Analysis by the recursion method of the electronic transfers involved in the dihydrogen chemisorption on a platinum cluster

465

Surface Science 205 (1988) 465-491 North-Holland, Amsterdam

ANALYSIS BY THE RECURSION METHOD OF THE ELECTRONIC TRANSFERS INVOLVED IN THE DIHYDROGEN CHEMISORPTION ON A PLATINUM CLUSTER Daniel SIMON and Bernard BIGOT Institut de Recherches SW la Catalyse *, 2 Avenue Albert Einstein, 69626 Villeurbanne France and Laboratoire de Chimie Theorique *, Ecole Normale Supdrieure de Lyon, 46 AllPe d’ltalie, 69364 Lyon Cedex 07, France

Cedex,

Received 10 March 1988; accepted for publication 1 July 1988

As a first example of a possible analysis of elementary steps of a heterogeneous catalytic reaction, the electronic transfers and the associated energy costs involved in the dihydrogen adsorption on various sites of a Pt,, cluster have been analysed in terms of the changes occurring in the local densities of states computed by the recursion method. The Hamiltonian defining the various metal-metal, hydrogen-hydrogen, and metal-hydrogen interactions is of extendedHtickel-type. This method gives local information on the behaviour of the surface orbitals along the reaction path. In particular, it shows the role of a late electron transfer from d-type to s or p-type metal orbitals, and it exhibits the role of electronic reservoir of the platinum atoms not directly bound to the adsorbate, in the electron transfer. Furthermore, it shows that the height of the activation barrier and the energy difference of the whole process are mainly related to the energy positions of the local HOMO and LUMO contributions of the metal atoms in direct interaction.

1. Introduction The hydrogen chemisorption on transition metal clusters or metallic surfaces is a basic process which gives rise to many experimental investigations [1,2]. In order to have a molecular description of these adsorption processes, essential to the understanding of catalytic phenomena, different theoretical approaches have been considered [3]. The theoretical understanding of the interactions between H, and the metallic surface involves, first the description of the geometrical, electronic and energetical properties of the naked surface or cluster [4] and, then, the modifications induced by the interaction [5]. Most of these theoretical studies * These laboratories are part (L.P. 5401) of CNRS (France).

0039-6028/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

466

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

proceed via global calculations, e.g. tight-binding methods for infinite surfaces or molecular orbitals determination for aggregates, followed by a projection on the local molecular system under study. In a previous paper [6] we reported the use of the recursion method [7] for the study of clusters. This technique of determination of the electronic properties of clusters has the advantage of allowing us to isolate the few atoms of main concern in the catalytic process without neglecting the rest of the system which is treated as a perturbation. This perturbation is not necessarily weak. This technique allows us to get local information without the need of global calculations on the whole system. We deduced for peculiar atoms of platinum clusters the local electronic structure expressed in terms of local densities of states associated with their atomic orbitals interacting in an extended-Htickel Hamiltonian scheme. As it is well documented, this scheme is adapted to give fruitful qualitative information on the electronic change occurring along a reaction path without pretending to generate quantitative detailed energetical or structural conclusions. In the present paper, as a model study to test its capabilities of analyzing the reaction path on a metal surface, the recursion method has been applied for the local description of H, chemisorption on peculiar sites of a Pt,, cluster. The evolutions of the electronic properties associated with Hz and Pt adsorption site orbitals allow us to specify the hydrogenation mechanism for a given reaction path. Interaction diagrams summarizing general principles for electron transfer have been drawn. Then, quantitative studies of electron transfer and energy behaviour along the reaction coordinate are discussed.

2. Calculations by using the recursion method The interactions between platinum and hydrogen atoms are described in an extended-Htickel formalism [8]. The parameters used in these calculations are given in table 1. The off-diagonal elements Hij are calculated from the Hii’s by using the modified Wolfsberg-Helmholtz formula [9]. The geometries of interaction between H, and the platinum cluster are described in the following section. During the approach of H, the Pt-Pt distances are maintained at a Table 1 Parameters used for the extended-Hiickel overlap and Hamiltonian matrices Orbital H Pt

4, WI

expl

IS

-

13.60

1.300

5d 6s 6~

- 12.59 - 10.00 - 5.415

6.013 2.554 2.554

exp2

c1

c2

2.696

0.6334

0.5513

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

467

fixed value of 2.77 A. This distance is similar to that found in the metal bulk

WI.

The treatment of the Hamiltonian and overlap matrices has been described in a previous paper [6]. The main calculation steps are: (i) a Schmidt orthogonalization of the atomic orbitals basis set, starting with a function 1x0); (ii) a recursive computation [7] generating a sequence of a, and bi coefficients associated with the initial function 1x0): these coefficients are the elements of a tridiagonal Hamiltonian matrix; and (iii) the calculation of the density of states associated with 1x0) by using the continuous fraction method [7]. This local density of states (DOS) represents the participation of 1x0) to a molecular orbital I#) at energy E: n(c; x0) = 1(x,-, ] 4) ] 2. So n(~; x0) is a projection on I x0) of the electronic spectrum of the system under study. The local DOS can be cumulated for orthogonal functions, in order to generate global DOS. The cumulation of the DOS for non-orthogonal orbitals would give an overestimated global density of state. A local DOS imposes a local point of view. In addition, the recursion calculation allows approximations yielding a broadening of the peaks. Therefore a local DOS appears as a continuous spectrum; this is consistent with the fact that platinum clusters have closely spaced energy levels yielding a smoothed band structure. The computation parameters used in the recursion method are the same as in our previous study [6].

3. Hydrogenation

me&a&m

Two hydrogenation sites have been considered. We describe here the approach of a H, molecule on particular platinum atoms belonging to a Pt,, cluster consisting of the packing of two CPTL layers with seven and six atoms respectively (see fig. 1). On this cluster, atoms 1 and 13 have been choosen as examples of hydrogenation sites: they have different coordination numbers (9 for atom 1 and 4 for atom 13), and are in different geometrical positions in Pt,,. Atom 1 may be considered as a surface atom and will be noted S-atom while atom 13 is rather an adatom, noted A-atom. In a first study [6] the features of the local electronic properties of the atomic orbitals of these atoms were analysed: these characteristics can be resumed by comparing the cumulated local densities of states of the nine atomic orbitals for the S-atom and A-atom (fig. 2). First it is observed that the total population, measured by the integrated density of states (IDOS) at the Fermi level, is different for the S-atom (64%) and A-atom (60%), the former atom being more negatively charged. Secondly we see that the population of each atom extends between -14.04 and -11.67 eV, but the energetical spectrum, illustrated by the DOS curves, differs in the S-atom and A-atom cases. Three zones can be distinguished in the S-atom spectrum: the - 14.04

468

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

Fig. 1. Structure of the Pt,, cluster with atom labeling. Atom 1 and 13 have been labeled S and A respectively. The local z-axis orientation is given for the S- and A-atoms. The upper view is a perspective drawing of the position of each Pt atom. The relations between the nearest neighbours are indicated by full or broken lines.

