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-A182 54? A CHEMICAL AND THEORETICAL WAY TO LOOKC AT BONDING ON ISURFACES(U) CORNELL UNIV ITHACA NdY LAB OF ATOMIC ANDSOLID STATE PHYSICS R HOFFMANN JUL 87 TR-21

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OFFICE OF NAVAL RESEARCH

Contract N00014-82-K-0576 O

00 TECHNICAL REPORT NO. 31

A CHEMICAL AND THEORETICAL WAY TOILOOK AT BONDING ON SURFACES

by

Roald Hoffmann

Department of Chemistry

Cornell University

Ithaca, NY 14853-2501

July, 1987

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• An account is given of a theoretical approach to surface structure and reactivitythat is within the framework of solid state theory, yet strives for chemical waysof interpretation. One begins then from highly delocalized band structures, butintroduces interpretational tools (density of states decompositions, crystal orbitaoverlap populations) that allow a tracing of local, chemical acts. It is quite

feasible to construct interaction diagrams for surfaces,and to make frontier orbita

arguments, just as for molecules. There are some interesting ways in which the

surface-adsorbate interaction differs from simple molecular binding - in particular

7 4 3 i71 - IZ NOV -5 IS ______

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in the way that two-orbital four- and zero-electron interactions can.turn intobonding. The surface and bulk acting as a reservoir of electrons or holes at theFermi level are important in this context. Chemisorption emerges as a compromisein a continuum of bonding whose extremes are dissociative adsorption andsurface reconstruction.

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A CHEMICAL AND THEORETICAL WAY TO LOOK AT BONDING ON SURFACES

Roald Hoffmann

p.. o Department of Chemistry and Materials Science Center

Baker Laboratory, Cornell University

Ithaca, NY 14853-1301

Abstract. An account is given of a theoretical approach to surface struc-

ture and reactivity that is within the framework of solid state theory, yet

strives for chemical ways of interpretation. One begins then from highly

delocalized band structures, but introduces interpretational tools (density

of states decompositions, crystal orbital overlap populations) that allow a

tracing of local, chemical acts. It is quite feasible to construct interac-

tion diagrams for surfaces, and to make frontier orbital arguments, just as

for molecules. There are some interesting ways in which the surface-adsorbate

interaction differs from simple molecular binding - in particular, in the way

that two-orbital four- and zero-electron interactions can turn into bonding.

,he surface and bulk acting as a reservoir of electrons or holes at the Fermi

level are important in this context. Chemlsorptlon emerges as a compromise

in a continuum of bonding whose extremes are dissociative adsorption and

surface reconstructiono

NTIS GRA&INt DTIC TASV" Umnanounced

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A surface - be it of a metal, an ionic or covalent solid, a semi-.!conductor - is a form of matter with its own chemistry. In its structure

and reactivity, it will bear resemblances to other forms of matter: bulk,

~discrete molecules in the gas phase and in solution, various aggregated

states. And it will have differences. It is important to find the simi-

larities and it is also important to note the differences - the similarities

connect the chemistry of surfaces to the rest of chemistry; the differences

are what make life interesting (and make surfaces economically useful).

Experimental surface science is a meeting ground of chemistry, physics,

and engineering.' New sDectroscopies have given us a wealth of information,

be it sometimes fragmentary, on the ways that atoms and molecules interact

with surfaces. The tools may come from physics, but the questions that

are asked are very chemical - what is the structure and reactivity of sur-

faces by themselves, and of surfaces with molecules on them? In fact, a

chemist who relaxes a little about the impressive spectroscopies will find

an amusing phenomenological resemblance between current surface science

studies and organic structure determinations by physical methods in the

early days of the application of these methods, say the forties. Great

stories, many of them true, are constructed about structures and reactions

on the basis of a few evanescent bumps in an often hard-to-come-by spectrum.

The special economic role of metal and oxide surfaces in heterogeneous

catalysis has provided a lot of the driving force behind current surfaceIB

chemistry and physics. We always knew that it was at the surface that the

chemistry took place. But it is only today that we are discovering the basic

v. mechanistic steps in heterogeneous catalysis. It's an exciting time - how

wonderful to learn precisely how DObereiner's lamp and the Haber process

work!U,,"2

0 . ., . - ----. -. . , ... .. ... . . - . - . .- . ,- --

-3-

There have been an extraordinary number of theoretical contributions

to surface science.2 These have come from physicists and chemists, they

have ranged from semiempirical MO calculations to state-of-the-art Hartree-

Fock self-consistent-field+CI and advanced density functional procedures.

Some people have used atom and cluster models, some extended slab or film

models for surfaces. I would like to present in this account some of the

things my coworkers and I have learned about surface-molecule interactions

from extended Hckel band calculations.3 This computational method is a

very approximate one (all other methods are superior to it), but its

transparency and the applicability to it of the simplest perturbation

theoretic reasoning makes the method well-suited to tracing origins and

interactions. Our choice of a translationally extended system (i.e. two-

dimensional film or slab model rather than a cluster) is intentional.

The aim is to build a bridge to physics, to do the calculations in the

framework or language with which most solid state physicists are likely

to feel comfortable. The special feature, what makes these calculations

more than the lowest quality band calculation, is that from the experience3J

of chemistry and quantum chemistry we can construct the interpretational

tools that will extract local, chemical actions from the delocalized orbi-

tals. The calculations are mediocre, on some absolute scale; the analysis

is, I hope, clever and chemical.

5 t

S .°

-4-

Setting Up: The Surface and the Adsorbate

The kind of problem that we want to study is how CO chemisorbs on

Ni, how H2 dissociates on a metal surface, how acetylene bonds to Pt(111)and then rearranges to vinylidene or ethylidyne, how surface carbide or

sulfide affects the chemistry of CO, how CH3 and CH2 bind, migrate, and

react on an iron surface. It makes sense to look first at structure and

bonding in the stable or metastable way points, the chemisorbed species.

Then one could proceed to construct potential energy surfaces for motion of

chemisorbed species on the surface, and eventually for reactions.

The very language I have used here conceals a trap. It puts the bur-

den of motion and reactive power on the chemisorbed molecules, and not on

the surface, which might be thought passive, untouched. Of course, this

can't be so. We now know that exposed surfaces reconstruct, i.e. make

adjustments in structure driven by their unsaturation.W They do so first

by themselves, without any adsorbate. And they do it again, in a different

way, in the presence of adsorbed molecules. The extent of reconstruction

is great in semiconductors and extended molecules, small in molecular

crystals and metals. The calculations I will discuss deal with metal sur-

*' faces. One is then reasonably safe (we hope) if one assumes no reconstruc-

tion. It will turn out, however, that the signs of eventual reconstruction

are to be seen even in these calculations.

It might be mentioned here that reconstruction is not a phenomenon

reserved for surfaces. In the most important development in theoretical

inorganic chemistry in the seventies, Wadesa and Mingos5b have provided us

with a set of skeletal electron pair counting rules. These rationalize the

related geometries of borane and transition metal clusters. One aspect of

their theory is that if the electron count increases or decreeaes from the

- 5 -

appropriate one for the given polyhedral geometry, that the cluster will ad-

just geometry - open a bond here, close one there - to compensate for the

different electron count. Discrete molecular transition metal clusters and

polyhedral boranes also reconstruct.

Returning to the surface, let's assume a specific surface plane cleaved

out, frozen in geometry, from the bulk. That piece of the solid is periodic in

two dimensions, semi-infinite, and aperiodic in the direction perpendicular to

the surface. Half of infinity is much more painful to deal with than infinity,

because translational symmetry is lost in that third dimension. And that sym-

-: metry is essential in simplifying the problem - one doesn't want to be diagonal-

izing matrices of the degree of Avogadro's number; with translational symnetry

and the apparatus of the theory of group representations one can reduce the

problem to the size of the number of orbitals in the unit cell.

So one chooses a slab of finite depth. 1 shows a four-layer slab

model of a Ni(111) surface, a typical close-packed hexagonal face. How

thick should the slab be? Thick enough so that its inner layers approach

the electronic properties of the bulk, the outer layers those of the true

surface. In practice, it is more often economics which dictates the typical

choice of three or four layers.

A

B

A

- Wp'I

"71 -Y 77 Y-W-

-6-

Molecules are then brought up to this slab. Not one molecule, for

that would ruin the desirable two-dimensional symmetry, but an entire array

or layer of molecules maintaining transtational symmetry. This immediately

introduces two of the basic questions of surface chemistry: coverage and

site preference. 2 shows a c(2x2)C0 array on Ni(lO), on-top adsorption,

coverage = . 3 shows four possible ways of adsorbing acetylene in a cov-

erage of i on top of Pt(111). The experimentally preferred mode is the

S three-foldbridgingonMany surface reactions are coverage depen-

dent. And the position where a molecule sits on a surface, its orientation

relative to the surface, is one of the things one wants to know.

0 Ni

2 0 C

0 0

a b5 3

U,•L d

IITW"d

S-7-

How to Think About Many Orbitals

So: a slab, three or four atoms thick, of a metal, and a monolayer

of adsorbed molecules. The thicker the layer and the smaller the coverage,

the more atoms in a unit cell. And, there are lots of unit cells. If there

are n valence orbitals in the unit cell (n might be -100), and N microscopic

unit cells in the macroscopic crystal (N approaches Avogadro's number)

then there are Nn orbitals in all. That's a large number, hence the title

of this section. At first sight, one is set back by the prospect of that

myriad of levels. A person addicted to frontier orbital arguments, such as

the author, one who would like to find the causes of a geometrical prefer-

*ence or a stereochemical preference in the nature of one orbital, might be

particularly discouraged. For there is no way in the world that one orbital

out of so many has the power to control or steer.

There is a way out of these quandaries. It is, first of all, symmetry,

translational symmetry, leading to band structures and crystal orbitals,

and, second, the language of densities of states.6 ,7

To introduce the idea of a band structure, let's begin with a simple

one-dimensional system, a chain of equally spaced H atoms, 4, or the iso-

morphic i-system of a non-bond-alternating polyene, 5. Such infinite

chains can be modeled as an imperceptibly bent part of a very large ring.

.... ........ t ...... H ....... H ....... H ........ W

4

- Vq

5

%".1

oooooo-.. -. -

L-8-

This is called applying cyclic boundary conditions.

The orbitals of the oligomers on the way to that very large ring are

very well known, 6. In hydrogen (or ethylene) there is a bonding ag (Tr)

level below an antibonding ou*(v*). In the three-membered ring (cyclic

H3, cyclopropenium) the pattern is 1 below 2; in cyclobutadiene we have

1 below 2 below 1. And so on. Levels come in pairs, except for the lowest

--

and, occasionally, the highest, and the number of nodes increases as one

goes up in energy. We'd expect the same for an infinite polymer, in the

chemist's representation of a band of levels that is given at right in 6.

There is a neat way to write out all those orbitals in the band, making

use of the translational syrmetry. If we have a lattice whose points are

labeled by an index n=0,1,2,3,4 as shown in 7, and if on each lattice point

there is a basis function (an H is orbital), X0,X1qx2, etc. then the appro-

priate symmietry adapted linear combinations are given in 7.

-f- --p.

-9-

7 n-O 1 2 3 4 ...

