Theory nof chemisorption and heterogeneous catalysis

Phvsiea 127B (1984) 193-.202 North-I-loiland, Amstc:rd:~,m

T H E O R Y e l f CLqiEMI$OI~FI'ION Ad~ID HETF~OGF_,N~OUS C&TALYSIS J.K. N O R S K O V NORDITA, Blegdarm:oe~ ][7, DK-2IO0 Copenhagen O~ Denmark "t/)e insight in,'~>~e properties of ehemisorbed atoms and molecules gained from the eflccdve medium th~Dry ~s reviewed. For ~:omie ehemiso~tion, the full potential energy Sm'f~ has been celeu]~ltedin a number of eases and the properties of ~." interaction potential can be related to the v,~rametersdescribing the atom and surface in question. For molecular ¢hem/s~rpt~onand su;faee reaetiom, the effective mer~lumtheory can be used to make comparisor~ between binding energies znd .letivaton energies. The trends in chemical reaefi'.Atiesfor a number of ¢ataly~Sereaetlom atong the tmmition metal series an, I the role of surface rectifiers (poisons, promoters, etc.) has been studied in this way.

T h e interaction o'f a~ atom or molecule with a metal :;,urfaee is described to a l.%rge extent by the ground state adiabatic potential energy surface, which is tht:. total ground state energy of the interacting system min~s that of the constituents, calculated as a function1 of the coordinates of the adsorbate.~. In the adiabatic approximation, this is the potenliat energy surface on which the adsorbate nueAei mc,ve 1"1,2]. It determines equilibrit~m positions,, chemisorpdon energies, vibrational frequencia~, activation energies and, me're generally, the dynamics of surface reactions. Even in c*~es where electronic excitations during a reaction are important, the adiabatic potential ener~,y strrface m a y serve as a starting point for a treatment of the dynamics ~1,.2]. Unfortunately, the combination oi a s e m i infinite solid a n d the tow symmetry tlaat the presence of the adsorbate usually impo~.~.~o n the system m a k e s a d.ire~.~:calculation of the potential energy surface very demanding, even wit1 efficient methods like t~e local demiry approximation to treat exchange and correlation effects [3]. Consequently, o~ly a few caleda~tions <~xist at present. O n e approach has been to approximate the surface by a (small) finite elu~ter of ~x~oms [4]. Alternad~dy, a (thin) slat, has been ~ d [5, 6]. ]f hip~h coverages of adsc,:d~a~es are considered, the t~ansiational symmetry along the surface can be exploited and the r~umber of rooms p e r unit t*ll be kept low. t:inally, perhaps

~he largest n u m b e r of total energy caleuIatious up to now have used a jellium model to describe the metal [7-9]. In this model, the metal ion cores have been smeared out 0~s a homogeneous positive background, which is abruptly truncated at the surface. A n alternative approach is to make suitable apprpxffxtations in the total energy calculation to enab'~e a treatment of these low symmetry syst e m s T h e present paper is an ove~wiew of tile insi#~t which has been gained using one sud~ method, the effective medium theory [10, 11]. In particular, an attempt will be m a d e to provide a conceptual picture of the interactions involved ira chemisorptior, and to point out the important substrate and adsorbate parameters determining the properties of the interaction potential In the following, the effective medium theory is first briefly described and compared 1:o results of more elaborate calculations. Then, in ,,;ection 3, the properties of potential energy surfaces for atomic adsorption ,are discussed using hydrogen a n d oxygen adsorption on transition metal surfaces as examples. Final~y, in seetlon 4, some properties of potential energy surfaces for molecular adsorption are discussed and the implications for surface reactions and cata~ysls are pointed out. 2, ~_~e e~cc~ve m redg~mt approach The," effective medium approach is a perturbation theory which ea~ be used to evaluate the