to - 13.6 eV zone in which the IDOS increases by 23%, a central zone (from -13.6 to -12.0 eV) in which it shows a 24% increase and the highest occupied molecular orbitals (HOMO) participations (between - 12.0 and - 11.67 eV) with an increase of 17% for the S-atom. The A-atom spectrum is different: the IDOS increases by 58, 49% and 6% respectively for the same energy zones as in the S-atom DOS. The contributions of its atomic orbitak are found mainly in the middle of the metallic band. Finally a more precise analysis has been made [6] that exhibits the electron donor or acceptor properties of these atoms measured by the HOMO or LUMO contributions respectively, for each atomic orbital. This contribution is given by the IDOS increase in the atomic orbital (a 100% value would correspond to 2 electrons). The main contributions are the following (the z-axis used in the S-atom or A-atom have a local orientation as indicated in fig. 1): concerning the HOMO levels, the S-atom has participations at - 11.67 eV through 5d,z_yZ and 5d,, (26% for each one), and at -11.84 eV due to 5d,2, 5d,,, 5d,, and 5d,, (27%, 9%, 32%, and 32%, respectively), while the A-atom shows peaks only at 5d,, and 5d,, (12.58, 1496, and 14%, respectively). -11.84 eV in 5d,,, Concerning the LUMO peaks, the S-atom has participations at - 11.57 eV due to 6p, and 6p, (6% each) and at -10.34 eV by mean of 6s and 6p, (8%

D. Simon, B. Bigot / Loco1 descri$tion of H2 chemisorption on a Pt cluster

469

A /n

II

imu n

”

DOS and

100s

.I

(X1

Fig. 2. Cumulated local densities of states (DOS) of the nine atomic orbitals for the S- and A-atoms in the Pt,, cluster. The integrated curve (IDOS) is also drawn. Arbitrary units are used for the DOS and a 100% value for the IDOS corresponds to 18 electrons for the whole atom. The broken line indicates the Fermi level.

and 78, respectively), while the A-atom shows only one contribution (12%) in the 6s spectrum at - 11.57 eV. So, acceptor and donor participations are more numerous in the S-atom than in the A-atom. Furthermore the topology of these HOMO or LUMO contributing atomic orbitals are more various in the S-atom than in the A-atom: this allows us to predict that during the approach of an adsorbate, the S-atom has S-type (5d,2_,,2, 5d,,), a-type (Sd,,, 5d,,) and u-type (5dZ2) donor properties and also q-type (6p,, 6p,) and u-type (6s, 6p,) acceptor properties, while the A-atom is available, as a donor, only in S-type (5d,,) or g-type (5d,,, 5d,) ~teractions and, as an acceptor, only in a u-type interaction (6s). The geometrical features of the H, molecular adsorption are depicted in fig. 3. The approaches of the S-atom and A-atom will be referred to as S-approach and A-approach respectively. The orientation of H, with respect to the Pt atoms has been choosen as a “side” one; as it has been mentioned [lla], this corresponds to a better overlapping between the orbitals of the cluster and H,. First, we approach H, in the local xz-plane without dissociation (distance fixed at 0:7415 A between the two H atoms), then, as the Pt-H distance becomes 1.6 A, a dissociation is achieved, by keeping the Pt-H distance fixed, till a bridged or face-centered position has been obtained for the H atoms. In the final geometry of S-approach, the two H atoms bridge S

470

D. Simon, B. Bigot / Local description of H, chemisorption on a Pt cluster Hp opprooching

&

S-otom

opproochi

ng

A-otom co

Pt-H-3.01 H-H- .74 i co

Pt-H-1.6 1 H-H- .74 i

Pt-H-1.6 x H-H-2.26 i

Pt-H-1.6 i H-H-2.77 x bridged face-centered

Pt-H-l.6 i H-H-l.64 i Fig. 3. Different views of the approach of Hz on the S- and A-atom. The geometries of Hz versus S- or A-atom are given by the Pt-H distance (Pt is S or A) and the H-H separation. The different views can be also labeled with the reaction coordinate 4, which is the algebraic abscissa of the center of H-H on the local z-axis: 4 equals 3,1.56,1.1,0.8 and - 1.3 A for the views from the top to the bottom of the figure in both S- and A-approaches. In the A-approach we illustrate a face-centered final H, position, but a final bridged position has been also used (see text).

to Pt number 2 and S to Pt number 5 respectively (see fig. 1 for the labeling of the Pt atoms). In the final geometry of A-approach, the two H atoms are face-centered in the triangle: A/Pt number 7/Pt number 11, and in the triangle: A/Pt number 9/Pt number 12, respectively. Another final geometry of A-approach has been investigated, in which the two H atoms bridge A to Pt number 11, and A to Pt number 12. The reaction coordinate 5 is taken as the distance between the Pt site and the middle of the H, bond. This hydrogenation path corresponds to the succession of a molecular adsorption step and a dissociative step. This second stage has been reported as a reductive step (Hz being dissociated into two H- ions) [12] and we study, in this paper, the local electronic characteristics of these two steps of adsorption, for this example of reaction path.

D. Simon, B. Bigot / Local description of H, chemisorption

on a Pt cluster

471

The outlines of the interaction between the local orbitals may be viewed as follows. H, has an occupied IJ; (at -17.56 eV) and an unoccupied u,’ (at + 4.175 eV) orbital. The Pt atomic orbitals contribute to an energy band lying from -14.04 to - 11.67 eV (the Fermi level) and to vacant orbitals above - 11.67 eV (fig. 2). The mean energy of these orbitals is about - 13 eV [6]. For the description of the interaction, a local orientation of the axis system is choosen so that the approach of H, is done along the z-axis; it allows the classification of the atomic orbitals of Pt atoms according to their symmetry properties: so 17,’ interacts with Z:(6s), Z:(6p,), Z>(5dZ2) and a ,2_y2(5dX2_yz) of the platinum atom adsorption site, and u,’ with II,(6p,) and II,,(5d,,) of the Pt site. In the molecular adsorption step, a stabilization may be obtained by interaction between u,’ and the Pt,, vacant levels having a contribution from atomic orbitals of the Pt site. uz has a high energy; so, little interaction is expected with occupied levels of Pt,,. In the dissociative step, the us+ energy increases to -13.86 eV and u,’ is much lowered, up to - 13.33 eV in the bridged position. Nevertheless, their energy remains different from the hydrogen atom one, so we did not consider that we have two independent H atoms. In this step, UC yet interacts with vacant orbitals of Pt,,, but u,’ should be populated by interaction with the Pt site atomic orbitals contributing to the occupied levels. The net population of the H, molecule (us+ depopulation and u,’ filling up) is actually increased, corresponding to a reduction of H,. During the hydrogenation, the Fermi level position, governed by the filling of the energy levels of the whole Pt,, cluster, is not significantly affected by the local interaction with H,. Within this scheme of the hydrogenation mechanism, the questions that the present study of the local densities of states could answer, are the following: (1) What electronic transfers occur during the molecular step and the dissociative step? (2) What is the energetic contribution of these transfers along the reaction path? (3) Is the adsorption mechanism connected to local properties of the naked cluster, and what are the local characteristics of the cluster energy levels that interact with IJ~ or u,‘? (4) What is the space range of the interaction?

