EHMO CALCULATION FOR HYDROGEN ADSORPTION ON NI AND CU ATOM CLUSTERS

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EHMO CALCULATION FOR HYDROGEN

ADSORPTION ON NI AND CU ATOM CLUSTERS

H. Itoh

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 7, Tome 38, Juillet 1977, page C2-23

EHMO CALCULATION FOR HYDROGEN ADSORPTION

ON

NI

AND CU ATOM CLUSTERS

Research Institute for Catalysis, Hokkaido University, Sapporo, 060 Japan

Abstract. - The extended Hiickel molecular orbital theory is applied to adsorption of atomic hydrogen on (Ill), (110) and (100) surfaces of Ni and Cu atom clusters containing up to ten atoms. The edge (or surface) effects play important roles in electronic populations of atoms in clusters and in adsorption energies. The edge atoms of clusters are the prefered sites for the H adatoms. From the orbital symmetry considerations, it is concluded that the edge Ni atoms compose active sites for a catalytic reaction but the edge Cu atoms do not.

1. Introduction.

-

Supported metal catalysts with very small particle sizes are often employed in industry. Several authors [I-31 have reported that the catalytic activity of metals increased as the particle size decreased. The small metallic particles as opposed to the bulk metals have very large surface/volume ratio. Then, the electronic energy levels (or band) in small particles are not quasi- continuous but discrete. The surface effects may play important roles in many physical and chemical properties of small particles. The small particles have many edge atoms, similar to the stepped surfaces on the bulk crystals.

In this paper, small clusters of Ni and Cu metals are selected because of the following reasons. In the periodic table Cu is next to Ni. The crystal structures of both bulk metals are the same (f.c.c.1 and their lattice constants are very similar. Howe- ver, photoemission spectroscopy experiments [4] showed that although 4s 4p bands of both metals are closely similar, the top of the 3d bands of Ni lies c.a. 2 eV above that of Cu. Moreover, it is well known that the catalytic activity of Ni is much higher than that of Cu.

S o far, in order to explain the difference of the catalytic activities of Ni and Cu, Fassaert et al. [5] applied the extended Hiickel molecular orbital (EHMO) theory to adsorption of atomic hydrogen on (1 ll), (110) and (100) surfaces of Ni and Cu clusters. However, they used the parameters of Ni in calculations of Cu because they assumed the rigid band model which is now considered to be incorrect. Later, Blyholder [6] applied the SCF CNDO (complete neglect of differential overlap) theory to adsorption of single H atoms on Ni clusters with various sizes and geometries and determined the equilibrium position of H atoms. However, in his calculation the stability of a diatomic hydride, NiH, does not agree with the experiment [7].

The purposes of the present paper are to apply the E H theory with the correct parameters to adsorption of hydrogen on small Ni and Cu metal clusters and to examine qualitatively the adsorptive and catalytic activities of them.

Although the supports such as silica and alumina are considered to affect the catalytic activities of metal clusters, the effects of them are neglected for simplicity in this paper.

2. Method and Model.

-

The EHMO theory is used. This theory is a simple one electron MO method involving two parameters, the valence state ionization potential (VSIP) and the orbital exponent for the Slater type orbital. The former represents an electronic energy of an atomic orbital and the latter represents an extension of the atomic orbital. The parameters, originally used by Zerner et aI. [8] t o

calculate properties of porphyrin, are used in the present calculation as well as the previous ones [9- 111. The values of the VSIPs of 3d orbitals are 7.9 eV for Ni and 10.6 eV for Cu. The values of the other parameters of both metals are closely similar. The orbital exponents for the 3d orbitals given by them were selected to reproduce the overlap of the very accurate 3 d atomic orbitals given by Watson [I21 and the ligand orbitals.

Although the linear models are most appropriate to examine the surface effects, the results for them were discussed in detail in references [9] and [11] and are briefly explained in 3.1. The model clusters used in this paper are the same as those used by Blyholder [6]. They contain metal atoms up to ten and simulate the (1 1 I), (1 10) and (100) surfaces. For atom coordinates and numbering for model clusters, see figure 1. The nearest neighbour distances in both Ni and Cu clusters are taken as 2.5

A.

The locations of H atoms on the model clusters are taken a s those determined by t h e CNDO calculations [6] because the E H theory is not

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4. 3. 4. 3. 8010,144,-204) '0 '011 25.1 25,-177) 5. l.(O,O,O~ 2*(2 5.0.01 5. 1.10,0,~12.~2 5,0,0) -30 '00 _loo _'0

=.