Xo X, X2 X3 X4

'#11 =e klXn.-. x.

." - Here a is the lattice spacing, the unit cell in one dimension, and k is

an index that labels which irreducible representation of the translation

group T transforms as. We will see in a moment that k is much more, but

for now k is just an index for an irreducible representation, just like

a, el, e2 in C5 point group symmetry are labels.

The process of symmetry adaptation is called in the solid state physics

trade "forming Bloch functions". 6'7 To reassure a chemist that one is getting

what one expects from 6, let's see in 8 what combinations are generated

for two specific values of k, k=O and k=7/a.

k-0 *. * @ X,-X.'""

S...; k-+ ,+X.+X (-..

Oaf - '- a -a X," a*-""

Referring back to 6, we see that the wave function corresponding to k=O

is the most bonding one, the one for kTr/a the top of the band. For other

values of k we get a neat description of the other levels in the band.

A, So k counts nodes as well. The larger the absolute value of k, the more

nodes one has in the wave function. But one has to be careful - there is

a range of k and if one goes outside of it one doesn't get a new wave

function, but repeats an old one. The unique values of k turr, out to be

.4

- 10 -

in the interval -n/a<ks i/a or JkJ5 iT/a. This is called the Brillouin

zone, the range of k.

How many values of k are there? As many as the number of translations

.4 in the crystal or, alternatively, as many as there are microscopic unit

cells in the macroscopic crystal. So let us say Avogadro's number, give

or take a few. There is an energy level for each value of k (actually two

for each k because there is an easily proved theorem that E(k) = E(-k)). Most

band structures do not draw the redundant E(-k), but plot E(Ikl) and label

it as E(k). The allowed values of k are equally spaced in the space of

k, which is called reciprocal space. Remarkable k is not only a symmetry

label and a node counter, but it is also a wave vector, and so related to

I momentum. 6,7

What a chemist then draws as a band in 6, repeated at left in 9 (and

the chemist tires and draws -20 lines or just a block instead of Avogadro's

number), the physicist will alternatively draw as an E(k) vs. k diagram at

right.

= E Wk

+W t

9 0 rio

Recall that k is quantized, and there is a finite, but large, number of

levels in the diagram at right. The reason the curve looks continuous is

that we have here a fine "dot matrix" printer at work - there are Avogadro's

number of points jammed in there, and so it's no wonder we see a line.

Graphs of E(k) vs. k are called band structures. You can be sure

-. S ..... .. .... + ........... .- - -. . .. - .. .. ..-.... ... -..... . d . . . . . ., , , - - .

- - 11 -

that they can be much more complicated than this simple one. For instance,

if we refer back to the CO on Ni(100) surface of 2, the band structure of

the CO monolayer by itself is given in Fig. 1, and that of the underlying

four-layer Ni slab by itself is in Fig. 2.8- 10

Figures 1 and 2

At first sight, these appear to be too complicated to be understood.

Not so:

1) What is being plotted: E vs. t. The lattice is two-dimensional.

k is now a vector, varying within a two-dimensional Brillouin zone, k =

t = (kxky). Some of the special points in this zone are given canonical

names: F(the zone center) = (0,0); X = (7/a,O), M = (/a,7/a). What is

'p being plotted is the variation of the energy along certain specific

directions in reciprocal space connecting these points.

2) How many lines there are: as many as there are orbitals in the

unit cell. Each line is a band, generated by a single orbital in the unit

cell. In the case of CO, there is one molecule per unit cell, and that

molecule has well-known 4a, 17, 5a, 2n* MO's. Each generates a band. In

the case of the four-layer Ni slab, the unit cell has.4 Ni atoms. Each has

five 3d, one 4s and three 4p basis functions. We see some, but not all, of

the many bands these orbitals generate in the energy window shown in Fig. 2.

3) Where (in energy) the bands are: The bands spread out, more or

less dispersed, around a "center of gravity". This is the energy of that

orbital in the unit cell which gives rise to the band. Therefore, 3d bands

lie below 4s and 4p for Ni, and 5a below 27* for CO.

4) Why some bands are steep, others flat: because there is much

inter-unit-cell overlap in one case, little in another. One very important

feature of a band is its dispersion, or band width, the diff.<ence in

0 *0 0

I ..' I ' * I...

172r

54o

-a __4-a

m Xr M PPX

Figure 1. Band structures of square monolayers of CO at two separations:r (a) left, 3.52 A, (b) right, 2.49 ~.These would correspond to j and fullcoverage of a Ni(1OO) surface.

" Ni

• -- 4 layer slab

p...1

-'I4

M Figure 2. The band structure of a four-layer Ni slab that serves as a model

for aNi(IO0) surface. T - flat bands are derived from Ni 3d, the more highlyaee

dispered ons aboe 4hlayere sslab

P XM

-'q

aid.

- '* ? , Figure '-'' 2.-Th ban strctur of a four-laye N- slab tha "" erves"'"' as -a model '""

- 12 -

energy between the highest and lowest levels in the band. Ahat .eter-ires

the width of bands? The same thing that determines the splitting of levels

in a dimer, ethylene, or H, namely the overlap between the interacting

orbitals (in the polymer the overlap is that between neighboring unit

cells). The greater the overlap between neighbors, the greater the band

width. ?

The CO monolayer bands in Fig. 1 are calculated at two different

CO-CO spacings, corresponding to different coverages. It's no surprise

that the bands are more dispersed when the CO's are closer together. In

the case of the Ni slab, the s,p bands are wider than the d bands, because

the 3d orbitals are more contracted, less diffuse than the sp.

There are more details to be understood, to be sure. But, in general,

these diagrams are complicated, not because of any mysterious phenomenon,

but because of richness, the natural accumulation of understandable and

understood components.

We still have the problem of how to talk about all these nighly Jelo-

calized orbitals, how to retrieve a local, chemical, or frontier orbital

language in the solid state. There is a way: perhaps we can talk about

bunches of levels. There are many ways to group levels, but one pretty

obvious one is to look at all the levels in a given energy interval. The

density of states (DOS) is defined as follows:

DOS(E)dE - number of levels between E and EwdE

'or a simple band of a chain of hydrogen atoms, the DOS curve takes on

the shape of I.

E~w M 0(E)

0 0 DOS -

I06

4 CO monolayer0 .01-3.52 A-4C C

C

40-

r X MI DOS-.

Figure 3. The density of states (right) corresponding to the band structure

(left) of a square monolayer of CO's, 3.29 A apart.

-13-

Note that because the levels are equally spaced along the k axis, and because

the E(k) curve, the band structure, has a simple cosine curve, there are

more states in a given energy interval at the top and bottom of this band.

In general, DOS(E) is inversely proportional to the slope of E(k) vs.

k or, to put it into plain English, the flatter the band, the greater the

density of states at that energy. 6'' An illustration of this point is pro-

vided by the DOS of a hypothetical array of non-interacting adsorbates, for

instance an overlayer at very low coverage. The plot would show single

lines (V-functions) at the energies of the MO's of one isolated adsorbate

molecule.

The shapes of DOS curves are predictable from the band structures.

Fig. 3 shows the DOS curve for one of the CO monolayers. It could have been

sketched from the band structure at left. In general, the construction of

these is a job best left for computers.

Figure 3

The density of states curve counts levels. The integral of DOS up to

the Fermi level is the total number of occupied MO's. Multiplied by two,

it's the total number of electrons. So the DOS curves plot the distribution

of electrons in energy.

One important aspect of the DOS curves is that they represent a

return from reciprocal space, the space of k, to real space. The DOS

is an average over the Brillouin zone, over all k that might give mole-

cular orbitals of the specified energy. The advantage here is largely

psychological. If I may be permitted to generalize, I think that chem-

ists (with the exception of crystallographers), by and large, feel them-

selves uncomfortable in reciprocal space. They'd rather '-Pjrn to. and

think in, real space.

-ar

- 14 -

There is another aspect of the return to real space that is significant:

chemists can sketch the DOS of any material, approximately, intuitively. All

that's involved is a knowledge of the atoms, their approximate ionization

potentials and electronegativities, and some judgment as to the extent of

inter-unit-cell overlap (usually apparent from the structure). For an

elaboration of this point, the reader is referred to another article dis-

cussing the general aspects of a theoretical and chemical approach to the

solid state.7c

To summarize: we go from orbitals in the unit cell(real space) to

band structures (reciprocal space) to densities of states (back in real

space). In the remainder of the paper, I will be showing only densities

of states, and we will draw chemical arguments from these. Occasionally

the crystal orbitals at certain k points will be required.

We still need two concepts the solid state analogue of a charge dis-

tribution, and some bond index. But to introduce these, we will use a

specific surface problem.4'..

'1

. o

S .• -

- a--- -- .~ ~- - ~ Y Y W U VWCD

I(2

4J cu

0 ba

(JN V04- (0 0o 0

(A 0* a 41)

0\ 4

.10 0 a

0 01 CL

sJ 4JUm 4) E

0>, .

(A*) .BOU

"4,Aidd' .

6 n-p

- -o1.

Su -

0 Ln

0 C CW to 41=

t:) - c l

%" • o

CPI 0 2

-~j (1 4-

0oN ,., "n 2, ,.,.. . e, m o*- L

T T V C -

C-~0

-4 J- '. o ... .. ... .. ... .. ... .. ... .. ... .. ... .. ................ ... ... ... ... ...

.. . -9"5.0 e-

,.-_.-_* ,.- .-U 0C

a ,ILI I 0 .I I IC

.20

.,. cAe 0 ~u

C.I'. .. _ .1. 0 0\ 0

0 02 j

0.0

T' T

(AS)- , -. ,..

K . 0 4-'- . .''.- : . ' r . e , . . * , . . - ,, . - . , e ' . , 'e : ", . . - ., . ' l , r . ' , .. . - - , . . - -

N-..- V% 7* Y. -

3 z,yzof surfaceNiatom zz,y of surface Ni atom 21A at CO 2 e of CO-4 Ni(lO) slab €(2x2)CO-Ni(lO) c(2x2) CO-Ni(0O0) CO monolayer

-5

6

W -10.-Il

-2-13

DOS- DOS-- DOS- DOS-

-3 1a of surfoce NI atom 2of surface NI atom 5'cO Sr of Co-4 Ni(lO0) slab c(W)CO-NIOOO) c(2x2)CO-Ni(lO0) CO monolayer

-5, -6

q -73-4 -a.

W -10* ~ -I I

-12

-13

DOS--n DOS- DOS- DOS-

Figure 6. "Interaction Diagrams" for So and 2ir* of c(2x2)CO-Ni(100). The

extreme left and right panels in each case show the contributions of the

appropriate orbitals (z2 for So, xz,yz for 27*) of a surface metal atom (left),

and of the corresponding isolated CO monolayer MO. The middle two panels

then show the contributions of the same fragment MO's to the DOS of the com-

posite chemisorption system.