0378-4363184/$93.09 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

194

J.K. Nor~'ko~ I The,,ry of cherrdaerpti~naud t~eterogencau$rxaatysis

difference 8 E in t h e binding energy of eat a t o m for molecule) when m o v e d from one host to another. Treating the difference betw~:=n the new and old host to first order: in the r e , o n 'a' close to the atom where t h e atomic p t>tentlal dominates, at~d the difference imtwe~u t h e h o s t with and without t h e atom to first o r d e r in the regio~ ot~tside, one ~gets [I ]]

1.0 00 -I,0

-2D' -30

el

(1)

Here ihe first, purely electrostatic term involves the difference &b~;"ir) in electrostatic pr~tential between the new a~td old hosts and the: a t o m induced charge density tin(r) in the ol,5 host. T h e integral is over the atomic region 'a" onty a n d the superscript --a on ~bo signifies that only the charge outside "a' mthst be included. In t h e second term z~n(e) ~is the atom-induced density of states and the term involves the difference in the sum of atom-induced one-electron energies evaluated for a rigidly shifted potential inside region 'a'. The result eq. (1) is derived within t h e local density approxiimation, but a simila:~- result can be obtained for a non-local e x c h a n g e correlation energy. Both the derivation a n d t h e result closely resembles ~he force calculations of ArJdersen ct al. [12]. T h e result eq. (1) can be used in two different ways. if the energy of, say, an atom ou~dde a metal surface is wan*ed, and it is possible to find a (hig.)x symmetry) system resembling the .,;urface in the vicinity ,of the atom in which the interaction energy is knowr~, then eq. (1) can he treed Io give the atrsolute in:teraction energy outside the surface. O n e very conveniem choice of starting t~liot is a h o m o g e n e o u s electre~ gas. tf the electron gas density is chosen a~s an average ft, of the true su:rfaee charge ,.4ensity ~z,(r) over the atominduccxl e,~eclrostatic potential, then the atomst~rfaee interaction energy. ~ E ~ n be written

D1I d E ( R ) = ...4~'~;"'(t,)Gl~))+ AE,,,~fB~I.

(2)

Here AE~;"¥ho) is the energy of the atom in a

L~__x_~ 000

001

p

, _u._l~

OOZ

003

% {~u.) Fig. L |meractior, ,:nerf.y '2E'~;"'(n~Oof tl~e He, H arm 0 with a homog.eoeous¢lecrtro,/as as ~ functioJlof etectroo gas densily n,. From reL 13.

h o m o g e n e o u s eEecltron gas of density ho including the electrostatic term ir~ eq. (1), which can be shown to depend on tic, only [11]. T h e second term in eq. (2) is just the one-electron energy term in eq. (1). A n atom e m b e d d e d in a homogeneous electron gas has s p h e . d ~ l symmetry and a n u m b e r of gJ'oups have calculated the binding energies [13]. Furthermore, the function AE~m(ttj) need only be calculated once and for all. It is a property of the atom in question. Examples are shown in fig. 1. For a rare gas like He, the interaction is al~ a y s repulsive.. It iis dominated by the kinetic ~=nergy cost on orthogonalizing m o r e ;and more electron gas states to the atomic stat~=s. ~:or reacfive gases like H and O, on the odaer hand, a m i n i m u m exists, indicating the willir,gness of lhese atoms to fon~ chemical bond.,;. T h e low density limit of ~he inter.~ction energy' is - A , where A is the atomic affinity. The decrease in energy a* densities larger than zero can be viewed as being due to the screening of the electron--electron repulsion in the negative ion. #d even higher densities, the kinetic energy repulsion takes over, as for the rarc gases.