4. Description of the evolution of the local densities of states 4.1. H, orbitals

Fig. 4 shows the evolution of the local density of states associated with u,’ and u,’ for different interaction geometries. On these graphs, an arrow indicates the position of the energy of ui or u,’ without interaction with Pt13.

412

D. Simon, B. Bigot / Local description of H, chemisorption on a Pt cluster

I

(___

gu+ (11.4

~

“_I

,I-i

u3+ _lo. t=1.4 A _r i _._______________~_~-_:_-____j_______

%I

fJ

i -15 <---

kl

U”+

09+

6 _1o t-1.1

f’

A

t-1.1

_ _____________f_

A

,__________

-13 <---

::

,y uu+ F-.sa

w9+ t= .8 A

-10

J!

<-I-------------

i II

-------------__

r’ .d ‘--i

a~~o I

b DOS Fig. 4. Local densities of states (DOS) orbitals of H, for different geometries a 2 electron occupancy. The broken indicates the

____ t+/

100s

10

(%I

and integrated densities of states (IDOS) of the 0,’ and 0: of approach on the S-atom. A 100% IDOS corresponds to line indicates the Fermi level. On each curve, an arrow 0,’ or 0,’ energy level in free H,.

A broken line gives the Fermi level, at - 11.67 eV. It is assumed constant as long as the adsorption occurs (the validity of this point has been tested). For u,’ a main peak emerges in the local densities of states curves, corresponding to an integrated density of states of about 90-95%. In all cases, this peak is lower than the energy level without interaction, indicating the formation of a bond. The contribution of u,’ to the energy levels of the metallic band (between - 14 and - 11.5 ev) is very low, and participations to unoccupied molecular orbitals appear, mainly during the dissociation step. This vacant character is consistent with the decrease of the total population at the Fermi level, but actually contributes little (6% maximum for the LUMO). For u,‘, approach is two phases can be clearly pointed out. First, the molecular

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

473

characterized by a progressive, but slow increase of participation (about 10%) to the energy levels of the metallic band; some vacant character is also present at -6 to - 7 eV, while its energy without interaction is much higher (at +4.175 ev). Then, the dissociative approach shows the appearance of a main peak, whose contribution raises up from 50% to 80%. This structure emerges as soon as the u,’ position without interaction with Pt,, reaches the - 5 to - 10 eV zone, where H, has a bond length of l-l.5 A: the interaction is important, allowing a lowering of this energy level. The participation to the metallic band diminishes (10% to 3%) and a set of 3 main vacant orbitals appears (the total contribution of u,’ to them is 16%). In the dissociative geometry, the general features of the IJ,’ density of states become comparable to those of u,‘. The two adsorption steps are clearly illustrated. The total population of H,, defined from the local density of states of up’ and u,’ has an evolution (table 2) consistent with a molecular step, followed by a reductive dissociation step. The A-approach has analogous features, except that the lowering of the metallic band contribution of u,’ occurs only when H, approaches the final face-centered or bridged positions. It can be noted that the participation occurs as soon as the approach of H, begins, even without dissociation, though its energy level in free H, remains high. So, a dissociating process is engaged by partially filling up an antibonding orbital, and we should try to understand whether it plays an activating role in the energetics of the reaction.

Table 2 Total H, population issued from local densities of state calculations for different geometries of approach H-H distance (A)

5 a) (A)

Population (in electrons) for S-approach

Population (in electrons) for A-approach

0.14 0.74 0.74 0.74 0.74 1.6 2.26 2.77 3.2 2.77 1.85 2.19

co + 2.47 + 1.97 + 1.76 + 1.56 + 1.39 +1.13 + 0.80 0.0 - 0.80 - 1.31 - 1.13

2 2.00 2.02 2.06 2.14 3.00 3.27 3.33

2 2.00 2.02 2.05 2.13 3.03 3.35 3.42 3.52 3.28 3.25 3.30

‘) b, ‘) d, =)

b,

”

d’ =)

6 is the reaction coordinate defined as the abscissa of the center of H, on the local z-axis. Molecular adsorption. Bridged for atom 1. Face-centered. Bridged.

414

D. Simon, B. Bigot / Local description of H, chemisorption

on a Pt cluster

4.2. Orbitals of the Pt atom adrrorption site In order to illustrate the features of the evolution of the local densities of states associated with atomic orbitals of the platinum atom under direct interaction, the contributions of the Z:, 23 and II,, atomic orbitals are represented, as examples, in fig. 5, for different geometries of S-approach. In the 2: orbital curves, the peak at low energy corresponds to a bonding with us+ of H,, since a 09’ contribution appears at the same energy for the same geometry. There is a decreasing participation to the molecular orbitals of the metallic band, and this band is depopulated and weakly pushed up: it is quite clear for the level initially at - 14.04 eV. The contribution to the lower vacant molecular orbital decreases in the molecular adsorption step and then a

DOS and

100s

(Xl

Fig. 5. Local densities of states (DOS) and integrated densities of and IIxz orbitals of the S-atom for H, approaching the S-atom at corresponds to the naked cluster, [ = 1.56 A to the top position of final position, and 6 = 1.1 A is an intermediate geometry (see fig. 3). an occupancy of 2 electrons. The broken line indicates

state (IDOS) of the Z:, 2s different distances: t infinite H,, 5 = 0.8 A to the bridged A 100% IDOS corresponds to the Fermi level.