- 15 -V

The Detective Work of Tracing Molecule-Surface Interactions: Decompositionof the DOS

We saw in the previous section the band structures and DOS of the CO

overlayer and the Ni slab separately (Fig. 1-3). Now let's put them to-

gether in Fig. 4. The adsorption geometry is that shown in 2, with Ni-C 1.8 A

Figure 4

It's clear that the composite system c(2x2)CO-Ni(100) is roughly a

superposition of the slab and CO layers. Yet things have happened. Some

of them are clear - the 5a peak in the DOS has moved down. Some are less

clear - where is the 27*, and which orbitals on the metal are active in

the interaction?

, . " These questions are basically ones of the location of electrons in space,

a matter of abiding interest to chemists. Given a molecular orbital, we

want to know how the electrons in that orbital are distributed. It's pos-

sible to do this for the highly delocalized Bloch functions as well, though

not without a computer. Orbital by orbital, atom by atom, band by band,

the computer partitions the electron density among the contributing orbitals

or atoms. The procedure is called a Mulliken population analysis." It is

repeated for several k points in the Brillouin zone, and then returns to

real space by averaging over these points. These decompositions of the

DOS are often called "projections of the DOS" or "local DOS" inthe solid

- state trade. The integral of these projections up to the Fermi level then

gives the total electron density in a given atom or in a specified orbital.

Let's see how this decomposition helps us to trace down the bonding

in the chemisorbed CO system. Figure 5 shows the 5a and 27* contributions

to the DOS. The dotted line is a simple integration of the DOS of the

Figure 5

_14 t

- 16 -

fragment of contributing orbital. The relevant scale, 0 to 100%, is

to be read at top. This integration shows the total percent of the

given orbital that's occupied at a specified energy. It is clear that

the 5a orbital, though pushed down in energy, remains quite localized.

Its occupation (the integral of this DOS contribution up to the Fermi

level) is 1.62 electrons. The 2n* orbital obviously is much more delo-

calized. It is mixing with the metal d band, and, as a result, there

is a total of 0.74 electrons in the 271* levels together.

Which levels on the metal surface are responsible for these interactions?

In discrete molecular systems we know that the important contributions to

bonding are forward donation, 114, from the carbonyl lone pair, 5u, to some

-" appropriate hybrid on a partner metal fragment, and back donation, 11b,

involving the 211* of CO and a d1 orbital, xz,yz, of the metal. We would

0'III

c C 2vT

ML0

a b

suspect that similar interactions are operative on the surface.

These can be looked for by setting side by side the d(z2 ) and 5a con-

tributions to the DOS, and d7 (xz,yz) and 27* contributions, in Fig. 6 the

7 interaction is clearest: note how 2,* picks up density where the d7T states

are, and vice versa, the d7 states have a "resonance" in the ?* density.

Figure 6

- 17 -

I haven't shown the DOS of other metal levels, but were I to do so, it would

be seen that such resonances are not found between those metal levels and

5c and 27*. The reader can confirm at least that 5a does not pick up density

where d., states are, nor 2Tr* where da states are mainly found. 9

Let's consider another system in order to reinforce our comfort with

these fragment analyses. In 3 we drew several acetylene-Pt(111) structures

with coverage = *. Consider one of these, the dibridged adsorption site

alternative 3b redrawn in 12. The acetylene brings to the adsorption process

two 7, and two Tr* orbitals. These are sketched in 13. If the acetylene is

S4:

12

13

bent, as it is in all molecular and surface complexes known, the degeneracy

of Tr and 7a, and of Tra* and n* is broken. We jump right away to the contribu-

tions of the various acetylene orbitals to the total DOS of 3b, shown in Fig.

7. The sticks show the positions of the acetylene orbitals in the isolated

Figure 7

molecule. It is clear that n and 7* interact less than 70 and 7,*. And

the overlap reasons behind that differential are obvious. Note the large

effect on 7*, analogous to what we saw for 27* of CO.

- A third system: in the early states of dissociative H, :hemisorption,

% -.. it is thought that H2 approaches perpendicular to the surface, as in 14.

Consider Ni(111), related to the Pt(111) surface we have discussed earlier.

K~~~i s......

-4

ach.Y

00

r_ 4- I

0 L0 N W E N (003

LM

In +

.) 4.)

c.. 4J

It 0)

61c 4-

--

O 1+-

-~s-

...........

T 'ti~ V T

(AO) A'4-

18-

H

H

14

Fig. 8 shows a series of three snapshots of the total DOS and its Gu*(H2)

projection. 3 These are computed at separations of 3.0, 2.5 and 2.0 A from

Figure 8

the nearest H of H2 to the Ni atom directly below it. The ag orbital of H2

(the lowest peak in the DOS in Fig. 8) remains quite localized. But the

aTu* interacts, is strongly delocalized, with its main density pushed up.

The primary mixing is with the Ni s,p band. As the H2 approaches some au*

density comes below the Fermi level.

Why does au* interact more than ag? The classical perturbation theoretic

measure of interactionAE IHij 2

Ei0-Ej0

helps one to understand this. au* is more in resonance in energy, at

least with the metal s,p band. In addition, its interaction with an appro-

priate symmetry metal orbital is greater than that of ag, at any given energy.

This is the consequence of including overlap in the normalization:.i

41tW42 2l±S ()

The au* coefficients are substantially greater than those in ag. This has

been pointed out by many people, but in the present context imoortantly

emphasized by Shustorovich and Baetzold.2, 4 ,

'

!--... .-.... .-.-.. ..-. . , .... ,- .. ...- .-. , ,,,,. - U.

0"

• .... = -

C ; o

SI I 4L iI

.. . . . . . . .. . . . . . . . .

AL, .. . . ". aIg I- *9- to

o . cu A *r

l.iltl. I I 1 I "-- L

... ~ i Io... .Ii .-OJ rM

.. lr. i In .. l . 9-

" a 4.

S. - igl II I0|C4-

-,~~ 0

- .' I e l

l Pvl l l I iC. 0

t '.)

.......... 0 ea

10. 4 -

04.

4- L

0l S- L.

0. > ICU

w cT0o (U

0 t 0 I ul 01 -15'

I7 ~~(Q .. OJG' : 9-3

3 au

-30-

c 20g

"Dos" - "coop"

Figure 9. the orbitals of N2 (left) and a "solid state way" to plot the

DOS and COOP curves for this molecule.

pf

r a e 1,r)e 1 n ds 7

Ahen CO or acetylene chemisorb partial bonds are formed to the surface.

3onds Within the adsorbed molecule weaken, and we see the evidence for that

.i-ectly in tne diminished frequencies for specific vibrational modes,

e.g. the -1 stretch. It behooves us to look for a theoretical index of

that bonding. This index, a CCOP curve, which we will define, will allow

is to push our detective investigation further, and it will help to restore

a local, cnemical viewpoint in an analysis of chemisorption.

The problem is how to find bonds in the highly delocalized bands.

The idea is to extend the Mulliken population analysis to the crystal. "on-

sider a two-center orbital:

c,: + c-,

We want to be normalized:

*dT 1 cIlc:: d - C+c* +2cjc:SI,

Another way to think about the normalization is that it also gives the dis-

tribution of an electron in .. It is clear that the overlap term 2cc:S. Is

a characteristic of bonding. If the overlap integral S1: is taken as posi-

tive (and it can always be arranged so) then this quantity scales as we

expect of a bond order: it is positive (bonding) if cl and c_ are of the

same sign, and negative if cl and c. are of opposite sign. And the magni-

tude of this Mulliken "overlap population", for that is what 2cc:S12'p

'summed over all orbitals on the two atoms, over all occupied 4O's) is called,

,4epends on ci,cjSij."

W, Before we move into the solid, we might take a look at how these overliD

populations might be used in a molecular problem. Fig. 9 shows tle familiar

energy levels of a diatomic, N., a "density of states" plot of these (just

sticks proportional to the number of levels, of length one for -, two Fcr

.nd the contributions of these levels to tle overlip populati-. i-a d

.- contribute little, because i s s7all betmeen tijht :;I

"0

-20-

2- is strongly bonding, 2-u and 3- are essentially non-bonding.

These are best characterized as lone pair combinations. - is bonding,

antibonding, 3:u the - level. The right-hand side of Fig. 9 characterizes

the bonding in N2 at a glance. It tells us that maximal bonding is there for

7 electron pairs; more or fewer electrons will lower the N-N overlap popula-

tion. It would be nice to have something like this for extended systems.

A bond indicator is easily constructed for the solid. An obvious pro-

cedure is to take all the states in a certain energy interval and interrogate

them as to their bonding proclivities, measured by the Mulliken overlap popu-

lation, 2cicjSij. What we are defining is an overlap population weighted

density of states. The beginning of the obvious acronym (OPWDOS) unfor-

tunately has been preempted by another common usage in solid state physics.

For that reason, we have called this quantity COOP, for crystal orbital

overlap population."' It's also nice to think of the suggestion of orbitals

working together to make bonds in the crystal, so the word is pronounced "co-op".

To get a feeling for this quantity, let's think what a COOP curve for

a hydrogen chain looks like. The simple band structure and DOS were given

earlier, IQ; they are repeated with the COOP curve in 15.

"-'"~~~~~~# .... ,- .-.-. -.. -H..-.. -

•bmiiiq bonding-

EE * .

DS 0 +

.coo

,.-" CO(OP

15

To calculate a COOP curve, one has to specify a bond. Let's take the

nearest neighbor 1,2 interaction. The bottom of the band is " tonding,

the riddle non-bonding, the top antibonding. The COOP curve iiously has

*'-e ha;e "cwn 3t r7;nt in 23. ut not 3ll C71P curves lcoo "'t way. :f

w ' .. .i " . . - . . . -,"-. , . . . ..- "- .- ' " '- . ' . . % -

- 21 -

we specify the 1,3 next-nearest-neighbor bond (silly for a linear crain,

not so silly if the chain is kinked), then the bottom and the top of the

band are 1,3 bonding, the middle non-bonding. That curve, the dotted line

in the drawing is different in shape. And, of course, its bonding and anti-

bonding amplitude is much smaller because of the rapid decrease of Sij with

distance.

Note the general characteristics of COOP curves - positive regions

which are bonding, negative regions which are antibonding. The amplitudes

of these curves depend on the number of states in that energy interval,

the magnitude of the coupling overlap, and the size of the coefficients in

* the MO's.

The integral of the COOP curve up to the Fermi level is the total

overlap population of the specified bond. This points us to another way

of thinking of the DOS and COOP curves. These are the differential versions

of electronic occupation and bond order indices in the crystal. The integral of

the DOS to the Fermi level gives the total number of electrons; the inte-

gral of the COOP curve gives the total overlap population, which is not

identical to the bond order, but which scales like it. It is the closest

a theoretician can get to that ill-defined but fantastically useful simple

concept of a bond order.

Let's see how the COOP curve can be used to support the picture of CO

chemisorption that was described above. The relevant curve is in Fig. 10.

The solid line describes Ni-C bonding, the dotted line C-0 bonding. Note

Figure 10

the major contribution to Ni-C bonding in both the 5: peak and the bottom

of the d band. The 5z contribution is due to - bonding, Ila. -ut tYe

bottom of the d band contributes through --bonding, llb. This i; evident

from the "mirroring" C-0 antibonding in the region. The ar" 'dlng .r '-

ponent of that d--2-* interaction is responsible for the ',-

* antibonding above the 7emi level.'