J.K. N¢,rsko~ I i['h¢o~.*6,f chemisorption and heterogeneow catat)'si~ (a,}

195

{b)

. . . . . .. "---"~o~--'-~

. _l,o

t----------~-------~--

~9, ~

~

m

'

8

r-

- . - - . ~ . . ~ . . ~

7

~

•

j

-3

-2

-T

0 DISTA

i

2 NCE

ALO

3

2

N~

(0011

~

0

1

z

- a.u,

Fig. 2. Comparison of the .,.elf-consL~tcnfly ~tleulated eleet~n density outside a Ni(lt0) surface (a) with the result from OverlappingatC~micden.,;i~:ie~(b). The constamde~ity contours (valae~ in a~7~')are shown in a plane perpendicular to the surface. The ba_~ line in the (00l) direction goes throughthe Ni atom in the second layer just below the ~enter hollowsite in the .~.urfac~ pIane. Ft~m ref. 14.

Apart Lrom the funetton " AE=jr h~. (no), - one needs the surface charge density no(r) to calculate the first term in eq. (2). Self-consi~tem calculations of surface electron densities do exist now, but fortunately a mere superposition of atomic densities is usua!ly an excellent apgroximation for the pres~.'nt purposes [14]. qfki~s is illustrated in fig. 2, AE~o~ refle~-~s the difference in the oneelectron specU'um on going from the hemogenepus electron gas to the metal surface. If it is a free-electron-like m e a l these changes are expected to be small To tinct order in (no(r)-~a) one gets ~11]

~E~(R) -

(no(r)- ~L) ~ V(Ir-" RI) dr,

(3)

u

where .~ V is the atom-nduced effective potential

in the homogeneous electron gas. For transition metals, the interaction ~ith the d-bands must be treated to higher order in the adsorbate-metal d interaction V~d. The starting point is, however, not the free atom, but a renormatized atom embedded in an electron gas. As discussed above, 2mch atoms can be regarded as screened negative ions and they have filled valence states well below the Fermi energy. This is illustrated in fig. 3 for oxygen. The renormalized atom thus has a "closed sheiF well below the metal d-bands and the interaction is fairly weak. l't is usurdly calculated using the resonant level model [15, 16] taking parameters describing the dbands and the hopping matrix element from ref, 1:2. For hydrogen chemisorbed orl a Ni(I00) surface, two different "ab initio' calculations using a nickel c l ~ t e r 1"4] :,nd a slab [6]. respectively, exist. In table I these results are compared with

196

J.K. No,key /,~7"i~eoO,o[ chcmisorp~Fonand heterOgeneo~rraealysis where they are not interest/ng. In ~,e following two sections, examples of the two t3g,~s of application of eq. (1) wiB be given. :~

I.

H

a: fI'

L,-

i

0

I

3. A t o n e ¢he~z~so~lion

~

2

r leVI

A~

t.

fi

Fig. 3. The induced stale density xlD(~) for O in a homogeneous elecmc)n gas at diffurcnt densitios no. The arrow.,, denote the pc~sitionof the Ferrtff level in ~=eh case. From ref 13.

the effective medium theory results and to extyeriment. The general agreement is seen to be very good. The resulu; indicate an absolnw accuracy of the effective medium theory of the order 0 . S e V wlrh a ~aueh smaller error in energy differenee~. Another use of eq. (1) is for egtimating differences in interaction energies in cases where it is not possible to calculate absolute e n e r g ~ , or

"Fable I Comparison:, between ~'s.Ult'; of differenl calculati0r~ for hydrogen chemi.'~rl-ar£1Jothe four-fold coordinate center site 0utglde a Ni(1001 surl'at'~:: the chemi:sorptian ,ene~ AFperpendicular ~ibrational frequeno', ~,. and the NI-H b.aad )ength dr~,.H are ~nduded; also, the experimgnt'.d x~u~. are shown when found. "lq~eresets show a remarkable simihri~' con:ddering ihc differ,enCes b~ra,oen the apprcmches (~e te.'~l. The value~; from Ll,'n.rigar.~ndWitkir~ ate only p.relimlnat3t. HINil ~.OO> cenlL:r

ceV) Up~on and Gg~td~rd [~'] klmriga~ argt ~,~lkirt', tb~ Pro'sent ~ork fL~qycrlme nml