D. Simon, B. Bigot / Local description of H, chemisorption

on a Pt cluster

415

new vacant level appears at - 11.5 to - 11.2 eV, to which the contribution of 2: is about 5%. For the A-approach, the evolution is similar, except for the emergence of a large participation (29%) to an unoccupied level at -7.65 eV in the face-centered geometry. Concerning the X,+2comportment, the interaction with H, seems to be the most important at the molecular adsorption step, since at this geometry the low energy peak is higher and the perturbation is the largest. This is consistent with the directional topology of the X,+2orbital. The more interesting deformations appear in the metallic band: while the - 14 to -13 eV Z: contribution seems to be little changed (though, as in the 2: case, a low increase in energy is accompanied by a low decrease in population), the contribution around the Fermi level is quite different: the HOMO peaks disappear and a new LUMO contribution, with a 33% participation, emerges at - 11.45 eV. Around - 10 eV the participation to a vacant orbital increases as the corresponding peak becomes higher in energy. It can be also noticed that the two HOMO levels, appearing in the S-atom X,+2density of states for the naked cluster, have no contribution from the other S-atom orbitals of the same symmetry (except a 2% participation of 2: at -11.84 eV [6]). In the molecular adsorption situation, the - 11.45 eV has, as far as the S-atom is concerned, a main participation from Z,‘2 (33%) and only 3% for Z:. This allows us to associate this local orbital under interaction with H, to a “pure d” orbital, passing through the Fermi level during the molecular adsorption. It is interesting to compare that point with the results obtained for the A-approach. Ef has, for the A-atom in the naked Pt,, cluster, its main contributions between - 13 and - 12.3 eV, with a HOMO peak of only 5% at - 12.08 eV. In the molecular adsorption of H, on the A-atom, the X,+2curve is little modified: the main contributions in the metallic band are a little pushed up in energy and, including the low energy peak (Pt-H, bond), the total population represents about 90%. Nevertheless a vacant orbital appears at - 11.4 eV with a 7% contribution. The evolution of the A,z_~z curves shows the same type of comportment as Z> but complementary in the sense that, for symmetry reasons, the maximum interaction occurs for the dissociative step. In the ZT densities of states, an important contribution to the lowest energy peak is observed, mainly for the molecular adsorption geometry (a 22% contribution at - 17.9 eV in this case). At the same time the participation of Z: to the metallic band increases. The main contribution to the unoccupied orbitals, which was 14% at - 10.34 eV in the naked cluster, disappears, but a low participation, as mentioned above, appears at - 11.45 eV. This kind of comportment is observed in both cases of S- and A-atom adsorption sites, except that for the final face-centered or bridged positions in the A-approach, the situation is more simple: a 20% contribution to the low energy peak, no metallic band participation, and an important contribution (43%) at -7.65 eV. So the Z: has a local density of states evolution comparable to that of Z:.

416

D. Simon, B. Bigot / Local description of H2 chemisorption

on a Pt cluster

The IIx. densities of states evolution (fig. 5) is characterized by, first, the appearance of a bond with u,’ (peak at the lowest energy), then the decrease of the contribution to the metallic band energy levels, and finally the emergence of a vacant level at - 11 to - 10 eV. Contrary to the case of X,+2 the metallic band participation is globaly reduced and no correlation seems obvious between the appearance of the new vacant level and the disappearance of a particular occupied level. This observation is available in both S-atom or A-atom site approaches. Finally, in the III, curves the main features are the bond with u,’ and the emergence of a vacant orbital participation at - 11 to - 10 eV. In the case of S-approach, the low energy peak is larger while the LUMO peak is lower than the corresponding peaks in the A-approach. Notice also the disappearance of the LUMO peak present, on the naked Pt,, cluster, at -11.57 eV in the S-atom. 4.3. Adjacent atoms Concerning the platinum atom different from the adsorption site, some results are illustrated in fig. 6. The densities of states, in a dissociative step geometry during the approach on the S-atom site, of the 2: orbital of atoms 2 and 3 (see fig. 1) are compared to Zz contributions of an equivalent atom in the naked cluster. These atoms have been chosen because atom 2 is in direct interaction with one hydrogen atom and atom 3 is considered as being at a greater distance from the interaction site. The main modification observed is the contribution to the bonds with u,’ and u,‘: the IDOS has an increase of 15% in atom 2 and of 3% only in atom 3. So, this contribution is larger for n&ad

cluster

H2 on

S-atom

H2 on S-atom

W

n

Y

atom 2: Ez

n

atom 2: Ez

100’

DOS and

n

100” 100s

atom 3: 1: 100

(Xl

Fig. 6. Z: local densities of states (DOS) and integrated densities yf states (IDOS) of atom 2, and atom 3, as H, approaches the S-atom (reaction coordinate 5 = 1.1 A), compared with ZZz of atom 2 in the naked cluster (atoms 2 and 3 are equivalent in the naked cluster). A 100% IDOS corresponds to an occupancy of 2 electrons. The broken line indicates the Fermi level.

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

411

atom 2. Concerning the total filling, it has a 40% value in the naked cluster, while under interaction, the Zz orbitals of atoms 2 and 3 have a 48% and 40% total population, respectively (including the -15.4 and -16.2 eV contributions). Nevertheless the main features of the density of states remain: by looking at the energy evolution of the IDOS we see that the aspect of the metallic band structure is preserved and that the participation to the unocuppied orbitals is little changed. This is mainly true for atom 3 and as the distance from the interaction site grows (e.g. for atoms 9, 10 . . .) these remarks become more and more justified. By looking at the energy, of the peak it is obvious that many of them have changed a little in position (e.g. the head of the band at - 14.04 eV is found at - 13.9 eV under interaction). One can conclude that the interaction is little perturbative for atoms considered as far from the adsorption site. It is characterized by a small variation in the energetic positions and a low changing in the total population. Nevertheless these small effects may have a significative influence on the adsorption energetic profile. 4.4. Interaction schemes The main features that we have considered and discussed in the preceding qualitative study of the local densities of states concern: (i) the bond, established between the atomic orbitals of the Pt site and up’ or u,‘, characterized by a low energy peak; (ii) the global evolution of the metallic band; (iii) the modifications of the levels around the Fermi energy. In order to emphasize these features we have drawn interaction schemes for selected geometries associated with molecular and dissociative adsorption (fig. 7). As it will be discussed in section 6, these geometries correspond to minima in the energetic profile. In these schemes the vertical axis represents the energy and the horizontal peaks or bands have a height corresponding to their total contribution (the convention used for a band is that the height, not the area, represents its whole contribution). From these schemes some general behaviours can be noticed, concerning each type of orbital. For a s or a d-type atomic orbital of the Pt adsorption site, a decrease in the population of the metallic band (between - 14 eV and the Fermi level) is observed. This decrease is achieved either without perceptible energetical shift, or due to HOMO levels passing through the Fermi level. For a p-type atomic orbital, an increase in the metallic band population is generally observed, without perceptible energetical shifting. In some cases (as the final face-centered geometry in the A-approach) the metallic band contribution of p-type atomic orbitals disappears. The bond established with the UC orbital is always characterized by an energy stabilization. The interaction with CJ,’ involves mainly Z,+ and Z: in the case of molecular adsorption. During the dissociation process, the interaction of u,’ with 2: becomes

418

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

S -

approach

A - approach

-10 *Ef

4

-I5

z A! 0 E

-18

-I5

-18

-18

=, 4

2 %3

09

i

2 “la+“2

pt13 + “2

“2

“2

(top)

(top)

11 -10

..Ef

-I5

-I5

18

03

%I

-18 pt13

-

"2 h3+

b)

"2

pt13

-

"2 %3+

"2

(f.-

c.)

Fig. 7. Interaction diagrams summarizing the properties of the local densities of states of the principal orbitals interacting at the molecular adsorption step (Pt-H =1.6 A; H-H = 0.74 & 5 = 1.56 A) and at dissociative steps (bridged, noted br., or face centered, noted f.-c.). In each figure, the left part depicts the local DOS of atomic orbitals of Pt,,, the right part gives the energy position of the free H, orbitals; the center of each interaction diagram represents the local DOS of the orbitals in the Pt,, + H, system. The broken lines indicate the Fermi level.