, . ." . ..-... , . ...- ~ / .- , L . f -. . .~ .. - % U " , '% . . . ...-- .- ,.- • • .-. .. . .. .

-20onibonding bonding

-Ni-C

........... ....... C-0-4.0

>-4:

S-6.0-

-8.0

-10.0 d block

-12.0

5a

-14.01

Figure 10. Crystal orbital overlap population for CO, on-top, in a

c(2x2)CO-Ni(100) model. Representative orbital combinations are drawn out.

22

yt Dy e Jsefl t, empnasize trat thiese cjrves are fot ofnly lescr- -

tve, but also form a part of the story of tracing down interaction. For

-nstance, supposing we were not so sure that it is the d-.-2-* interaction

o. 'cr is responsible for a good part of the bonding. Instead, we could

nave '-a '-ed nonding between I- and some unfiled d- orbitals. re

0

r.C

d, IIrr W

M

tant, tne I block orbitals,interacting in an antibonding way with DeloA

them, srould become in part Ni-C antibonding and C-0 bonding. 'Notning ot

tnis sort is seen in Fig. 9. The C-3 antibonding in the d blocK -e'Oon

is, instead, diagnostic of 2-' mixing being important.

-nc'dentally, tre integrated overlap PoPuiations jP to te Fermi 'evel

are 'd 3-i >4, C-J 1.04. In free CO the corresponding overlap population

s 1.2'. The bond weakening is largely due to population of '-* on cnemi-

;or:t'on.

.rott'er ,''stration of tne y o* Cs j ed e't

a ;~est';n ot :-emisor tion site 2refer-rce. n .rany races,

-- : , a i.3rticularly stable dead end 'n tne surface chemistry ot icety-

Pre is ethylidyne, CLH,." -ow trat - ydroqgen 's i ed -v 's 3j2'-

't"'. 1je',t'on. _ut 'et's ty ass t-at and think about ohere tle "-.,ant S

* P r 7,OwS tproe 3lt.,rnativeS - A ri :r n-tcr*, r- r i c 4.

' ~ - e r r en t e,, er ~ ~ t ;,n *'ie 4

I ~ .

-23-

CN4 04 C MCC

17

The important frontier orbitals of a carbyne, CR, are shown in 18.

The C 2p orbitals, the e set, are a particularly attractive acceptor set,

certain to be important in any chemistry of this fragment. We could trace

its involvement in the three alternative geometries 17 via DOS plots, but

instead we choose to show in Fig. 11 the Pt-C COOP curve for 1-fold and

3-fold adsorption.

Figure 11

In both on-top and capping sites the carbyne e set finds metal orbitals

to interact with. Bonding and antibonding combinations form. The coupling

overlaps are much better in the capping site. The result is that the carbon-

metal e-type antibonding combinations do not rise above the Fermi level

in the 1-fold case, but do so in the 3-fold case. Figure 11 clearly shows

this - the bonding and antibonding combinations are responsible for recog-

nizable positive and negative COOP peaks. The total surface-CCH 3 overlap

populations are 0.777 in the 1-fold case, 1.600 in the 3-fold case. The

,* total energy follows these bonding considerations; the capping Lite is

-much preferred."

'doL6

.L - """-'"i"" - .''-. . ..- -• .'"'" .. • " * ""-".' * -' - -' " . .*' " ',' ." " , - -

"-' - - -, -', " -.. . €5

.5Il(

C C-

CC

0 4-

olo

u 0.)

0

-/ 4-j

CC

4

S- 4-o 0

0 a~cm

No 0

%~ S-

a) 4-

> 4-

- 24-

Orbital Interactions in the Solid

The apparatus of densities of states and crystal orbital overlap popu-

lations has restored to us a frontier orbital or interaction diagram way18

of thinking about the way molecules bond to surfaces. Whether it is 27*

CO with d., of Ni(100), or e of CR with some part of the Pt(111) band, in

either case we can describe what happens in terms of local action. The

only novel feature so far is that the interacting orbitals in the solid

often are not single orbitals localized in energy or space, but bands.

A side-by-side comparison of orbital interactions in discrete molecules

and of a molecule with a surface is revealing. 19 is a typical molecular

interaction diagram, 20 a molecule-surface one. Even though a molecule is,

-ow• °0

A B A Surface

19 20

in general, a many-level system, let's assume that a small set of frontier

orbitals dominate. This is why the squiggly lines symbolizin interaction

go to the HOMO and LUMO of each component.

. -' -. .- .. " -. - . . . . - - -i

-25-

Within a one-electron picture the following statements can be made

(and they apply to both the molecule and the surface unless specifically

said not to do so).

(i) The controlling interactions, are likely to be the two-

orbital, two-electron stabilizing interaction Q and . Depending on

the relative energy of the orbitals and the quality of the overlap, each

of these interactions will involve charge transfer from one system to the

other. In interaction @, A is the donor or base, B, or the surface, the

acceptor or acid. In interaction Q1, these roles are reversed.

(ii) Interaction (D is a two-orbital, four-electron one. It is

destabilizing, repulsive, as 21a shows. In one-electron theories, this

is where steric effects, lone pair repulsions, etc. are to be found.18 These

interactions may be important. They may prevent bonding, interactions

(D, (D from being realized. There is a special variant of this interac-

tion which may occur in the solid, but is unlikely in discrete molecules.

This is sketchedin 21b - the antibonding component of a four-electron, two-

orbital interaction may rise above the Fermi level. It will dump its elec-

trons at the Fermi level, and can no longer destabilize the system. Only

the intersystem bonding combination remains filled.

repulsion attraction

* 21 b

5-

1j

- 26 -

The effect on molecule-surface bonding is clear - it is improved by this

situation. What happens in the surface is less clear; let's defer discussion

until we get to interaction .

(iii) Interaction ( involves two empty orbitals. In general, it

would be discounted as having no energetic consequences. This is strictly

true in molecular cases, 22a. But in the solid, where there is a continuum

of levels, the result of such interaction may be that the bonding combina-

tion of the two interacting levels may fall below the Fermi level (22b).

Becoming occupied, it will enhance fragment A - surface bonding. Again,

no Offect ottroction

S22 b

there may be an effect on the surface, because it has to supply the elec-

trons for the occupation of that level.

(iv) Interaction @ is something special to the metallic solid, that

comes from the states of the metal surface forming a continuum. The inter-

action describes the second order energetic and bonding consequences of

shifts of electron density around the Fermi level. First order interactions

Q, (, ( and ( all will move metal levels up and down. These metal

levels, the ones that move, will belong to the atoms on the surface interac-

ting with the adsorbate. The Fermi level remains constant - the bulk and

surface are a nice reservoir of electrons. So electrons (holes) will flow

in the surface and in the bulk underneath it, in order to compensate for the

primary interactions. These compensating electrons or holes are, however,

I"

-.. .."...

S 9 5 -" . . . . . .

- 27 -

not innocent of bonding themselves. Depending on the electron filling,

they may be bonding or antibonding in the bulk, between surface atoms not

involved with the adsorbate, even in surface atoms so involved, but in

orbitals that are not used in bonding to the chemisorbed molecule.

Before I leave this section, I should like to say quite explicitly

that there is little novel in the use my coworkers and I have made of inter-

action diagrams and perturbation theory applied to surfaces. A. B. Anderson2

has consistently couched his explanations in that language, and so have

Shustorovich and Baetzold 2 - Shustorovich's account of chemisorption is

based on an explicit perturbation-theoretic model. There is a very nice,

4 quite chemical treatment of such a model in the work of Gadzukl9 a, based on

earlier considerations by Grimleyl~b and van Santen1c draws interaction dia-

grams quite analogous to ours. Salem and his coworkersl9d have developed

a related perturbation theory based on a way of thinking about catalysis

that includes a discussion of model finite Hrckel crystals, privileged

orbitals, generalized interactions diagrams, and the dissolution of adsorbate

into catalyst bands.

Let's make these interactions and interactions diagrams come to life

'- .through some specific applications.

!..........................................

.iio"IL

- 28 -

A Case Study: CO on Ni(100)

The Ni(100)-CO system already discussed9 seemed to provide an excellent

example of the primary two-electron interactions at work. We found charge

transfer from 5o (its population going from 2.0 in the free CO to 1.62 in

the CO-surface complex) and back donation from the surface to 2,* (whose

population rose from 0 to 0.74). Actually, there is an interesting wrinkle

here, in that the 4 and 0 electron interactions mentioned in point (3), above,

manifest themselves.

To set a basis for what we will discuss, let's prepare a model molecular

system for comparison. We'll build a metal-carbonyl bond between a d6 MLs

system and a carbon monoxide. The interaction diagram, 23, should certainly

be familiar; the acceptor function of the MLn fragment is provided by a

low-lying dsp hybrid.20 The two-electron bonding interactions are quite

;C0 0C C

.'.

hy

xy 0xz,yz -" C

'5,a

0

2 3

explicit. They result (M Ni"*, L H-, M - H 1.7 A, M - CC 1.9 A) in a

depopulation of 5j by 0.41, and a population of 2-'* by 0.51 Electrons.

*°

...--- *-..---.-.-....'-:--.--:'r" '.".j'.", ,. i- ',"# ,...'."../','".' '", .""..i ," ",,.".. . '. " ",.".'" :,.: :."--",: -'- _w -",,

Table 1. Some Electron Densities in a Model H5NiC0*,and the c(2x2)CO-Ni(100)System

NiHs NiH5(CO) CO Ni(100) c(2x2)CO-Ni(100) CO

5a -- 1.59 2.0 5a ~ - 1.62 2.0

27r* -- 0.51 0.0 2Tr* -- 0.74 0.0

hy 0.0 0.48 d- da 1.93 1.43 -

d~r 4.0 3.52 d- da 3.81 3.31 -

CO -- 10.01 10.0 CO -- 10.25 10.0

/H 5Ni 16.0 15.99 -- Nia 10.17b 9.37 -

a) for those surface atoms which have CO on them.

b) this number is not 10.0, because the surface layer of the slab is nega-tive relative to the inner layer.

p , r

-29-

The metal functions involved in these interactions react correspondingly:

so xz,yz loses 0.48 electrons, and the hybrid orbital gains 0.48 . The

net charge drifts are pretty well-described by the sum of what happens in

these orbitals: CO as a whole gains O.Ole-, and the MLn fragment loses the

same. The information is summarized in Table 1.

If one just looks at the CO, what happens on the surface seems to be

similar, as I noted above. And the d,. orbitals, xz,yz are depopulated in

c(2x2)CO-Ni(100). But the d., the z2 , the surface analogue of the hybrid,

actually loses electron density on chemisorption of CO.

What is happening here is that the CO 5a is interacting with the entire

z2 band, but perhaps more with its bottom, where the coupling overlap is

greater. The z2 band is nearly filled (1.93 in the metal slab). The net

5 -d band interaction would be repulsive, mainly due to four-electron two-

orbital interactions, were it not for the pushing of someantibonding combinations

24

.°o

above the Fermi level (see 24 for a schematic). The net result is some

loss of z2 density and concomitant bonding.2

Where do those "lost" electrons go? Table 1 indicates that some, but

certainly not all, go to the CO. Many are "dumped" at the Fermi level into

orbitals that are mainly metal d band, but on the inner metal atoms, or on

. . . . . . .