~3.0 - 5.4 -.2.7 -2.7

(raeV'~

tA)

73 90 76 74

1.78

l.gO 1,91

For atomic ehemisorption the absolute intera,-tion energies and their variation with the atomic positions can be well described starting from the atoms embedded in a homogeneous electron gas via eq. (2). In the present section, properties .of the atomic potential energy surface like the ehemisorption energy, the bond Ien~h, the ribrationed excitation energi~; and the activation energies for diffusion wilt be treated separately, and the main atom and sn~fface parameters determining them will be disct~sed.

3.i. The chemisorption energy In fig. 4 the calculated chemk~orption energies from eq- (2) for ihydrogen on all the transkion metals are compared to exper/mentul values where four~d [153. It is clear that the absolute magnitude as well as the trends are well described. Outside a surface, the optimum value of the density where AE~'(ff0) has its minimum can always be found. The z~%. ..... in eq, (2) thus a~ways contributes the same a m o u n t / o the chemisorption energy. The trends are therefore governed by AE~,~ or. equivalently, by the in~ teraction with the metal d-electrons. The increasing binding strength towards the left in the series can simply be related to a decrease in the occupancy, of the and-bonding hydrogen--meted d levels as the d-band occupancy decreases. "To second order in the in,~eraclion V,~. the interaction is simply [11, 15~ -2(1-.f)l'~,#(Ca-e~). where Cd is the center of the d-~,~nds, e. the renormalized hydrogen atomic level, and f the deflree of filling of /he d-band. "The ( 1 - D behaviour is very pronounced ia fig. 4. Similar trends are found for oxygen ehemiso'~ption ener~:,'s [17] and are ",alsoexpected for ot'~er eleeU~onc,~tive adsorb~te~ producing a 'closed shell' wall below the Fermi level when embedded in a homogeneous eleciron gas.

1. K. Norskov I Theory of ehemisorption and heterogtneous catalysis

L

Sd

• ,TKEORV 0 leXflEI~EMENT

~t

19~,

AE tnV)

Z(~}

~,

I"

0.5

r.O

I$

AEI~t,

-t.O

.~.

.

-I

%. -~-------¢--~--~

.....

5e

ka

Hf

" 1

"! ~1 W

Re

Or;

Ir

Pt

An

Fig. 4* Comparison I:~e~.v.':,,:ncalcv!Ia;:ed and experimental eltemisorotion energies ter hydrogen on the rileS) el~e, paelted surface of 'each o'.fthe transition metals. "~nehorizonta! dashed line indicate~ the contrib,et:iou to the ¢hemlsorodon energy from ~E~"(;) in eq. (2). "fhlsconmbutien is the same for all of the metals, slincethe optimumsaffaeeelectron density where 2tE~'~'(/~o)h~lsits min~mt2mvalue of -2,45 eV can always be found ont~it'Ma su~a,c¢, The trends aloRg the ~efi~.~ are given by A~',¢ (see eq. (2)), In the ¢aleolated valu~, no correction fe,r ~e hydrogenzero-point energy has been indeded. From ref. 15.

Fig. 5. Binding energy of a hydrogen atont as ~t function of distance oul's~dc the fourfold coordinated centre site on a Ni(100) surface, Boll) the total bindingenergy .~E~,,~.;rod the various coml~neats in .e.~. (2) ~tre shown. AE,~ is spit! up into first (AE¢+aE~. see aL~o ref. IS) and higher order (..4Et'~q tern)s. From ref. l& harmonic approximation [15] .~

& 2 . Bond let,galls

Where~s , ~ . ~ , determine~; the trends in binding erter~ies "along the transition metal series, it varies very weakly w~th distance oumide a sur~'aee, as shown in fig. 3, The bond length is thus determined mainly by the requirement that the surface electron densiLY is equal to the optimum ~..alue. Th~s, fi~r instance, means that the bond i:ngth increases rapidly with coordination rmmber, as illnstrmed in table II, where bond lengths and vlb~tional freqaeneies for hydrogen and oxygen o.~ Nit100) and (t11) are shown. 3:3. Vibrational exci~affom

