusters, as summarized in table 2, are very similar to the results shown in table 1. In order to determine the effects of special relativity on the electronic structures of these transitionmetal aggregates and hydrogen bonded thereon, particularly for palladium and platinum clusters where such effects are expected to be most important, we have calculated the relativistic corrections to the results shown in fig. 1 using the relativistic version of the Xcu scattered-wave method recently developed by
CHEMICAL
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PHYSICS
Table 2 partial-wave decomposition of the metal-atom contributions to alg molecular-orbital charge distributions of octahedral clusters with and without interstitial atomic hydrogen Cluster
Orbital energy <-e in Rydberg units)
S
Nis
0.653
NisH
0.981
Pd6 PdBH R6
QH
Fractional partial-wave character P
d
0.67
0.15
0.42
0.28
0.646 0.952
0.09 0.23
0.06 0.20
0.18 0.31 0.85 0.57
0.706 i -024
0.07 0.19
0.06 0.18
0.86 0.62
Yang and Rabii [8] . These results, which include the relativistic energy-level shifts and spin-orbit splittings, are shown in fig. 2. The manifolds of energy levels in fig. 2, including the splitting off of a hydrogenmetal bonding orbital from the bottom of each dband, are qualitatively similar to the nonrelativistic results of fig. 1. The principal effect of relativity is to widen the Pt4 d-band and to lower its center of gravity with respect to the H Is orbital energy. The latter result implies a relativistic increase in the effective group orbital electronegativity of the platinum aggregate, makiig it somewhat of an electron acceptor with respect to hydrogen, rather than an electron donor as implied by the respective positions of the nonreIativistic Pt4 energies and H 1 s level in fig. 1. This finding is consistent with the slight decrease in Nb
N&H
H
Pd4
P4H
Pts
H
Pt,,H
L October
LETTERS
1977
the work function of platinum upon hydrogen chemisorption observed in photoemission measurements [lo], whereas the slight increases in work function observed for hydrogen chemisorption on nickel and palladium are explicable in terms of the relative positions of the corresponding energy levels in figs. 1 and 2. The relativistic effects on the electronic structures of I’d4 and PdaH are qualitatively similar to those for Pt4 and Pt,H,
respectively,
although they are too the chemistry and the interpretation of photoemission data. The relativistic contributions to the electronic structure of Ni, and small
to significantly
NiaH
are negligible.
affect
The most striking confirmation of these theoretical results are the photoemission spectra recently measured by Demuth [lo] for hydrogen chemisorbed on the (Ill) faces of nickel, palladium, and platinum, which are reproduced in fig. 3. For each metal, the data clearly show a chemisorption:induced photoemisI
cl6L
I
H20N
I
I
Ni (18)
,
,
hrr =212av
=+H++=
H
-a+
-0.3
l-
SPY-
sp{=
-
= SP{Z
-
=K=H=H= c) 3L H20NPt(lll)
spd,
hv = 2l.PaV
-
I
I
I
I
I
I
I2 IO B 6 4 2 ELECTRONBINDING ENEfi 2. SCF Xor orbital energies of tetrahedral group-VIII transition-metal clusters with and without interstitial atomic hydrogen, including relativistic corrections for the Pde, PdQH, Fig.
pt4, and Pt4H clusters.