° .

V

surface atoms not under CO. me 4i1 return to the bonding consequences ut

these electrons, interaction (, in a while.

3efore leaving this instructive example, trust tte point is not

lost that the primary bonding interactions and 01 are refrarkably ald IIe

in the molecule and on the surface. These forward and tack donations are.

of course, the consequence of :ne classical ewar-Chatt-,uncanson -odel of

ethylene or another fragment bonding in an organometallic molecule. :n tre

surface case, this is often termed the Blyholder model, the reference being

to a perceptive early suggestion of such bonding for CO on surfaces. b More

generally, interactions Q and Q are the fundamental electronic origins

* of the cluster-surface analogy. This is a remarkably useful construc-

tion of a structural, spectroscopic and thermodynamic link between organo-

metallic chemistry and surface science.23

....

.%

IUw

9.

.. .- ", " ",: -. - -:.:..'....-'.-''.' .' .. '.-' . .. ",". . - .'. . -' . ... . . . v ... ' . .'. ' S' ., ., ,

p 31

.arrers to Ckemisorption

The repulsive two-orbital four-electron interaction that turns into

an attractive, bonding force when the electrons, rising in energy, are

dumped at the Fermi level is not just a curiosity. I think that it is res-

ponsible for observea kinetic barriers to chemisorption and the possible

existence of several independent potential energy minima as a molecule

approaches a surface.

Consider a model molecule, simplified here to a single occupied level,

approaching a surface. Some schematic level diagrams and an associated

total energy curve are drawn in Fig. 12. The approach coordinate trans-

Figure 12

. lates into electron interaction, Far away there is just repulsion,

which grows as the molecule approaches the surface. But when the antibonding

combination is pushed up to the Fermi level, the electrons leave it for the

reservoir of hole states, empty metal band levels. Further interaction is

attractive.

This simple picture was first given, to my knowledge, by E.L. Garfunkel

and by C. Minot and their coworkers.2" In reality, the repulsion at large

metal adsorbate distances will be mitigated and, in some cases overcome, by

attractive two-electron interactions of type (D or T (see 20). But the

presence of the interaction, I think, is quite general. It is responsible, in

my opinion, for some of the large kinetic barriers to CO chemisorption and CH,

decomposition measured in the elegant beam experiments of S.T. Ceyer and coworkers.

7,n reality, what we are describing is a surface crossing. And there

may be not one, but several such, for it is not a single level, but groups

of levels which are pushed" above the Fermi level. There may be several

metastable minima, precursor states, as a molecule approaches a surface.-'

04

.7 T- 7 - - 7T - - -T V

"" T

R

7,7/7/7//

I0

'.°

Figure 12. A schematic drawing showing how the interactions of levels (bottom)

can lead to a potential energy curve (top) which has a substantial barrier

to chemisorption. R measures the approach of a molecule, symbolized by a

single interacting electron pair, to a surface. At large R repulsive four-

electron interactions dominate. At some R (second point from left), the anti-

bonding combination crosses the Fermi level, and dumps its electrons. At

shorter R there is bonding.

J 12

.1

. . . . . . -I n ' ,, '- : - , -. . :; ,. '

: i t- s ection v e "ave mentioned, for the second tv-e, *me ondlr.

.2 -onsecqences 31 emptying, at the Fermi level, molecular orbltals delocalzed

ver adsorbate and surface, and antibonding between the two. Salahub- and

Znderson- stress the same effect. There is a close relationship between this

phenomenon and a clever suggestion made some time ago by Mango and Schacnt-

scnneider -' on the way in which metal atoms (with associated ligands) lower

the activation barriers for forbidden concerted reactions. They pointed out

that such electrons, instead of proceeding on to high antibonding levels, can

be transferred to the metal. We, and others, have worked out the details of

this kind of catalysis for some specific organometallic reactions, such as

reductive elimination.,' It's quite a general phenomenon, and we will return

N..- to it again in a subsequent section.0O

.d'."

, " . .

-

S£. ............................

. . . . .. . . . . . . . . . . . . . .

33-

e~~2res t'ol is j lomprormrse

.onsider again the basic rnolecule-sArface interaction diagram 25, now

drawn s~eciffing the bonding witnin each component. The occupied orbitals

ontibcndil'1 4111111 nitoflding

A Surface

0bonding bonding

in A inurface

4 25 A Surface

of the molecule A are generally bonding or nonbonding within that molecule,

the unfilled orbitals of A are usually antibonding. The situation on the

metal depends on where in a band the Fermi level lies: the bottom of the d

band is metal-metal bonding, the top is metal-metal antibonding. This is

why the cohesive energy of the transition metals reaches a maximum around

the middle of the transition series. Most of the metals of catalytic

interest are in the middle or right part of the transition series. It

follows that at the Fermi level the orbitals are generally metal-metal

antibonding.

What is the effect of the various interactions on bonding within and

between the adsorbate and the surface? Interactions (Q and Q are easiest

to analyze - they bind the molecule to the surface, and in the process they

transfer electron density from generally bonding orbitals -,,e component

I

- 34 -

to antibonding orbitals in the other. The net result: a bond is formed

between the adsorbed molecule A and the surface. But bonding within the

surface and within A is weakened.

Bowding

26

Schematically this is indicated in 26. What about interactions © and

For moderate interaction is repulsive and 0 has no effect.Neither does anything to bonding within A or the surface. When interaction

grows, and antibonding ()or bonding ()states are swept past the

Fermi level, these interactions provide molecule-surface bonding. At the

same time, they weaken bonding in A, transferring electron density into

".-

antibonding levels and out of bonding ones. What the effect of such strong

interaction of tyc 0 or or, more generally, of second order electron

eshifts, type antis on bonding within the surface - that depends on the

position of the Fermi level and the net electron drift.

The sum total of these interactions is still the picture of 26: metal-

adsorbate bonding is accomplished at the expense of bonding within the metal

and the adsorbed molecule. This is the compromise alluded to in the heading

of this section.

A specific case will illustrate this point, and show the way to an

important consequence of this very simple notion.

Earlier we drew four possible geometries for a layer of acetylene,

coverage ads on top of Pt(111), 3. Table 2 shows some of the indices

.4 4..

. .. . . . . . . . . . . . . ..ection.

35

*Z of the interaction in the four alternative geometries, in particular the

occupations of the four acetylene fragment orbitals (7,7,,*,7*), the

d various overlap populations, and calculated binding energies.

Table 2

The three-fold bridging geometry (3c) is favored, in agreement with

experiment and other theoretical results. 2 One should say right away that

this may be an accident - the extended H~ckel method is not especially good

at predicting binding energies. The two-fold (3b) and four-fold (3d) sites

are slightly less bound, but more stable than the one-fold site, 3a. But

this order of stability is not a reflection of the extent of interaction.

Let's see how and why this is so.

The magnitude of interaction could be gauged by looking at the acety-

lene fragment orbital populations, or the overlap population. In the

detailed discussion of the two-fold site in an earlier section, we saw - and

-.*more or less unaffected, 70 depopulated 'T* occupied. As a consequence,

Pt-C bonds are formed, the C-C bond weakened, and (interaction ) some Pt-Pt

bonds on the surface weakened. A glance at the fragment MO populations and

overlap populations in Table 2 shows that all this happens much more in the

-four-fold site 3d - note that even 7 and 7* get strongly involved. The

most effective interaction here is that shown in 27. Note that it is pri-

marily of type .

2Z~

27

I

.-. -° °. , - ° - . , .- .- . ° . =- • o , . . - _ . • . o . . . ..

-36-

By any measure, interaction is least in the on-top or one-fold geometry,

most in the four-fold one. See, for instance, the trend in C-C overlap

populations, or the Pt-Pt bond weakening. In the four-fold geometry one

Pt-Pt overlap population is even negative - bonding between metal atoms

in the surface is being destroyed. It is clear that the favorable condition

for chemisorption, or the preference of a hydrocarbon fragment for a

specific surface site, are determined by a balance between increased sur-

face-adsorbate bonding and loss of bonding within the surface or in the

adsorbed molecule.

Adsorbate induced surface reconstruction and dissociative chemisorption

are merely natural extremes of this delicate balance. In each case, strong

surface-adsorbate interactions direct the course of the transformation,

either breaking up bonding in the surface so that it reconstructs, or

disrupting the adsorbed molecules. An incisive discussion of the latter

situation, for the case of acetylene on iron and vanadium surfaces has been

provided by A. B. Anderson."

..€.A',

4

-" -. -'-. . " "- .. -_ i, - C C *., ..... " '.F - A . . x..' A ,''A ,t5£ ' ' A: . a.r' ' - "

Table 2. Bonding Characteristics of Several Acetylene Adsorption Siteson Pt(111).

C2H2 BareSurface

Bindingenergya 3.56 4.68 4.74 4.46(eV)

Overlap populationC-C 1.703 1.405 1.319 1.206 1.080Pt1-Pt2 0.136 0.126 0.077 0.088 -0.024Pt2-Pt3 0.136 0.139 0.126 0.067 0.062Ptj-Pt, 0.136 0.130 0.126 0.149 0.062Pt1 -Cb 0.295 0.543 0.517 0.330Pt3-C 0.001 0.005 0.193 0.266

Occupations** 0.0 0.078 0.166 0.330 0.533r* 0.0 0.811 1.059 1.028 0.893

TT 2.0 1.733 1.588 1.591 1.566T- 2.0 1.959 1.956 1.731 1.530

a Taken as the difference: E(slab) + E(C2H2) - E(geometry) in eV.

b The carbon atom here is the closest to the particular Pt atom underconsideration.

I

-37-

Qualitative Reasoning About Orbital Interactions on Surfaces

The previous sections have shown that one can work back from band

structu.es and densities of states to local chemical actions - electron

transfer and bond formation. It may still seem that the qualitative con-

struction of surface-adsorbate orbital interaction diagrams, in the forward

direction, is difficult. There are all these orbitals. How to estimate

their relative interaction?

Symmetry and perturbation theory make such a forward construction

relatively simple, as they do for molecules. First, in extended systems

the wave vector k is also a symmetry label, classifying different irreducible

e representations of the translation group. In molecules, only levels belong-

ing to the same irreducible representation interact. Similarly, in the solid

only levels of the same k can mix with each other."

Second, the strength of any interaction is measured by the same expres-

sion as for molecules:.,'-" [Hij J2

Eio-EJo

Overlap and separation in energy matter, and can be estimated.7d,18~19

There are some complicating consequences of there being a multitude

of levels, to be sure. Instead of just saying "this level does (or does

not) interact with another one", we may have to say "this level interacts

more (or less) effectively with such and such part of a band". Let me

illustrate this with some examples.

Consider the interaction of methyl, CHj, with a surface, in on-top

and bridging sites, 28.31 Let's assume low coverage. The important methyl

I

- 38 -

%C C

on-top brdging

a 26 b

orbital is obviously its lone pair n, for it will have the greatest overlap

with any surface orbitals. The position of the lone pair relative to a

metal d band is sketched in 29. How to analyze the interactions?