It is clear from fig. 5 that the perpendicular vilbradonal frequency o~x is also determined by A,E~(ffo). it is then easy to show that in the

i

.. ¥

m

Id ~,aE~"~,'(;~.)dno . . . . ., an~

a~

(4)

where M is the atomic (reduced) mass and z denotes the direction perpendicu/ar to the surface. For a given atom, w~t is thus mainly determined by the perpendicular derivative of the surface electron density. Assuming that n0(r) can be described by a superoosition of exponentially de,'aylng atomic densities:

R

and considering enly high symmetry sites, one gets

[t5]

oJ~ ~cod3 cos O.

(6)

where 0 is the bond angle with the surface

198

1.1C Norskov / Theo~ of dtenaixorption and heterogeneous catalysfs Table I!

Compar~or~ of theoretical and experimenlal bond lengths and perpendicular ~'requenclt~

(%armonieapprox.) for H an,d O d)emiSorlx~t on Ni(100) and (II 1). For OINi{100), the experimental frequency x;aown is the "static lallice" value [17, 2;0.]. For experimental ~t~re~ces. see refs. 15 and 17. Coordination number 'Theory

Bond length ()i,) Theory

Exp.

Vibrational f~queney (rneV) Theory Exp.

H/Ni(100) H/Ni(I l l)

4 3

1.91 1.81

1.84

76 131

O/Ni(tOD)

,4

1.83

t -98

30

( !,6'~

O/Ni(l I I I

3

1.76

1.88

62

72

normal and

74 139

3.4. Migrati, m imo the metal

T h e ra~gration int~ the metal is again dominated by the density-dependent term AE~d'(~o) is a constant ,depending on the atom only. Since the density decay oonstam/3 changes only slowly from surface to surface, ~oz ~s giver~ ba~;icalIy by the bond angle and thereby by the the coordination n u m b e r and the substrate geometry. Parallel to the surface, A~=~.~ ~)"("'(n~) - only gives rise to a corrugation of the cl~¢misorpt~on well. Differences N~tweert differen'~ sites, parMlel vibrational frequencies, and surface diffusion energies are therefore .given by zld~,~ [18]. (3enerally this gives rise to rather small activation barriers. as shown e.g. in fig. 6 for hydrogen or~ Ni(lt'rl0). T h e hydrogen mobitiE¢ is thus expected to be large and tunneling is an irnportant n~igratlion mechanism at low temperat~ares, as is also observed experim~mally in one case [ t 9 ] . T h e energy bands c:dculaled by solvhng the SchrSdinger equatkm for a proton i~ t h e p o t e n tial of fig. 6 is shown in fig. 7 [20]. T h e b a n d width of excited states is seen to be substantial. This m a y be of smaller importance at high coverages. The ,.'cry anharmonie nature of the polentia/paralle~ to the surface is expected t~:~,persist at higher coverages, though. The second excited band is basi~tlly the perpendicuk~r vibration {20] and the energy position of thins band is reasormbly welt given in the harmonic approximation used above.

Z tO OA ¢-¢.

~5

I.U

5~

....

[011]

~ ,.

[0011

I:i~, 6. Contou~ of constalzt ~tent~a.I energy for hydro,g,Jn outside a Ni{l(10~ surface. Twe, cult arc shown: (b) paralM t0 the surface thzlo~gh the abso~ut~ m~n~mum, and (a) pc~,en*

dieular to the su~ce along the diagonal in (b). The comou~

arc shown ~n steps of 0.05eV the lowest value being ~2.7 eV. Ul~dea'neathlh'¢ ¢orr~..~pondinghydrog,znwavefanetions (left) ~md densities (righl~ are shown. Front ref. 20.