' 0 6. (I I I ) SURFACE (100) SURFACE 49 3.(2.5,3.5.~r '0 '0 5~(375,1.77,-125) l.lo,o,oo,o, 2. (1 10) SURFACE

FIG. I .

-

Atom coordinates and numbering for metal clusters.

appropriate to determine the equilibrium positions. Three ty&s of adsorption sites are considered: single metal atom-, surface hole- and bridge-sites.

3. Results and Discussion.

-

3.1 ADSORPTION

ON LINEAR CLUSTERS.

-

Since the E H results for

linear clusters were discussed in refreferences [PI and [ll], they are briefly explained in the following. At first the results on the pure metal clusters are described. The 3d-bands of Ni and Cu exist around the negatives of the VSIPs of their 3d orbitals described above, respectively. The 3d band widths of both metals are much narrower than the 4s 4p band widths because the 3d orbitals are much localized than the 4s and 4p ones. The characters of both the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) are 3d-like for Ni and 4s 4p-like for Cu. The energy gap between HOMO and LUMO is much smaller for Ni than for Cu. The 3d bands of Ni do not coexist with the 4s 4p-bands within the common energy region.

There exist oscillations in total-, 3d- and 4s 4p-electronic populations except for the Cu 3d- orbitals which are completely occupied. These oscillations may be considered to be the Friedel oscillations due to the influence of the surface (or end) 1131. The 4s 4p-populations of both metals are similar to each other. As a result of the Friedel oscillation, the surface atoms of the Ni cluster have negative net charge, mainly due to the accumulation of the 3d-electrons on them. The surface atoms of the Cu have positive net charge.

Next the results [lo, 111 on the adsorption of hydrogen are discussed. As a result of an examina- tion of roles of the 3d- and 4s 4p-orbitals of metals in adsorption, it was concluded that the 4s 4p- orbitals of both metals contribute mainly to adsorption bond and the 3d-orbitals of Ni contribute mainly to dissociation of hydrogen molecule and to weakening adatom-adatom interaction.

There exist also oscillations in atomic and molecular adsorption energies due to the influence of the surface (or end). It was concluded that the adsorption energy of atomic hydrogen is largest over the end (surface) atoms and the activation energy barrier is smallest over the surface atoms.

3 . 2 A D S O R P T I O N O N T W O - A N D T H R E E -

DIMENSIONAL CLUSTERS.

-

NOW the E H results on

the two- and three-dimensional clusters described in 2 are discussed. The 3d-band positions of these metal clusters are similar to those of the linear clusters and are consistent with those given by the SCF Xa-SW (scattering wave) method [14]. The electronic populations of the clusters are also similar to those of the linear clusters and are closely similar to the E H results reported by Fassaert et al.

' [5]. The negative net charges (-0.1 e

-

- 0.25 e) on

the edge atoms of the Ni clusters given by the present calculation are contrary to the positive net charges on them given by both t h e SCF Xcr- SW [14] and the CNDO [15]. There is no experimental evidence to determine which method gives the correct net charge.

Next the results on the adsorption energies of atomic hydrogen, which are shown in tables I, I1 and 111, are reported. The experimental binding energies [7] of the diatomic hydrides, NiH and CuH are 3.1 eV and 2.9 eV, respectively. As seen from table I, although the calculated values are much larger than the experimental ones, they are qualitatively consistent with the experiments.

From these tables, it is seen that the adsorption energies are always smaller than the binding energies of the diatomic hydrides. The fact that the adsorption energies depend upon the sizes and the geometries of the model clusters may be due to the surface (or edge) effects. Although the adsorption energies over surface holes are always larger on Ni than on Cu, those over single metal atoms are not always so because of the edge effects. This result is consistent with the results [ll] on the linear clusters which showed that the edge (surface) effects are more remarkable in adsorption over single metal atoms. ~ x ~ e r i m e n t a l adsorption energies of atomic hydrogen are 2.9 eV on the (1 11) and (100) planes and 2.8 eV on the (110) plane of the Ni single crystal surface [l6] and 2.4 eV on the poly- crystalline Cu surface. Then, it seems to be inappropriate to use small clusters in determining adsorption energies on each plane on bulk crystals. Comparison of lines 5 to 7 of table I shows that an adsorption energy on a relatively isolated edge atom for both metals is larger than that on a central metal atom surrounded by several metal atoms, agreeing with the results on the linear clusters. This result is contrary to that given by the CNDO 161 which codld not give a stability to the NiH.