29

It's useful to take things apart and consider the metal levels one

by one. 30, below, illustrates schematically some representative orbitals

in the z' and xz bands. The orbitals at the bottom of a band are metal-metal

bonding, those in the middle non-bonding, at the top of the band antibonding.

While things are assuredly more complicated in three dimension;, these one-

dimensional pictures are indicative of what transpires.

so k. t N.

- 39 -

The methyl lone pair (it's really a band, but the band is narrow for

low coverage) interacts with the entire z2 and xz bands of the metal, except

at a few special symmetry-determined points where the overlap is zero. But

it's easy to rank the magnitude of the overlaps, as I've done in 31 for

on-top adsorption.

* / /

Ii 0,-7.1 2 211

031 b

n interacts with the entire z2 band, butbecause of the betterenergy match,

- more strongly so with the bottom of the band, as 32 shows. For interaction with xz,

n the overlap is zero at the top and bottom of the band , and never very efficient else-

L"' where (33). For adsorption in the bridge , as in 28b, we would estimate the

004

O- ,

Co>32

7W __

-40-

4,34

wI

Pq

/ // ] ///

I.""' "

// / t

. 34

overlaps to go as 34. There is nothing mysterious in these constructions.

The use of the perturbation theoretic apparatus and specifically the role of

k in delimiting interactions on surfaces goes back to the work of Grimley,,b

*1 and Gadzuklsc, and has been consistently stressed by Salem.i9d

For a second example, let's return to acetylene on Pt(111), specifi-

cally in the two-fold and four-fold geometries. 2 In the two-fold geometry,

we saw earlier (from the decompostion of the DOS) that the most important

acetylene orbitals were 7. and ra*. These point toward the surface. Not

surprisingly, their major interaction is with the surface z2 band. But 7

and 7T* interact preferentially with different parts of the band, picking

out those metal surface orbitals which have similar nodal patterns as the

adsorbate. 35 shows this - in the two-fold geometry at hand the ,. orbital

interacts better with the bottom of the surface z2 band and the 7* with

,'.

, 35

4,.

-41-

the top of that band.

Note the "restructuring" of the z' band that results: in that band

*some metal-metal bonding levels that were at the bottom of the band are

pushed up, while some of the metal-"'tal antibonding levels are pushed down.

Here, very clearly, is part of the reason for weakening of metal-metal bon-

ding on chemisorption.

We pointed out earlier that four-fold site chemisorption was particu-

larly effective in weakening the surface bonding, and transferring electrons

into 7* as well as Ira*, thus also weakening C-C bonding. The interaction

responsible was drawn out in 27. Note that it involves the overlap of ,*

specifically with the top of the xz band. Two formally empty orbitals

interact strongly, and their bonding component (which is antibonding within

the metal and within the molecule) is occupied.

In general, it is possible to carry over frontier orbital arguments, the

language of one-electron perturbation theory, to the analysis of surfaces.

-7e-

4 . . ... .b - -t a .W.

- 42 -

The Fermi Level Matters

Ultimately one wants to understand the catalytic reactivity of metal

surfaces. What we have learned experimentally is that reactivity depends

in interesting ways on the metal, on the surface exposed, on the impurities

or coadsorbates on that surface, on defects, on the coverage of the surface.

Theory is quite far behind in understanding these determining factors of

surface reactivity, but some pieces of understanding emerge. One such is

the role of the Fermi level.

The Fermi level in all transition series falls in the d band - if there

is a total of x electrons in the (n)d and (n+l)s levels, then not a bad

approximation to the configuration or effective valence state of any metal

is dx-Is1. The filling of the d band increases as one goes to the right

in the transition series. But what about the position of the Fermi level?

Over the greater part of the transition series it falls, or its magnitude

is greater.

4hat actually happens is shown schematically in 36, perhaps the single

-ost iTportant diagram of metal physics. For a detailed discussion of

too of dbond

3S E

ri V Cr Mn Feg Co Ni

I

-t-.-..-~~~~~~~~~.'... .< ...... . .. . .-/'.-.--.....-... .. ..

-43-

the band structure the reader is directed to the definite work of 0. K.

Andersen. 32 Roughly, what transpires is that the center of gravity of the

d band falls as one moves to the right in the transition series. This is

a consequence of the ineffective shielding of the nucleus for one d electron

by all the other d electrons. The ionization potential of a single d elec-

tron increases to the right. The orbitals also become more contracted,

therefore the less dispersed band at the right. At the same time, the band

filling increases. The position of the band center of gravity and the filling

compete; the former wins out. Thus the Fermi level falls at the right side

of the transition series. What happens in the middle is a little more

* complicated.32

Let's see the consequences of this trend for two chemical reactions.

One is well-studied, the dissociative chemisorption of CO. The other is

less well-known, but certainly matters, for it must occur in Fischer-Tropsch

catalysis. This is the coupling of two alkyl groups on a surface to give

an alkane.

In general, early and middle transition metals break up carbon mono-

xide, late ones just bind it molecularly.33 How the CO is broken up, in detail,

is not known. Obviously, at some point the oxygen end of the molecule must

come in contact with the metal atoms, even though the common coordination

mode on surfaces, as in molecular complexes, is through the carbon. In the

context of pathways of dissociation, the recent discovery of CO lying down

on some surfaces, 37, is intriguing. Perhaps such geometries intervene

C-6

37

on trie way to splitting the diatorrc *o c"erisorted ators.

-' , , . ' . , - -. .... - . . ., , .. ,. . ,. - .- .. . .. , .. . . . . . .. . . . . _ .

- 44 -

Parenthetically, the discovery of 37, and of some other surface species

bound in ways no molecular complex shows, should make inorganic and organo-

metallic chemists read the surface literature not only to find references

with which to decorate grant applications. The surface-cluster analogy,

of course, is a two-way street. So far, it has been used largely to provide

information (or comfort for speculations) for surface studies, drawing on

known molecular inorganic examples of binding of small molecules. But now

surface structural studies are better, and cases are emerging of entirely

novel surface binding modes. Can one design molecular complexes inspired

by structures such as 37?

* Returning to the problem of the metal surface influence onthe disso-

ciation of CO, we cannot study the reaction path, yet. But we can look at

molecular chemisorption, C end bonded, and see if there are any clues.

Table 3 shows one symptom of the bonding on several different surfaces,

Table 3

the population of CO 5a and 27*. 9

The population of 5a is almost constant, rising slowly as one moves

from the right to the middle. The population of 27*, however, rises sharply.

Not much is left of the CO bond by the time one gets to Ti. If one were

to couple, dynamically, further geometry changes - allowing the CO to stretch,

tilt toward the surface, etc. - one would surely get dissociation on the left

side of the series.

- The reason for these bonding trends is obvious. 38 superimposes the

position of CO 5o and 2* levels with the metal d band. 5o will interact

more weakly as one moves to the left, but the dramatic effect is on 27*.

.•. . .,

. . . . . .. . . . . . . . . . . . . . . . . .

'a Table 3. Some Orbital Populations in CO Chemisorbed on FirstTransition Series Surfaces (From Ref. 9)

Electron Densities in Fragment Orbitals

Ti(OOO1) Cr(11O) Fe(11O) Co(OOO1) Ni(100) Ni(111)

5cyS 1.73 1.67 1.62 1.60 1.60 1.59

2ir* 1.61 0.74 0.54 0.43 0.39 0.40

Aw% 4

am

- 45 -

top of dband

S.• ofttm

" ,of d bn

~carbonTi V CrI M ae Co Ni monoxide

3.

At the right it interacts, that is required for chemisorption. But 2-*

lies above the d band. In the middle and left of the transition series,

the Fermi level rises above 27*. 27* interacts more, is occupied to a greater

extent. This is the initial indicator of CO disruption.9

The second case we studied is one specific reaction likely to be impor-

tant in the reductive oligomerization of carbon monoxide over a heteroge-

neous catalyst, the Fischer-Tropsch synthesis. The reaction is complicated

and many mechanisms have been suggested. In the one I think likely, the

"carbide/methylene" mechanism", one follows a sequence of breaking up CO and H2,

hydrogenating the carbon to produce methyl, methylene, methyne on the sur-

face, followed by various chain-forming associations of these and termi-

nating reductive eliminations. It is one of those terminal steps I want to

discuss here, a prototype dissociation of two adsorbed methyls to give

ethane, 39. "

*u ". 'H

cN, cx,127~o ""%77-. T7TT/

39

A .7!

46 -

It's simple to write down 39, but it hides a wonderful variety of pro-

cesses. First, given a surface and a coverage, there is a preferred site

which methyls occupy, perhaps an equilibrium between several sites. Second,

.- .these methyls must migrate over the surface so as to come near each other.

A barrier, call it the "migration energy", may intervene. Third, one methyl

coming into the neighborhood of another may not be enough. It may have to

come really close, for instance, on-top of a neighboring metal atom. That

may cost energy, for one is creating locally a high-coverage situation,

one so high that it might normally be inaccessible. One could call this a

steric effect, but let's call it a "proximity energy". Fourth, there is

the activation energy to the actual C-C bond formation, once the components

are in place. Let's call this the "coupling barrier". Fifth, there might

be an energy binding the product molecule to the surface. It is unlikely

to be important for ethane, but might be substantial for other molecules.

It is artificial to dissect the reaction in this way, nature does it all at

once. But in our poor approach to reality (and here we are thinking in

terms of static energy surfaces; we haven't even begun to do dynamics, to

allow molecules to move on these surfaces), we can think of the components

of the barrier impeding coupling: binding + migration + proximity + coupling

+ desorption energies.

To be specific, let's choose three dense surfaces: Ti(001), Cr(11O)

and Co(O001). The calculations we carried out were for a 3-layer slab,

and initially a coverage = 1/3. Three binding sites that were considered

were on-top or one-fold, 40, bridging or two-fold, 41, capping or three-

fold, 42. The preferred site for each metal is the on-top site, 40.31

40 41 42

O4

- 47 -

The total binding energy is greater for Ti than Cr than Co. 43 is an

interaction diagram for CH3 chemisorption. The CH3 frontier orbital, a

carbon-based directed radical lobe, interacts with metal s and z2, much like

the CO 5j. Some z2 states are pushed up above the Fermi level, and this

is one component of the bonding. The other is an electron transfer factor.

We started with a neutral surface and a neutral methyl. But the methyl

43

lobe has room for 2 electrons. Metal electrons readily occupy it. This

provides an additional binding energy. And because the Fermi levels increase

to the left in the transition series, this ionic component contributes more

for Ti than for Co.31

In a sense, these binding energies of a single ligand are not relevant

to the estimation of relative coupling rates of two ligands on different

surfaces. But even they show the effect of the Fermi level. A first step

in coupling methyls is to consider the migration barriers of isolated groups.

This is done in 44. The relative energy zero in each case is the most

stable on-top geometry.

€L

448

.V V V V V V

Rsbatiw E (eV):

Co 0.0 1.1 1.4Cr : 0.0 0.9 0.?