J,g, Norskov I Theo~' of "-misorpdOna~d heterogeneo~a"catalys~"

Ni li001 I~----~* 150 _ _ . _ ~ ~

~CEI00

'

' ~

50

A~

l

0

i

r

X

M

P

F'tg. 7. ~l~e band structure for hy¢~rogenchcnli~rbed on 1he Ni(100) surface shown along tire hlgh.-symmetrydi~ctions indicated in the inset. Only the sllales he[onging to the A t ~¢:gresert~,tionof the Ca,, point greup are showrl.The zero of er'ergy is lhe ground.sta'te energy (-2,6eV) at the F poim. This ineJludesa zero-I~.~intenergy tat'0.1 eV. in tl~e inset the ~irillouin zone has been totaled 45° relative 1o tile corlvenlion used in fig. 6, From ref, 20. or', equivalently, by the kinc:tic energy repulsion. In. fig. 8 an example of a pt,tential energy variation for an oxygen atom moving into a N i ( l l l ) st~face is shown. "~te huge activation barrier is a

consequence of the large electron density in the first metal layer. If the metal atoms are allowed to rela,~: away from the oxygen atom, the electron density decreases and the barrier decreases, q'iae interstitial electron density inside a txansition metal is larger than the o p t i m u m value in fig. 1. T h e energy o f the c~xygen (or hydrogen) atom inside the metal is therefore basically linearly d e p e n d e n t o n the interstitial electron densily [11], As seen in fig. 8, the energy can be reduced considerably by relaxing the nearest neighbour metal atoms outwards from the oxygen (hydrogen) atom. T h e cost of relaxing a surface atom is smaller than the cost for a bulk atom and a s u ~ u r f a c ¢ site is therefore typic~lly more stable than erie further into the bulk [I7]. It should be mentioned that the outwards relaxations of the metal lattice induced by the oxygen atoms inside the metal gives rise to a very strong attractive oxygen-oxygen interaetio~, [17]. Oxygen atoms close to each other can sly.are the cost of relaxing the nearest neighbour metal atoms. This is consistent with the strong tendency for island formation observed in oxidation reactions [21:1.

4, M o l ~ -1

~.~ ~-

ATIC

z~5~g

/

~-~ o _~

ADIABAT~C DISTANCE

R~CMFIRSTLAYER(a,~)

Fig, 8, Energy of oxygen mtlside a Ni(11tl surface os lunclion of distance from the first[ayer.Bolh th~ staticlattiec~ pol:cntialand one where the Ni at,~rn~huge been allowed to reh¢~: to give the. minimum encr~, l'adlabatlc') art; shown,

The: Ni-Ni interactkn~,~are dLcseffbedby a pair potential, Fr(:~*nref. 17.

199

a~orpfion, ca~'ysis

For molecular adsorption and reactions on surfaces, even the evaluation eq. (2) can be rather demanding. In studying the trends in molecular binding energies and activation energies, it can therefore be more instructive to apply eq. (1) directly to get energy differences. The starting point is the molecule outside one surface and eq. (1) then gives the energy change when the surface is modified somehow.

4.1. Trends in reactivity along the trans'~tion metal romans &s the first example, consider the tre~ds in the reactivity of the transition metals for a given catalytic reaction, Experhnentatty, one finds 'volcano' curves as illust~'ated in fig. 9 for a largen u m b e r of very different reactions [22]. THee 'universality' of the vollcano curves has led to a

200

J.K. Norskov I Thereat,of ehemisorpir~on and heterogergeouscatalysis

5.0

~,0 -0,5 "-I

"

C~ o q

0,5

~.o

l

== 3.G

m N)

Re

E,O

3.0

=*,

~.G

-OA

=

l,ll

:,O

CH, ~l.O

0,0 0,4

0.~

0,0

~t,O

poPcent:age O=band o~ouparlcy,

. 0.4

e~,,

, , l , ..k O,IB C . e l.O

br+cnv -0,2

popcontag~

O-oan~

ocou~rlcy,

Fig. 9. Semilogarithmic plots of t.~e ammonia (left) and olethane (right) activitiesas function,',of the occupancy of the substrate d-band [31,32].