SVI
Fig. 3. Photoemission energy distribution curves N(E) relative to the Fermi Ievel EF for cIean (solid curve) and near saturation coverages of hydrogen (dashed curve) for (a) Ni( 11 l), (b) Pd(l11) and (c) Pt( 111). Experimental results of ref. [IO] . 87
CHEMICAL
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PHYSICS
don peak at an energy slightly higher than the metal d-band photoemission peaks, suggestive of a hydrogenmetal bonding state Or “resonance” split off from the manifold of d-orbitals as predicted in figs. 1 and 2. On the basis of the intensity and width of the chemisorption-induced photoemission structure as a function of incident photon energy, Demuth [lo] concludes that hydrogen chemisorption on Ni( 1 II) occurs primarily via the s-orbitals (with some d-orbital participation), whereas the metal d-orbitals dominate hydrogen chemisorption on Pd( 111) and Pt( 111). This interpretation is completely consistent with the partial-wave decomposition of the hydrogen-metal bonding orbitals of a1 and aIg symmetries described above and summarized respectively in tables 1 and 2. Furthermore, the chemisorption-induced spectral modification of d-band photoemission from Pd( 111) and Pt(ll1) surfaces [lo] (fig. 3) is explicable in terms of the calculated shifts of d-manifold energy levels in going from Pd, to Pd,H and from Pt4 to Pt4H (fig. 2). On the other hand, the uniform enhancement of the d-band photoemission from the Ni( 111) surface upon hydrogen chemisorption is consistent with the almost negligible shifts calculated for the d-orbital manifold in going from Ni4 to Ni4H. Note that the hydrogeninduced d-level shifts for Pt4H and Pd4H are significantly larger and in better agreement with experiment (fig. 3) for the relativistic limit (fig. 2) than in the
nonrelativistic limit (fig. l), showing the role of relativistic contributions to the electronic structure in elucidating certain details of the chemistry of heavy transition-metal aggregates_ It may seem inappropriate for one to interpret experimental results for hydrogen chemisolption on nickel, palladium, and platinum surfaces in terms of
ENERGY BELOW EF kV)
’
Fig. 4. Photoemission energy distribution curves for Pd (dashed curve) ant? a two-phase mixture of p-PdH and Pd (solid curve). 88
LETTERS
1 October 1977
a theoretical model which presumes hydrogen atoms in interstitial environments. However, it should be emphasized that the photoemission spectrum for the interstitial bulk hydride, /3-PdH [9] (reproduced in fig. 4), is qualitatively similar to that for hydrogen chemisorbed on palladium (fig. 3b), particularly in regard to the appearance of a hydrogen-induced “resonance” below the d-band. Moreover, recent cluster modets for hydrogen chemisorption on nickel surfaces also yield hydrogen bonding orbitals at energies below the d-manifold [ 18]_ Thus it has not been possible, thus far, to dinstinguish either experimentally or theoretically between hydrogen chemisorption and absorption in such transition metals. In regard to the well known fact that atomic hydrogen is more soluble in palladium than in nickel or platinum [3], the almost perfect tuning of the palladium cluster d-orbital electronegativities to the hydrogen &orbital electronegativity, as indicated in fig. 2 by the relative positions of the corresponding energy levels, suggests almost perfect covalency between palladium, in aggregate form, and atomic hydrogen. In contrast, nickel and platinum aggregates are respectively electropositive and electronegative with respect to hydrogen_ The strength of a heteronuclear chemical bond, as originally described by Pauling 1191, can be viewed as having covalent and ionic contributions in general. It is welI known that the solubility of an impurity in a metal generally decreases with increasing electronegativity difference between solute and solvent, other factors such as atomic size factor remaining constant [20]. Thus the attainment of nearly zero net orbital electronegativity difference between palladium aggregates and atomic hydrogen, thereby minimizing ionic contributions to the bonding and optimizing Pd(4d)-H( 1s) covalency, is consistent with the higher solubility of hydrogen in palladium, as compared with nickel and platinum_ The labile exchange of dissociatively chemisorbed hydrogen atoms between the surface and underlying interstices, making the metal a reservoir for atomic hydrogen, couid facilitate the reactivity of hydrogen with other chemisorbed molecules [6], offering a possible explanation of why palladium is an order of magnitude more active in catalyzing hydrogenation reactions than nickel or platinum [21] _ Although the metal-metal internuclear distances in the clusters have been constrained in the present studies to the