-.- Ti : 0.0 0.5 0.5

*The implication of 44 is that for Co the preferred migration itineraries

are via bridged transition states, 45, but for Ti and Cr surfaces, 45 and 46

are competitive. For the reasons behind the magnitudes of the computed bar-

riers, the reader is referred to our full paper.3" Could one design an

45 46

_212

; experiment to probe these migration alternatives? CH3 is still an unconinon

surface fragment. 25

If we bring two methyl groups to on-top sites on adjacent metals, we see

a splitting in the occupied CH3 states. This is a typical two-orbital four-

electron interaction, the way steric effects manifest themselves in one-electron

calculations. If we compare the binding energy per methyl group in these

proximate structures to the same energy for low coverage isolated methyls,

@.4

:..2" i

- 49 -

44

we get the calculated proximity energies of 47. The destabilization increases

MI

Co 0.77 oV47 Cr 0.53

Ti -0.05

with d electron count because some of the d levels occupied carry CH3 lone

pair contributions.

What happens when two CH3 groups actually couple? The reaction begins

with both CH3 lone pairs nearly filled, i.e. a representation near CH3-. A

new C-Ca bond forms, and, as usual, we must consider a and a* combinations,

nltn 2 . Both are filled initially, but as the C-C bond forms, the 0* combina-

tion will be pushed up. Eventually, it will dump its electrons into the metal

d-band.

The actual evolution of the DOS and COOP curves allows one to follow this

process in detail. For instance, Fig. 13 shows the contribution of the methyl

n orbital, the radical lobe, to the total DOS along a hypothetical coupling

reaction coordinate. Note the gradual formation of a two-peaked structure.

Figure 13

COOP curves show the lower peak is C-C bonding, the upper one C-C antibonding.

These are the a and a* bonds of the ethane that is being formed.

The total energy of the system increases along the reaction path, as

nl-nz becomes more antibonding. At the Fermi Level, there is a turning point

in the total energy. o* = n1-n2 is vacated. The energy decreases, following

nl+n2. The position of the Fermi level determines the tirning point. So

the coupling activation energy is greater for Ti than for Cr bnan for CO.

...........

......................

o04 -*

so I -a - U) 4- :: ca

0 0 c,.. b 4-' u 0.

........ (..(A" (A 0

S-3:

•.- (: -

E.

"'_-. L... ....-. . .- ... .. . ... . c0

4-)

* 0 0 "

"' 0 0 E* "p. - --I ¢.

OCD a) r_ J

b 4- > --

o o 0a 0)

- 0 ---

........

0 4 *4- m .0

= 0 0

CD o U

0) U..4..) 0)

L )0 --- 4

p" ,Q"0 .4:. 0• .'- . . .A .,-

b :(AO) AU3.~~ .- .- . . . .

0. 0 A

0) S..

r._' " " - , " - - ' " " , " '.- . - -.- , ' ' -. .-.-' ii:'.-J ' . . . . _',, :L_64'.,... _ . . ,-0 0.-,...'.'JI T e,..'.". 'w. .r ' '. . '. '. '.. .' ' . /€ . - ..'-"- .e " ",. ,' .'',. " '- v,' .' . - '-,." - - - "0-) -(A e.,e 4-) '

-50-

The reader familiar with reductive eliminations in organometallic chemis-

try will note essential similarities. 9 We also mention here again the rela-

tionship of our argument to the qualitative notions of Mango and Schacht-

schneider on how coordinated metal atoms affect organic reactions."2

The position of the Fermi level clearly is an important factor in

determining binding and reactivity on metal surfaces.

"I

Mi - 51-

Remarks

What I have tried to do in this work is to move simultaneously in two

directions to form a link between chemistry and physics by introducing

simple band structure perspectives into chemical thinking about surfaces.

And I have tried to interpret these delocalized band structures from a very

chemical point of view - frontier orbital considerations based on interaction

diagrams.

The elements of solid state physics, the ideas of Bloch functions, band

structures, and densities of states need more exposure among chemists. And,

incidentally, physicists might benefit from learning to explain these ideas,

with which they are so familiar, with words and pictures rather than equa-

tions. I suspect that they would find that in the process they would under-

stand their own physics better.

Ultimately, the treatment of electronic structure in extended systems

is no more complicated (nor is it less so) than in discrete molecules. The

brio to local chemical action is through decompositions of the DOS and the

Crystal Orbital Overlap Population (COOP) curves. These deal with the funda-

mental questions: Where are the electrons? Where can I find the bonds?

With these tools in hand, one can construct interaction diagrams for

surface reactions, as one does for discrete molecules. The warning is that

these diagrams are qualitative constructs, within the framework of a one-

electron theory. This is not to downgrade them - witness how much they've

contributed to our understanding of molecular chemistry.

In general, the interactions on a surface resemble those in molecules.

The interesting and important differences are two: 1) There are essential

consequences of strong four- and zero-electron two-orbital inte"actions

turning into two-electron ones. 2) As a corrolary, there ,- 7hifts of

.. .

52

electron density around the Fermi level which have bonding consequences.

In addition to providing a general picture of bonding of molecules to

surfaces, the orbital interaction model, buttressed by detailed DOS and COOP

tracing of consequences, provides us with many concepts. We see how effec-

tive chemisorption is one point, a compromise, in a continuum which embraces

dissociative chemisorption and surface reconstruction. We see now barriers

to chemisorption can arise. We see how in detail the Fermi level can influ-

ence reactivity. And, not the least, we can see the essential electronic

similarities, and the important differences between bonding in discrete

molecules and on surfaces.

1

r

'4

.°

. .. .... .. .. .... ..., , ....

-53-

Acknowledgment

The theoretical work of my group in the surface chemistry area was

supported initially by the Materials Science Center (MSC) atCornell University,

funded by the Materials Research Division of the National Science Foun-

dation. MSCfurnishedan interdisciplinary setting, a means of interacting

with other researchers in the surface science area, that was very effective

in introducing a novice to the important work in the field. I am grateful to

Robert E. Hughes, Herb H. Johnson, and Robert H. Silsbee, the MSC directors,

for providing that supporting structure. In the last five years my surface-

related research has been generously supported by the Office of Naval esearch.

That support is in the form of a joint research program with 2ohn Wilkins,

and led to some joint group meetings that were extremely instructive.

Thor Rhodin has been mainly responsible for introducing me to tne intel-

lectual riches of surface chemistry and physics, and I am grateful to him and

his students for their instruction.

The calculations used in our work required much programming and inter-

pretational work. I owe all of this to a remarkable group of coworkers who

implemented the band structure programs and associated graphics. These are

Myung-Hwan Whangbo, Charles Wilker, Miklos Kertesz, Tim Hughbanks, Sunil

Wijeyesekera, Chong Zheng and Maria Zonnevylle. Some important ideas were

borrowed from Jeremy Burdett.

Al Anderson was instrumental in getting me started in thinking about

applying extended HUckel calculations to surfaces. The band approach, coupled

to an interaction diagram and frontier orbital way of thinking, evolved from

a study that Jean-Yves Saillard carried out of molecular and surface C-H and

H-H activation. We learned a lot together. A subsequent coll3boration with

J'r6me Silvestre helped to focus many of the ideas in this paper. important

"--. ."' ' .. ' . '. - -I ' , ," , '- . -: '-' " . -' .' ' ' -. ', -'".'." -'-' ', --. ' i,: '- .' ' ".? ' - , , " *4

.- - 54 -

2ontributions were also made by Shen-Shu Sung, Chong Zheng, Yitzhak Apeloig,

Sariel :eroka, Maria Zonnevylle, Susan Jansen, Dragan Vu~kovic.

1 am grateful to Elisabeth Fields and Jane Jorgensen for the great

drawings and to Linda Kapitany for her expert secretarial help. This manu-

script was written while I held the Tage Erlander Professorship of the Swedisn

Science Research Council. The hospitality of Per Siegbahn at the Institute

of 'neoretical Physics of the University of Stockholm, and Sten Andersson and

5alo Gronowitz of the Chemical Center in Lund, and their staffs, is gratefully

acknowledged, as well as the assistance of J~r~me Silvestre, Jing Li and Marja

Zonnevylle in the writing and associated computations.

0

:.

-4,

°°

V"

* ..

" REFERENCES

1. For a highly readable introduction to surface chemistry, see Somoriai,G. A. "Chemistry in Two Dimensions: SurfacesI, Cornell -nvers'ty ress,

Ithaca (1931). See also Rhodin, T. N., Ertl, G. EdS., "The Nature of

the Surface Chemical Bond", North-Holland, Amsterdam, 1979.

2. 1 cannot orovide here a bibliography of all theoretical studies in the

surface area, because they are too many. But I do want to mention here

the worko 1 three groups that have made, in my opinion, important contri-

butions to a chemical and theoretical understanding of surface reactions.

One is Alfred B. Anderson, who has analyzed most important catalytic

0 reactions, anticipating many of the results presented in this paper.

A leading reference to his work is Kang, D. B., Anderson, A. B. Surf.

Sci. 1985, 155, 639. Further references will come up below. Evgeny

Shustorovich and Roger C. Baetzold, working separately and together, have

both carried out detailed calculations and come up with an important

" erturbation-theory-based model for chemisorption phenomena: Shustorovich, .,

Surf. Sci. Reports 1986, 6, 1 and references therein; Shustorovich, L.,

Baetzold, R.C. Science 1985, 227, 876. Christian Minot has worked out some

;eneral and specific chemisorption problems: Minot, C., Bigot, B.;

Harati, A. Nouv. J. Chim. 1986, 10, 461; J. Amer. Chem. Soc. 1986, 108,

196; Minot, C.; Van Hove, M.A.; Somorjai, G.A. Surf. Sci. 1983, 127,441;

Bigot, B.; Minot, C. J. Amer. Chem. Soc. 1984, 106, 6601, and subsequent

re,_ ,rences.

:eviews of some of the theoretical work of other groups may be found

in Gavezzotti, A.; Simonetta, M. Adv. Quantum Chem. 1980, 12, 103.;

Messmer, R.P. in "Semiempirical Methods in Electronic Structure Calcu-

lations, Part B: Applications", Ed. Segal, G.A., Plenum, 'ew York, 1977;

Koutecky, ].; Fantucci, P. Chem. evs. 1986, 86, 539; Coren, M.L., Arn.

. . . 4, 34, 537.

e e

- 56 -

3. The extended Huckel method was devised for molecules by Hoffmann, .

.iscomb, '4. N. j. Chem. Phys. 1963, 39, 1397. The band structure pro-

grams using this method evolved in my group in a collaborative effort

involving coworkers acknowledged in the Appendix.

4. The following references are just ways in to the vast literature of

reconstruction: Kleinle, G.; Penka, V., Behm, R. J.; Ertl, G.;

Moritz, W. Phys. Rev. Lett. 1987, 58, 148, Daum, W.; Lehwald, S.; Ibach,

H. Surf. Sci. 1986, 178, 528; Van Hove, M. A.; Koestner, R. J.; Stair,

P. C.; Biberian, J. P.; Kesmodel, L. L.; Bartos, I.; Somorjai, G. A.

Surf. Sci. 1981, 103, Inglesfield, J. E.; Progr. Surf. Sci. 1985, 20,

105; King, D. A. Phys. Scripta 1983, 4, 34; Chan, C.-M.; Van Hove, M.A.