°" ....

n u m b e r of discussions of the role of d-electrons in catalysis [22]. Typically, a surface reaction consists of m a n y elementary steps. T h e 'universality' of the volcano curves indicates that their explanation does not depend on these details. Most reactions do, however, include the dissociation of (some of) the reactants and the further reaction of the atomic fragments. It is themfo+'e useful to apply eq. (1) to a comparison of activation energies for dissociation and of atomic binding energies along the transitior~ metal tows. The main difference from one transition me~:+! to another is the position of the d-bands relative to .the Fermi level. As a first appreximatior=, we can thus consider the trends in the ~t~cond te~-ra in eq. (1) as the position of the d-bands is varied. This has been done [23] within the resonant level model following the work of Newns [16]. Fig. 10 shows ~E~o, calculated as a function of the d-band position for two positions of the adsorbate valence level e~, [23]. O n e is for e . well below the d-bands. Aq discussed in sections 2 and 3. this is the situation encountered for chemisorbcd simple gas atoms and the trend seen in fig. I0 is exactly that seen in fig+ 4. T h e increasing strength ef the chem~sorption bond towards the left in the series inhibits the further reaction of these atoms. This is the usual explanation for the small reactivity in the left part of the series, The present analysis shows thet this is due to a decreased occupancy of the adsorba~emetal d aoti-bonding states and that the general-

l

, I

__l

Fig. IO, The co,/alent contribution to th¢~ chemi~iorption energy ,gE~o.plotlJe¢l as a Iunction of the d-band position for an adsorbate with a single electronic level at the Fermi lewl (t~,,= 0.0), and with a position well below the band center (1~. =-1.5). C~dculationsare performed within the resonant level [aodel (after Newns [16]) using a semi-elliptical band. Energies are measured with resp~.ctto the Fermi level and tin units of one-half of the bai~d width. ity of the argument hinges on the fact that most simple chemisorbed atoms have a valence level below the d-bands, T h e small reactivity towards the right in the series, on the other hand, can be related to the adsorption rates. A dissociating molecule is characterized by an anti-bonding molecular level getting Pdled as the molecule approaches the surface [~,, 9j+ This is what drives the dissociation process. A r o u n d the top of the activation bai',rier for dissociation, we thus expect the main contribution to &E.~. to involve a molecular level around the Fermi level interacting with the dbands. This is illustrated by the other curve in fig. I0. It is seen how A / ~ , , and thereby e.g. the activation barrier tends to increase twoards ~he right in tile series, explaining the lower activity o~ these metals. Again, these arguments are expected to be quite general. 4..2. Poisoning and promotion Exl. (1) has also been applie~ to a study of the interaction between adsorbing molecules and

IJ¢. N~rskov t Thea~yof chemisorption and he~erogeneot~"catalysis

pre-adsorbed atoms. Generally, electro-ne.gative pre-adsorbates like CI, S or O are known to decrease the adscxpdon rate of molecules like CO, Nz or Ha [24], whereas electro-positive pn=,adsorbates like Li, Na or K increase it [25], I~xperimentally, thi.s effect has been related to a decreased/increased interaction of the molectde with the surface due to the presence of the co-adsorbate [~24, 25]. Exceptions to this picture are l'ffls and I-IzO adsorption where electronegatire co-adsorbates increase [26] the adsorption strength and the alkali's decrease it [27]. In terms of eq. (1), a co-adsorbed atom can change the interaction energy of the adsorbing molecule with the ,~urface in two ways. The coadsorl~ate induced electrostatic potential 8~b0 will interact with ~:he rrnolecu!e. This is described by the first tezTn. "i~he. second describes both the direct ~nteraction d~Le to an overlap between the molecule and eo-ad!Lorbate orbitals as well as the indirect one mediated through the surface elecirons. In the following, only the first one will be considered. This does not, of course, imply that the second one is unimportant. In fig. 11 the self-consistently screened electrostatic potential ~2ffodue to an electro-positive and an eleetro-neg~!!~,tive atom chemisorbed on a jellium surface is shown, It is clear that a

zo ",{o '\ '~ \

A.-,'"