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

479

more important, and the energy level is hardly higher than in the case of molecular adsorption, despite of the lengthening of the H, bond. Concerning the interaction of II, and III,, with u,’ both atomic orbitals participate, and the resulting level has an energy of - 15 to - 15.5 eV. So, the transfer of two electrons coming from the cluster metallic band should be energetically favorable.

5. Quantitative interpretation

5.1. Analysis of occupancy and energy behauiour Now we study in a systematic quantitative way, the observations issued from the preceding section by analysing and interpreting, for each orbital, in a first step its total occupancy and energy evolutions, then, in a second step the contributions of the HOMO and LUMO along the reaction coordinate. The occupancy N is the total filling of the orbital up to the Fermi level eF: N=

I”

n(e; x0) de.

The energy associated, E, is the sum of the energies of the occupied levels, modulated by the local contribution: E=

[”

n(c; xO)e de.

J-03

E represents the energy contribution of the atomic orbitals to the total energy of the system. The mean energy, (E) = E/N, has an evolution related to the stabilization of the orbital 1x0) [6]. The evolutions of occupancy of UC and u,’ are presented in fig. 8. The features arf analogous for both S- and A-approaches. At first (from 5 infinite to .$ = 1.6 A) al remains nearly full and u,’ nearly empty. This constitutes the molecular adsorption step, H, having a population of about 2 electrons (table 2). Then, from 6 = 1.5 A to the final position, uz gets a population comparable to that of ul (about 85%). This is the reductive step in which H, is dissociated and has a 3.3 electron population (table 2). It can be represented by two hydride Ha- ions with a partial charge 6 = 0.65 e-. We illustrate the energetical behaviour of u,’ and u,’ by depicting their mean energy evolution in fig. 8. up’ and u,’ present always a stabilization compared to their energy in free H,. In the molecular step this stabilization is weak for u,’ and large for u,‘. But in the u,’ case it concerns a low population due to weak contributions to levels below the Fermi energy. So, it has a little weight in the total energy of the system. In the reductive step the u,’ mean energy increases while the u,’ mean energy decreases; both behaviours are due

480

D. Simon, B. Bigot / Local description of H, chemisorption

on a Pt cluster

100 7,‘;

N(Xl-

-A-approach ---S-approach-

<&’

(eV)

-15

-10/ 4

I

-E (A) ’

1

1

I

I

0

-1

Fig. 8. Occupancy N (upper figure) and mean energy (c) (lower figure) of the up’ and u,’ H, orbitals along the reaction coordinate & A 100% value of N corresponds to an occupancy of 2 electrons.

to the lengthening of the H-H

bond. But the stabilization compared to the u,’ and u,’ energies in free Hz is large and similar for up’ and uz (about 2.5 eV). The maximum stabilizations are obtained in the final positions S- and A-approaches. In fig. 9 the variation of the occupancy of the Pt atomic orbitals allows us to distinguish the evolution of s, p- and d-type orbitals, in both cases of S- and A-approach. Initially, the d-type orbitals are nearly full, the s orbitals are about half-full and the p-type orbitals are nearly empty. During the molecular adsorption (till [ = 1.6 A), the d-type orbital populations vary little except for the Z,+Zorbital in the S-approach. This orbital loses 50% of its electrons. In the same step the 2: orbitals increase their population a little (they reach a 55% to 60% occupancy at 5 = 1.6 A) and, concerning the p-type orbitals, only Z: is affected and shows an incre?se from a 10% to a 45% occupancy. In the dissociative step (from [ = 1.5 A to the final positions), III,, loses 25% of its electrons in the S-approach and 35% in the A-approach, while Z,‘2 and AX2_y~ show a variation of the order of 10%. The minimum of occupancy of II,, is

D. Simon, B. Bigot / Local description of Hz chemisorption on a Pt cluster

OLCS-appropch1 ’

o’f

2

*

1

0

481

-1

Fig. 9. Occupancy N for atomic orbitals of the S- and A-atoms along the reaction coordinate 6 describing H, approaching S and A, respectively. A 100% value of N corresponds to an occupancy of 2 electrons.

obtained for e = l-l.25 A, i.e. when the H atoms are in the direction of the lobes of III,, (maximum overlapping between u,’ and II,,). In this dissociate step the 2: orbitals continue to increase their occupancy to reach a 70% value and they are emptied a little at the final positions; 2: decreases to its initial occupancy and II, shows a large increase up to maximum occupancies of 50% and 65% in the S- and A-approach, respectively. The huge transfer of electrons from X,+2 (in the S-approach) and II,, (in the S- and A-approaches) can be associated, as illustrated by the interaction diagrams (fig. 7), with a HOMO contribution passing through the Fermi level and emerging as a LUMO contribution (at -11.5 eV in 2,: for the molecular adsorption step of S-approach, or at -10 to -10.5 eV in II,, for both approaches). The 2: population curves can be associated with a combination of a decrease in the metallic band and the appearance of the bond with IS,‘. The p-type orbitals, Z: and II,, behave as if they receive the electrons given by the d-type orbitals, since their occupancy increases as that of Z,+Zand IIx. decreases. In fig. 10, the behaviour of the mean energy (E) allows us to point out for each orbital the occurence of a stabilization compared to the mean energy without interaction (tO infinite). In the S-approach, Z: and Z$ show a minimum for 5 = 1.6 A (molecular adsorption step), the Z: and II, mean energy curves decrease regularly till the final dissociative position and II,, and A,z_~z have a weak minimum in the dissociative phase (for 5 = 1.1 A and

D. Simon, B. Bigot / Local description of H, chemisorption on a Pt cluster

482


CeV) -15

A-approach

Fig. 10. Mean energy(6) for atomic orbitals of the S- and A-atoms along the reaction coordinate 6 describing H, approaching S and A, respectively. The value for .$= + cc is the mean energy without interaction with H,.

5 = 0.8 A respectively). In the A-approach Z,i has two minima, one for t = 1.6 A, the other for the final position; Z: and n, show again a decrease till the final position. But now, contrary to the S-approach case,0 Z> has a weak variation and n,, presents a marked minimum for 6 = 1.1 A. By comparison with the total population curves (fig. 9) we see that the minima in (c) are obtained when the population curves present their minima or maxima, and, moreover, that the depth of the mean energy minima is correlated with the size of the corresponding population extremum: for instance compare Z,i2 at 5 = 1.6 A in the S-approach (large population and large mean energy minima), to Z,+Zin the A-approach (weak population and weak mean energy minima). So, we can conclude that the orbitals submitted to a large transfer of electrons show the best s~b~tion. What are the consequences of these stabilizing transfers of electrons on the contribution of the corresponding orbitals to the total adsorption energy? In order to discuss that point, let us study the contribution E of each orbital. E = N(z), and (e) always decreases along the reaction path. What does E? Is E controlled by N or by (E) evolution? The energy evolution of each atomic orbital is depicted in fig. 11. These curves characterize a local ~n~bution to the total adsorption energy. The global evolution of the adsorption energy, taking into account the modifications induced in the whole cluster, will be evaluated in section 6. If we compare, for each orbital, its E evolution to its N evolution (fig. 9), we see that they are in good agreement. For instance, let us look at Z,+Zin the S-approach, the minimum in its N curve (E = 1.6 A) corresponds to a maximum of the same order of magnitude in its E carve; in the A-approach the weak energy variations correspond to weak population variations. Our conclusion is that the electron transfer drives the energy contribution of each orbital. The importance emphasized here of the electronic transfers is related to the existence of a Fermi level, fixed at a constant energy value as it will be