Surf. Sci. 1986, 171, 226; Estrup, P. J. in "Chemistry and Physics of

Solids", Vol. V, ed. , p. 203, Thiry,

P. A. J. Elec. Spectr. Rel. Phen. 1986, 39, 273.

5 a. Wade, K. Chem. Commun. 1971, 792; Inorg. Nucl. Lett. 1972, 8, 559;

"Electron Deficient Compounds", Nelson, London, 1971.

b. Mingos, D.M.P. Nature (London) Phys. Sci., 1972, 236, 99.

6. The modern classic solid state physics text is by Ashcroft, N. W.;

Mermin, N. D.: "Solid State Physics" Holt, Rinehart and Winston, New

York, 1976. Three other introductions to the field, ones which I think

are pedagogically effective and accessible to chemists are:

Harrison, W. A. "Solid State Theory", Dover, New York, 1980; Harrison,

W. A. "Electronic Structure and Properties of Solids", Freeman,

San Francisco, 1980; Altman, S. A. "Band Theory of Metals", Per-

gamon Press, New York, 1970.

7. Three review articles and a chapter of a book, all written by chemists

also provide an introduction to band theory:

a. Burdett, J. K. Progr. Solid State Them. 1994, 15, 173.

'I

S-.,-v

- 57

b. Whangbo, M.-H. in "Crystal Chemistry and Properties of Materials with

Quasi One-Dimensional Structures" Rouxel, J., Ed., Reidel, Dordrecht

1986, p. 27.

C. Hoffmann, R. Angew. Chem. 1987,

d. Albright, T. A., Burdett, J. K.; Whangbo, M.-H. "Orbital Interactions

in Chemistry", Wiley-lnterscience, New York, 1985, Chapter 20.

8. The results shown here and elsewhere in this paper are taken from ex-

tended H~ckel band calculations. These are then essentially "tight-

* binding calculations", overlap included, with the usual approximations

of the extended Huckel method for the wave functions and Hamiltonian

matrix elements. See Ref. 3.

9. For further details see Sung, S., Hoffmann, R. J. Amer. Chem. Soc.

1985, 107, 578.

10. For a discussion of other calculations of CO on Ni surfaces see Kasowski,

R. V.; Rhodin, T.; Tsai, M.-H. Appl. Phys. 1986, A41, 61, and references

therein.

11. Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833, 2343.

12. For further details see Silvestre, J., Hoffmann, R. Langmuir 1985, 1,

621.

13. See Saillard, J.-Y., Hoffmann, R. J. Amer. Chem. Soc. 1984, 106, 2006

for further details.

14. Shustorovich, E. J. Phys. Chem. 1983, 87, 14.

15. There is actually some disagreement in the literature on the relative

role of C-H and H-H i and z* levels in interactions with metal surfaces.

• .A. B. Anderson finds i donation playing the major role. See e.g.

Anderson, A. B. J. Amer. Chem. Soc. 1977, 99, 696 and subsequent papers.

r. A-

p.°°

@4°

, •* ~ -

-58 -

16. COOP was introduced for extended systems in papers by Hughbanks, T.,

Hoffmann, R. J. Amer. Chem. Soc. 1983, 105, 3528; Wijeyesekera, S. D.,

Hoffmann, R. Organometal. j984, 3, 949; Kertesz, M.; Hoffmann, R. J.

Amer. Chem. Soc. 1984, 106, 3453. An analogous index in the HJckel

model, a bond order density, was introduced earlier by van Doorn, W.,

Kouteck', J. Int. J. Quantum Chem. 1977, 12, Suppl. 2, 13.

17. For some references to this rich story, see footnote 5 in Ref. 12.

An important early LEED analysis here was by Kesmodel, L. L.; Dubois,

L. H.; Somorjai, G. A. J. Chem. Phys. 1979, 70, 2180.

18 a. The frontier orbital concept is a torrent into which flowed many streams.

The ideas of Fukui were a crucial early contribution (the relevant

papers are cited by Fukui, K. Science 1982, 218, 747.) as was the per-

turbation theory based PMO approach of Dewar (see Dewar, M.J.S. "The

Molecular Orbital Theory of Organic Chemistry." McGraw-Hill, New York

1969 for the original references). The work of Salem was important

See :or-ensen, W.L., Salem, L. "The Organic Chemist's Book of Orbitals",

Adacemic Press, New York, 1973, for references and a model portrayal, in

the discussion preceeding the drawings, of the way of thinking which my

coworkers and I also espoused). The Albright, Burdett and Whangbo text

(Ref. 7d) carries through this philosophy for inorganic systems, and is

also an excellent source of references.

b. For surfaces, the frontier orbital approach is really there in the pio-

neering work of Blyholder, G., J. Phys. Chem. 1964, 68, 2772. In our

.ork in the surface field, we first used this way of thinking in Ref.

13, a side-by-side analysis of molecular and surface H-H and C-H acti-

vation. See also Ref. 19.

6

- 59 -

19 a. Gadzuk, J.A. Surf. Sci. 1974, 43, 44.

b. Grimley, T.B. J. Vac. Sci. Technol. 1971, 8, 31; in "Adsorption-Desorp-

tion Phenomena", ed. Ricca, F. 1972, Academic Press, New York, p. 215

and subsequent papers. See also Thorpe, B.J. Surf. Sci. 1972, 33, 306.

c. van Santen, R.A. Proc. 8th Int. Congr. Catal., Springer Verlag, Berlin,

1984, Vol. IV, p. 97; Far. Symp. Chem. Soc. 1986, 21,

d. Salem, L.; Leforestier, C. Surf. Sci. 1979, 82, 390; Salem, L., Elliott,

R. J. Mol. Struct. Theochem. 1983, 93, 75; Salem, L. J. Phys. Chem. 1985,

89, 5576; Salem. L.; Lefebvre, R. Chem. Phys. Lett. 1985, 122, 342.

e. There are several other papers that have discussed interaction diagrams,

privileged orbital sets or hybrids, or orbital symmetry considerations

in the solid. Among them, see Banholzer, W.F.; Park, Y.O.; Mak, K.M.,

Aasel, R.I., Surf. Sci. 1983, 128, 176; Masel, R.I., to be ublisted.

22. See Elian, M.; Hoffmann, R. Tnorg. Chem. 1975, 14, 1058.

21. The effect mentioned here has also been noted by Raatz, F.; Salahub,

0. R. Surf. Sci. 1984, 146, L609; Salahub, D. R.; Raatz, F. Int. J.

Quantum Chem. 1984, Symp. No. 18, 173; Andzelm, J.; Salahub, D. R.

int. -J. Quantum Chem. 1986, 29, 1091.

22. Dewar, M.J.S. Bull. Soc. Chim. Fr. 1951, 18, C71; Chatt, J.; Duncanson,

L. 4. 0. Them. Soc. 1153, 2939.

23. Muetterties, E. L. Chem. Soc. ?evs. 1982, 11, 283; Angew. Chem. :nt. Ed.

E-j l. 1978, 17, 545.

24. uarfunkel, E.L.; Minot, . ; 5avezzotti , '.,i imonetta, M. -ur . C .

-p36, 167, 177; ]arfunkel, E.L.; Feng, X. ..urf. Sci. 1986, 115, 445;

, inot, .; iot, B., Harati, A. Nouv. J. ChiM. 1986, 10, 461. Jee also

'ef. 21 and Shustorovich, E.M. Curf, Sci. 1985, 150, L115. For a dif-

.erent picture of tne barrier to cnemisorption, see Nirskov, :.K.;

-olloway, S.; ong, N.D. Surf. . ci. 1984, 137, 65; N0rskov, ,

. -'ou-Aeller, A.; .ohansson, O.K.; [.ndqvist, B.1. Phys. ev. ett. 1931,

!.,. .p

- 60 -

46, 257. See also Gadzuk, J. W.; Holloway, S. Chem. Phys. Lett. 1985,

114, 314.

25. 'ang, S. L.; Lee, M. B.; Beckerle, J. D.; Hines, M. A.; Ceyer, S. T.

J. Chem. Phys. 1985, 82, 2826; Tang, S. L.; Beckerle, J. D.; Lee, M. B.;

Ceyer, S. T. ibid. 1986, 84, 6488. See also Lo, T.-C.; Ehrlich, G.

Surf. Sci. 1987, 179, L19; Steinruck, H. P.; Hamza, A. V.; Madix, R. J.

Surf. Sci. 1986, 173, L571; King, D. A. CPC Critical ev. Sol. State

Sci. 1978, 7, 167; Cardillo, M. J.; Balooch, M.; Stickney, R. E.

Surf. Sci. 1974, 44, 358; Bickley, H.; Arlow, J. S.; Morris, M. j.;

King, D. A. Vacuum 1981, 31, 507, and references therein.

26. Several such minima have been computed in the interaction of atomic and

molecular adsorbates with Ni clusters: P.E.M. Siegbahn, private commu-

nication.

27. Kang and Anderson in Ref. 2 and papers cited there.

28. Mango, F. D.; Schachtschneider, J. H. J. Amer. Chem. Soc. 1967, 89,

2484; Mango, F. D. Coord. Chem. Revs. 1975, 15, 109.

29. Hoffmann, R. in "IUPAC. Frontiers of Chemistry", ed. Laidler, K.

Pergamon Press, Oxford 1982; Tatsumi, K., Hoffmann, R., Yamamoto, A.;

Stille, J. K. Bull. Chem. Soc. Jpn. 1981, 54, 1857. and references

therein.

30. Anderson, A. B., Mehandru, S. P. Surf. Sci. 1984, 136, 398; Kang, D. B.;

Anderson, A. B. ibid. 1986, 165, 221.

31. Zheng, C.; Apeloig, Y.; Hoffmann, R. J. Amer. Chem. Soc. 1987, 109,

32. Andersen, 0. K. in "The Electronic Structure of Complex Systems", ed.

Phariseau, P.; Temnmerman, W. M., Plenum Press, New York, 1984; idem, in

"Highlights of Condensed Matter Physics:, ed. Bassani, F.; Fumi, F.,

"Tossi, M. P., North-Holland, New York, 1985.

33. Broden, G.; Rhodin, T. N.; Brucker, C.; Benbow, H.; Z . . Surf.

Sci i976, 59, 593; --gel, dv.tl , . d. Catal >>, A, 1

-61-

34. Shinn, N. D.; Madey, T. E. Phys. Rev. Lett. 1984, 53, 2481; J Chem.

Phys. 1985, 83, 5928. On Pt3Ti a similar assignment has been made:

Bardi, U.; Dahlgren, D.; Ross, N. J. Catal. 1986, 100, 196. Also for

-1 CN on Cu and Pd surfaces: Kordesch, M. E., Stenzel, W.; Conrad, H.

J. Electr. Spectr. Rel. Phen. 1986, 38, 89; Somers, J. Kordesch, M. E.,

*i Lindner, Th., Conrad, H.; Bradshaw, A.M.; Williams, G. P. Phys. Pev. Lett.

1987, , For relevant theoretical work, see Mehandru, S. P.;

Anderson, A. B. Surf. Sci. 1986, 169, L281; Mehandru, S. P.;

Anderson, A. B.;Ross, P. N. J. Catal. 1986, 100, 210.

. 35. For a recent review, see Anderson, R. B. 'The Fischer-Tropsch Synthesis",

Academic Press, New York, 1984.

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