Volume 5 1, number 1
CHEMICAL PHYSICS LETTERS
values for the corresponding bulk crystalline metals, previous theoretical work on the cohesive energies of metal clusters has shown that the equilibrium internuclear distance decreases somewhat with decreasing number of atoms in the cluster [22] _ The latter fmding suggests that the size factor for small metal clusters is less favorable for interstitial hydrogen incorporation than larger particles or crystallites, thus providing a possible explanation of the observed reduction of hydrogen solubility with decreasing particle size [23]_ Finally, the SCF Xar SW values for the relative 4sand 3d-like partial-wave components of the Ni4-H aI bonding orbital have already been used by Schiinhammer 1241 to parameterize an Anderson-type hamiltonian for hydrogen chemisorption on nickel. From this, Schijnhammer has calculated the adsorbate Green’s function and the width of the chemisorptioninduced photoemission peak, yielding a result in excellent agreement with the measurements of Demuth
WI References [l] G-C. Bond, Catalysis by metals (Academic Press, New York, 1962). [2] J.R. Anderson, The structure of metallic catalysts (Academic Press, New York, 1975). [ 31 F.A. Lewis, The palladium/hydrogen system (Academic Press, New York, 1967). [4] R.P. Messmer, SK. Knudson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev. B13 (1976) 1396. [5] J.C. Slater and K.H. Johnson, Phys. Rev. B5 (1972) 844; K-H. Johnson, in: Advances in quantum chemistry, Vol. 7, ed. P.-O. LEwdin (Academic Press, New York, 1973) p_ 143; J-C. Slater, Quantum theory of molecules and solids, Vol. 4. The self-consistent field for molecules and solids (McGraw-Hill, New York, 1974); K.H. Johnson, in: Annual review of physical chemistry,
1 October 1977
Vol. 26, eds. H. Eyring, C.J. Christensen and H.S. Johnston (Annual Reviews, Palo Alto, 1975) p. 39. [6] K.H. Johnson and A. Balars, to be published. [ 7 ] G.A. Somorjai, in: The physic& basis for heterogeneous catalysis, eds. E. Drauglis and R-1. Jaffee (Plenum Press, New York, 1975) p_ 395. [8] C-Y. Yang and S. Rabii, Phys. Rev. Al2 (1975) 362; C.Y. Yang, Chem. Phvs. Letters 41 (1976) 588 PI D.E. Eastman, J.K. Chshion and A.& Swiiendick, Phys. Rev. Letters 27 (1971) 35. 1101 I.E. Demuth, to be published; private communication. 1111J. Hinze, M.A. Whitehead and H.H. Jaffe, J. Am. Cbem. Sot. 85 (1963) 148. [I21 K.H. Johnson, Intern. J. Quantum Chem. 1 lS, to be published. [131 L-H. Bennett, ed., Electronic density of states. National Bureau of Standards Special Publication 323, Washington, D-C. (1971). 1141 R.S. hiulliken, J. Chem. Phys. 46 (1949) 497. [IS] R.G. Woodward and R. Hoffmann, Accounts Chem. Res. 1 (1968) 17; The conservation of orbital symmetry (Academic Press, New York, 1969). t161 A.B. Kunz, M.P. Guse and R.J. Blint, J. Phys. B8 (1975) L358; R.J. Blint, A.B. Kunz and M.P. Cuse, Chem. Phys. Letters 36 (1975) 19 1; A.B. Kunz, M.P. Guse and R.J. Blint, in: Elcctrocatalysis on non-metallic surfaces, ed. A-D. Franklin, Nationai Bureau of Standards Special Publication 455, Washington, D.C. (1976) p- 53. t171 CF. Melius, Chem. Phys. Letters 39 (1976) 287; CF. Melius, J-W. Moskowitz, A-P. Mortofa, h1.B. BaiUe and M.A. Ratner, Surface Sci. 59 (1976) 279. [ISI D.E. Ellis, H. Adachi and F-W. Averill, Surface Sci. 58 (1976) 497. [I91 L. Pauling, The nature of the chemical bond (Cornell Univ. Press, Ithaca, 1960) p. 80. 1201 W. Hume-Rothery, The structure of metals and alloys (Institute of ,MetaIs, London, 1936). 1211 G.C.A. Schuit and L-L. van Reijen, Advan. Catalysis 10 (1958) 242. 1221 3-G. Fripiat, K.T. Chow, M. Boudart, J-B. Diamond and K.H. Johnson, J. Mol. Catalysis 1 (1975) 59. [23] M. Boudart, private communication_ [24] K. Scho’nhammer, Solid State Commun. 22 (1977) 51.
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