D. Simon, B. Bigot / Local description of HI chemisorption on a Pt cluster

me 2

I

0

483

-1

Fig. 11. Energy E of the electrons filling each atomic orbital of the S- or A-atoms, up to the Fermi level. The reaction coordinate & describes S- or A-approaches.

explained in section 6. As soon as an atomic orbital has a contribution which passes through the Fermi level, it is filled or emptied. For example we have already shown that, in d-type orbitals, large population loss occurs, due to HOMO levels passing through the Fermi barrier. Can we observe this electron transfer in the behaviour of the participation of the atomic orbitals to the frontier orbitals, along the reaction path? We present, in fig. 12, histograms of the evolution of HOMO’s and LUMO’s contributions of the local densities of states associated with selected atomic orbitals of the Pt sites. The figures depict their contribution, in a frontier zone below and above the Fermi level (between - 12.5 and - 10.0 eV). These contributions change in weight and in energy position during the reaction, from 5 infinite to t = 0.8 A (bridged Hz) in the S-approach and 5 = - 1.1 A (face-centered Hz) in the A-approach. Let us consider the lTXz histogram (fig. 12a). For 5 infinite a HOMO contribution is present. As 5 decreases a large LUMO contribution emerges around - 11 eV, but a HOMO peak remains. For 5 = 1.1 A, a maximum transfer occurs to the LUMO and consequently the HOMO contribution nearly disappears. This comportment is consistent with the largest population loss observed for II,, at this < value (fig. 9). For the final reaction coordinate value a balance is obtained between the HOMO’s and LUMO’s contributions. The A,z_~z histogram (fig. 12b) is characterized by a very weak HOMO contribution for E infinite. We observe that HOMO and LUMO peaks appear as the reaction occurs. The HOMO contribution has a maximum height at 5 = 0.8 A. The LUMO peak remains weak even between t = 0.8 A and .$ = 0.0 A where the low population loss is observed (fig. 9). Particular consideration must be given to the Z> (S-atom) behaviour in fig. 12~. X,+2interacts with u,’ but the very low energy position of u,’ (- 17.56 eV

484

D. Simon, B. Bigot / Local description of H, ckemisorption on a Pt cluster

Fig. 12. Histograms representing the HOMO and LUMO behaviours of: (a) IIxz of the A-atom; (b) Ax~_Yzof the A-atom; (c) X3 of the S-atom; (d) II, of the S-atom; (e) Z: of the g-atom. In each histogram, Ha is approaching the corresponding Pt atom (S or A). The broken lines indicate the Fermi level. The occupancy of each HOMO or LUMO is the area of the corresponding peak in the density of states concerned. A 100% value would correspond to an occupancy of 2 electrons.

in Hz) produces a weak interaction. So, the HOMO of X,‘z is weakly perturbed in p~~ipation but it passes through the Fermi level. For 5 = 1.6 A the resulting LUMO peak has the highest height and energy. This behaviour is consistent with the large electron decrease observed in the population curve (fig. 12~). This effect is not observed in Z> of the A-atom because its HOMO is far from the Fermi level. As $ continues to decrease a balance between HOMO and LUMO contributions is observed as in the II,, case (fig. 12a). Now, let us look at the p-type orbitals. They increase their population under interaction. We may observe that this is due to their LUMU getting contributions at lower energy, under the Fermi level. This point is particularly evident in the case of II, of ~the S-atom, where the LUMO passes directly under the Fermi level (see fig. 12d). A contribution at - 10 eV appears at the end of the reaction, due, either to the part of the initial LUMO peak being pushed up by interaction with UC, or to higher unoccupied cont~butions coming down. The Zc orbital (fig. 12e) shows also, at E infinite, a LUMO contribution at - 10.3 eV. It disappears as the reaction proceeds. The total population curve (fig. 9) of 2: presents a maximum at t = 1.5-1.0 A, where the histograms of fig. 12e show a very weak LUMO peak around -11.5 eV. Thus, as in the

D. Simon, B. Bigot / Local description of H2 chemisorption on a Pt cluster

485

p-type case, this LUMO disappearance can be connected with the increase in population (fig. 9). The LUMO participation has partially passed through the Fermi level, getting rather low energy position since no HOMO contribution is found in the frontier zone. This behaviour is also observed for the Zz orbital of the A-atom. So, we can say that the atomic orbitals are submitted to an electronic transfer observed in the behaviour of their contributions to the HOMO and the LUMO: in the cases of 23, IIx. (respectively II,), the HOMO (respectively LUMO) contribution passes through the Fermi level; in other cases (such as A,~_,,z or Z:) a HOMO or LUMO contribution appears or disappears during the interaction.

5.2. General interaction outlines As a conclusion of the preceding analysis, we think that along the reaction coordinate the following general outlines may be emphasized: (1) bon& are formed with a+-type orbitals of H,; (2) the metallic band contribution is little modified in energy; (3) d-type orbitals loose electrons, characterized by their HOMO contribution passing through the Fermi level; (4) s and p-type orbitals win electrons by means of their LUMO contributions which get participations below the Fermi level. We illustrate these four points in fig. 13 by using a simplified interaction diagram. The major contributions described just above are symbolised by a solid arrow. The dashed arrows correspond to other characteristic interactions. The u+ orbital of H, contributes to the formation of a low energy bond (point 1) and gets participations in the whole energetical spectrum of the Pt,, + H,

pt13

Pt13+cr+

u+(H$

Fig. 13. Main interactions in the Pt,, +H, system during chemisorption. The HOMO levels, appearing mainly in the DOS of the d-type orbitals, have been artificially separated from the rest of the metallic band. The LUMO levels of Pt,, are referred to the DOS of p- (or s-) type atomic orbitals. The important behaviours are represented by a solid arrow (see text). Other characteristic evolutions are symbolized by a broken arrow.

486

D. Simon, B. Bigot / Local description of H2 chemisovtion on a Pt cluster

system. The main behaviour of the metallic band (point 2) is illustrated by a modification in the relative participations of the d- and p- (or s-) parts (decrease for d- and increase for p- or s-parts) occurring without noticeable change in energy. The striking feature of the HOMO and LUMO contributions (points 3 and 4) of p (or s) and d atomic orbitals of the Pt site is represented by an arrow passing through the Fermi energy. A general problem arises from this quantitative study of occupancy and energy behaviour of the local orbitals: we need to precise the local shape of the molecular orbital interacting with Hz and the correlation of these orbitals with those of the naked cluster [13]. The answer to this question would allow us to identify in the naked cluster what are the topological properties and energetical positions that authorize an interaction with H,.