Since the results on adsorption 'isf.atomic hydrogen on two- and three-dimensional clusters are similar to those on the linear clusters, it may be expected that the results on adsorption of molecular hydrogen will be also similar.

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EHMO CALCULATION FOR HYDROGEN ADSORPTION ON NI AND CU ATOM CLUSTERS C2-25

Cluster structure (")

-

TABLE I

Adsorption energies o f atomic hydrogen on (1 11) surface clusters

H atom location ( b )

<;i>

-

over one atom (0, 0, 1.6) (0, 0, 1.55) (0, 0, 1.6) (0, 0, 1.6) (0, 0, 1.6) (2.5, 0, 1.6) (4.1, 0, 0) (0, 1.44, -3.65) (0, 0, 1.6) over hole (1.25, 0.72, 1.0) (0, 1.44, 1.0) (0, 1.44, 1.0) (1.25, 0.72, 1.0) (1.25, 0.72, 0.95) (1.25, 0.72, 1.0) (0, 1.44, 1.0) (0, 0, -3.04) over bridge (1.25, 0, 1.0) (1.25, 0, 1.0)

Adsorption energy (eV)

Ni Cu

(") The numbers in parentheses after each metal (M) cluster refer to the atom numbers from figure 1 in each cluster.

( b ) The x, y, and z coordinates, respectively, for the H atom are given.

TABLE 11

Adsorption energies of atomic hydrogen on (1 10) surface clusters

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Cluster structure

-

TABLE I11

Adsorption energies of atomic hydrogen on (100) surface cluster H atom location

Adsorption energy

Ni Cu

over one atom (0, 0, 1.6) (0, 0, 1-61 (1.25, 1.25-3.37) (2.5, 0, 1.5) over hole (1.25, 1.25, 0.1) (1.25, 1.25, 0) (0, 0, -1.77) over bridge (1.25, 0, 1.1) (1.25, 0, 1.1)

simple catalytic reaction. When HZ and D2 molecules are dissociatively adsorbed on a metal surface, they must surmount an activation energy barrier which if exists. Then, they are dissociated into H- and D-adatoms. While these adatoms migrate on a surface, they collide with each other to form new molecules, HD, and finally desorb as the HD molecules from the surface.

The fact that the activation energy barrier of dissociative adsorption on Ni is lower than that on Cu is simply explained by orbital symmetry considerations as the following [17-191. In the dissociative adsorption process, a flow of electrons (or an electron delocalization) from the HOMO of the one molecule to the LUMO of the other should take place. The electron delocalization between the HOMO and the LUMO cannot occur unless these orbitals meet the symmetry requirement that they have a net overlap. The directional 3d-character of both the LUMO and the HOMO of Ni clusters is more suitable for positive overlap with those of the HZ molecule than the less directional 4s- and 4p-characters of those of Cu. Then, the electron delocalization and the dissociative adsorption are much easier for Ni than for Cu. This conclusion is supported by the direct EH calculations [lo, 11, 201.

Finally, the catalytic activity of small particles is

discussed. Small particles have many edge atoms. The 3d-populations on the edge atoms of Ni clusters are increased due to the edge effects. This 'implies that the 3d-orbitals at the edge Ni atoms are more suitable for positive overlap with the adsorba- tes, HZ or Dz, than those at the other Ni atoms because of spatially extended 3d-electrons due to their coulomb repulsions at the edge atoms. In fact, the calculations [ll] have shown that the activation energy barrier is lowest at the edge atoms. Moreo- ver, the edge atoms are the preffered sites for the adatoms. Then, the edge Ni atoms compose active sites for the catalytic reaction. This is one of the reasons why the size dependent catalytic activities are present in some transition metal catalysts. However, an enhanced activity of small Cu catalysts may not be expected to occur because of energetical unfavor of Cu 3d-orbitals at least for the HZ-DZ exchange reaction.

In conclusion the edge atoms of Ni fine particles compose active sites for catalysis. The catalytic activity of Ni increases as the particle size decreases because the number of the edge atoms increase as the particle size decreases. For Cu fine particle the conclusion on the Ni does not hold.

The present calculations were performed on the FACOM 230-75 computer at Hokkaido University Computing Center.

References

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EHMO CALCULATION FOR HYDROGEN ADSORPTION ON NI AND CU ATOM CLUSTERS C2-27

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