6. Energy profile for chemisorption A difficulty due to the local character of the recursion method is to calculate global properties. In our previous paper [6] we mentioned the way to estimate the Fermi level position. Here, an analogous method is used to calculate the total energy of the Pt,, + H, system. The sum of the total energies E of each orbital is allowed only for orthogonalized orbitals. The Schmidt orbitals, obtained from the atomic orbital basis set by a Schmidt orthogonalization have that property. Nevertheless the recursion technique should be applied for each Schmidt orbital (119 times in our case!). But two types of simplications may be performed. First, we have supposed, and verified, that, for atoms in equivalent position in the cluster, the corresponding Schmidt orthogonahzed orbitals have equivalent density of states and so, have the same total energy E. Then, as we have shown in section 3, the interaction of H, with Pt,, may be supposed to be of low extension. The weak perturbations, due to the H, approach, on the Schmidt orbitals built from the farthest atoms orbitals concern mainly their occupancy. They behave as a reservoir of electrons, being able to give or receive a low fraction of electrons during the interaction. Two questions arise: (i) what is the energy of this fraction of electrons in these reservoir atoms?, and (ii) what is the size of the reservoir? The answer to these questions can be given by studying the average energy variation (ratio energy variation/occupancy variation) for different sizes of reservoirs. We find that the stability of the average energy is obtained as soon as the electron reservoir takes into account the atoms not directly bound to H,. The value of this average energy is - 11.7 +_0.5 eV. This is close to the Fermi level (- 11.67 eV) as would be expected in a reservoir role. The fraction of electrons exchanged between the reservoir and the interaction zone has a typical value of the order of f0.5 electrons. The interesting point from this discussion is that we can make a simplified

D. Simon, B. Bigot / Local descn’ption of Hz chemisorption

on a Pt cluster

487

-2.0 -

Fig. 14. Chemisorption energy variations of Pt13 +H, with H, approaching either S- or A-sites. The top, bridged, and face-centered geometries correspond respectively to molecular adsorption (S- or A-approaches), dissociative adsorption in the bridged final positions (S- or A-approaches) and dissociative adsorption in the face-centered final position (in A-approach only).

calculation of the total energy variation along the adsorption coordinate. For a given geometry of H, approach only the nearest atoms are, first, considered: H,, Pt number S, 2, 5, for S-approach; H,, Pt number A, 7, 9, 11, 12 for A-approach. Their total occupancy and energy variations are calculated by summing the results issued from densities of states of Schmidt orbitals (the Schmidt orthogonalization is performed by starting with H, orbitals). Their total occupancy variation corresponds to the electron fraction transferred to or from the reservoir since the total electron number must be unchanged. The corresponding energy variation in the reservoir is obtained by considering this fraction of electrons as having the Fermi energy. We get so the total energy variations along the reaction path as illustrated for S- and A-approaches in fig. 14. These curves have similar features. First, they present two minima corresponding to the molecular adsorption ([ = 1.56 A) and the reductive dissociation (bridged positions for S-approach and face-centered or bridged position for A-approach). Then, an activation energy is observed for a distance between H, and the Pt site of about 2.0 to 2.2 A. The energetical values are different for S- and A-approaches, as resumed in table 3. Can we give a general interpretation of these energetical values in connection with the simplified interaction diagram (fig. 13)? The activation barrier is due to the occupied-occupied orbital interactions which are energetically unfavorable (similar arguments are developed elsewhere [llb,14]). It concerns mainly up+ interaction with the X,+2 orbital: it can be observed that for the

488

D. Simon, B. Bigot / Local description of Hz chemisorption on a Pt cluster

Table 3 Energy data for hydrogenation Pt adsorption site

Activation barrier (ev)

Molecular adsorption stabilization

Dissociative adsorption stabilization

(ev)

(ev)

S-atom

+ 0.32

-0.12

- 1.42

A-atom

+ 0.21

- 0.39

- 1.04 (face-centered) - 1.16 (bridged)

S-atom the HOMO contributions in the 23 local density of states are pushed up an reach the Fermi level for a geometry of approach of H, corresponding to the activation barrier position. The molecular adsorption minimum is achieved by stabilization terms in the Z: and 2: LUMO contributions interacting with u,’ . In the dissociative step, the energetical stabilization is much larger. This can be associated, firstly with the fact that both uz and u,’ orbitals of H, are concerned for bond formations, and secondly with the geometrical possibility of favorable interactions with adjacent atoms. As we explained in section 5, the main feature of the interaction is electron transfers. These transfers appear to be energetically favorable in the total energy curves since the energy minima correspond to maximum variations of the occupancy of the atomic orbitals involved in the interaction. Thus the global processes can be understood as follows. The reservoir plays a buffer role in electron transfers. The electrons involved in these transfers have a Fermi energy in the reservoir. Concerning H,, we have shown that a stabilization occurs, mainly in the dissociative step, where the electron transfer to 0,’ occurs: the electrons passing from the reservoir to uz are stabilized. Conceming the Pt site, the electron transfer has been connected with frontier orbital contributions. So, the electron loss from the d-type orbitals to the reservoir occurs without energy variation, as it concerns mainly HOMO near the Fermi level. On the contrary, the s and p orbitals win electrons by mean of their LUMO contributions, getting participations below the Fermi level during the interaction. This transfer from the reservoir is energetically favorable. So, we see that for both local points of view, H, or the Pt site, the LUMO contribution, respectively u,’ or s- and p-type platinum orbitals, which get participations below the Fermi level are stabilizing. They are related with the minima in the energetical profile of the reaction. Concerning the differences between the two approaches, we find that for the S-approach the interaction is less stabilizing than for the A-approach, in the molecular adsorption step. In the dissociative step on the other hand, the A-approach appears as being more favorable. These two points can be related to the LUMO contributions of the orbitals of the Pt site. For the molecular

D. Simon, B. Bigot / Local description of H, chemisorption on a Pt cluster

489

adsorption case, the LUMO contribution of ZT is larger, and just above the Fermi energy, in the A-atom case. Consequently it allows a better stabilization during H, approach. For the dissociative adsorption case on the other hand, the S-atom exhibits a larger LUMO contribution of II, (see fig. 7, and gives a better stabilization during H, approach. Nevertheless this interpretation is incomplete, since the values of the energetical stabilization should be mainly related to the actual energy position [13] where s- or p-orbitals get a participation during the interaction. Finally let us correlate these observations with the coordination number of the Pt site (9 and 4 for S- and A-atoms, respectively). We see that for higher coordinated Pt atoms, as the S-atom, the interaction with ai is less favorable. A particular illustration is the height of the activation barrier. This result is analogous to other published results on clusters [llb]. On the contrary, the u,’ interaction is less favorable for the low coordinated atoms. In the bridged position for S-approach the dissociated H, is bound to atoms having coordination 9 and 5. For A-approach H, is bound to atoms of coordination 4, 7 and 5 in the face-centered position, or coordination 4 and 5 for the bridged position. The bridged position in the S-approach appears to be stabilized, by 0.26 eV compared to the bridged geometry of the A-approach, and by 0.38 eV compared to the face-centered geometry of the A-approach. This result seems different to that of bridging hydrogenation of platinum clusters as studied by Minot, Bigot and Hariti [ll]. These authors find that the more favorable first hydrogenation bridges two of the six bonds connecting the vertices of the Pt, triangle to the vertices of the Pt, hexagone (see fig. 1 for the geometry of the Pt,, cluster). Nevertheless we think that our results should be compared to larger clusters or irregular surfaces since we postulate a reservoir role for the atoms being far from the interaction zone.

7. Conclusions The analysis of occupancy and energetical behaviour of local orbitals involved in the chemisorption of H, on a Pt,, cluster has been achieved by using the recursion method in association with an extended-Htickel Hamiltonian. The setting up of bonds between us+(H2), uc(H2) and orbitals of Pt,, has been shown and illustrates the mechanism of hydrogenation: a molecular adsorption step, followed by a dissociative step yielding the reduction of H, into two hydride ions. Transfer of electrons occurs, decreasing the population of d-type orbitals and increasing the population of s and p-type orbitals. This transfer is favorized for d orbitals having important contribution to a HOMO since during the interaction this HOMO passes through the Fermi level and becomes a LUMO. We propose a diagram allowing a general description of

490

D. Simon, B. Bigot / Local description of H, chemisorption on a Pt cluster

the interaction of the two-level H, system with the metallic-type energy distribution of the atomic orbitals of the platinum adsorption site. The energetical profile of H, approach along the reaction coordinate can be related, concerning the activation barrier, to the HOMO peak of d-type orbitals of the Pt site, and as far as the energy minima are concerned, to the LUMO contribution of s and p-type orbitals.

Acknowledgements The authors thank J.M. Palomares for computational and technical help. We acknowledge the Computing Center of CNRS (CIRCE) at Orsay (France) where the computations have been performed.

References [l] P. GaIIezot, in: CataIyse per les Mttaux, Eds. B. Imelik, G.A. Martin and A.J. Renouprez (Editions CNRS, Paris, 1984) pp. 215-229; J.P. Fraissard, T. Ito, L.C. de MenorvaI and M.A. Springuel-Huet, in: Metals Microstructures in Zeolites, Ed. P.A. Jacobs (Elsevier, Amsterdam, 1982). [2] T. Ito and J.P. Fraissard, J. Chem. Phys. 76 (1982) 5225; A.J. Renouprez, in: CataIyse par les Metaux, Eds. B. Imehk, G.A. Martin and A.J. Renouprez (Editions CNRS, Paris, 1984) pp. 163-179. [3] M. Boudart and G. Djega-Mariadassou, Cinetique des Reactions en Catalyse HCterog&ne (Masson, Paris, 1982); H. Gasser, An Introduction to Chemisorption and Catalysis by Metals (Clarendon, Oxford, 1985); F. Zarea, A.J. GeIIman and G.A. Somorjai, Act. Chem. Res. 19 (1986) 24; D.A. King and D.P. Woodruff, Eds., The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, Vol. 4, Fundamental Studies of Heterogeneous Catalysis (Ekevier, Amsterdam, 1982); M. Siionetta, Nouv. J. Chim. 10 (1986) 53; L. Salem, J. Phys. Chem 89 (1985) 5576; G.A. Somorjai and F. Zaera, J. Phys. Chem. 86 (1982) 3070; E. Shustorovitch, R.C. Baetzold and E.L. Muetterties, J. Phys. Chem. 87 (1983) 1100; N.D.S. Canning and R.J. Madix, J. Phys. Chem. 88 (1984) 2437. [4] B. Bigot and C. Minot, J. Am. Chem. Sot. 106 (1984) 6601, and references therein; P.E.M. Siegbahn, M.R.A. Blomberg and C.W. Bausch&her, J. Chem. Phys. 81 (1984) 2103; M. Tomorani, H. Tayewaki and T. Nakamura, J. Chem. Phys. 85 (1986) 2875; R. Harris and B.N. McNaster, J. Phys. C (Solid State Phys) 19 (1986) 7217. [5] J. SiIvestre and R. Hoffmann, Langmuir 1 (1985) 621; S. Sung, R. Hoffmann and P.A. Thiel, J. Phys. Chem. 90 (1986) 1380; S. Sung and R. Hoffmann, J. Am. Chem. Sot. 107 (1985) 578; F. Ruette, A. Hemandez and E.V. Ludena, Surface Sci. 151 (1985) 103; A.B. Anderson and Md.K. Awad, J. Am. Chem. Sot. 107 (1985) 7854; C.W. Bauschlicher, J. Chem. Phys. 83 (1985) 3129;

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P.S. Bagus, C.W. Bauschlicher, C.J. Nelin, B.C. Laskowski and M. Seel, J. Chem. Phys. 81 (1984) 3594; J. Flad, G. Igel-Mann, M. Dolg, H. Preuss and H. Stall, Surface Sci. 63 (1985) 285; H. Nakatsuji and M. Hada, J. Am. Chem. Sot. 107 (1985) 8264; J.P. Jardin, M.C. Desjonqueres and D. Spanjaard, Surface Sci. 162 (1985) 224. [6] B. Bigot, Y. Boudeville and D. Simon, J. Phys. Chem. 91 (1987) 891. (71 R. Haydock, V. Heine and M.J. Kelly, J. Phys. C (Solid State Phys.) 5 (1972) 2845; R. Haydock and M.J. Kelly, J. Phys. C (Solid State Phys.) 8 (1975) L290; V. Heine, in: Solid State Physics, Vol. 35, Eds. E. Ehrenreich, F. Seitz and D. Tumbull (Academic Press, New York, 1980) pp. l-25; R. Haydock, in: Solid State Physics, Vol. 35, Eds. E. Ehrenreich, F. Seitz and D. Tumbull (Academic Press, New York, 1980) pp. 215-294; M. Kelly, in: Solid State Physics, Vol. 35, Eds. E. Ehrenreich, F. Seitz and D. Tumbull (Academic Press, New York, 1980) pp. 295-383; D.G. Pettifor and D.L. Weaire, in: The Recursion Method and its Application, Vol. 58 of Springer Series in Solid State Sciences (Springer, New York 1985). [8] R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [9] R. Hoffmann and P. Hoffmann, J. Am. Chem. Sot. 98 (1976) 598. [lo] N.N. Greenwood and A. Eamshaw, Chemistry of the Elements (Pergamon, Oxford, 1984) p. 1333. [ll] (a) C. Minot, B. Bigot and A. Hariti, J. Am. Chem. Sot. 108 (1986) 196; (b) C. Minot, B. Bigot and A. Hariti, Nouv. J. Chim. 10 (1986) 461. [12] E.I. Muetterties, Angew. Chem. Intern. Ed. 17 (1972) 545. [13] B. Bigot, Y. Boudeville and D. Simon, to be published. [14] E.L. Garfunkel and X. Feng, Surface Sci. 176 (1986) 445.