7.,,~r, na~ No // /

20~

molecule like CO, which exlracts electrons from the surface (into the anti-bonding 2¢f* orbital) will be stabilized by nearby electro-positive coadsorbates and de-stabilized by electro-negative co-adsorbates. Molecules like NH3 or H20 which, when adsorbed, have a large haernal charge transfer towards the surface wilI react in an opposite way. The electrostatic term alone can thus explain the trends observed experimentally [28]. It is also clear from fig. t l that the electrostatic term is short-ranged. Only the nearest and perhaps next nearest neighbours are affected. More long-ranged effects must therefore be due to the second term in eq. (1) [29]. The size of the effect has been estimated [28]. For CO/Na adsorption on Fe(ll0), and increase in the COmetal interaction of 0.06-0.3 eV is found [28]. This lies well within the experimentally determined values [25].

5. C o n d u s i o ~

The effective medium theory, which is a method for comparing total interaction energies of an atom or molecule with different solids has been described. For atomic ehemlsorption, detailed potential energy surfaces can be calculated ,,cry easily starting from the atom in a hon,~geneous electron gas. Furthermore, the propea*ies of the interaction potential can be related ~.'~the properties of the surface and atom in question. The approach can also be used m compare interaction or activation energies in more complicated situations. Again, the simplicity of the approach allows a beginning under.~tanding of some of the parameters determining the reactivity and catalytic activity of surfaces.

A,dmowledl~ements Fig. It. Variation of the; s~lf-consi~;te~t¢leea~.~tati¢l~)tential ~'~1 taken perpendiet.lar to a jellJum surface [or O and Na. (nn) and (nnn) coati;spend to dlsl!ance.~of 2.5 A. and 3.5 A in the surface from,the adsorbeflatom, which are the near and ne~.t-neareslneilghbourd[stance~on Ni(100). From ~ ref. 28.

Without the collaboration with Bulbul Chak.raborty, S. Holloway, N. Lang, B. Lundqvist, M. Manninen, R. Nieminen, P. Nordlander and lvI. Puska, this work wrJuld not have appeared.

202

£ K, N#rskov / Theory o f chemisorption and heterogeneous' catalysis

R~e_~euc~ [1] J.R. Sehr~ell,er, J. Vac, Sei. Teehnol. 13 (1976) 335, [2~ J.K. NeOn;key, J. Vae. Sei. Tedmol. 18 (1981) 420. [3~ For a f e i n t review, ~ e e.g, Theory of the Inhomogeneotis F_..lectro~ Ga~. S. Ltmdqvisx ~nd N.H. March, eds. (Plenum, New York, 1983). [4] T,H~ Upton and W.A. Goddard, Phys. Ray, Left. ,~2 (1979) 472. [5] P.J. Feibelman and D.R. Hamann, Solid St. Commun. 3,~ (198113 215. [6] C. Umrigar and J.W. Wilkins. to be published. [7] N.D. Lane a:n~d A.R. Williams, Phys. Ray. 1118 (1978) 616, 118] B.I, l.undqvi:;t. O. Gunnarsson. H. Hiclmberg and J.K. Norskov. Surf. ~,~ei.89 (1979) 196. 19] J.K. Nc.rskov. A. Houmofier. P, Johansson and B.1. Lundqvisl. Phys. Ray. 1.-ett. 46 (]981) 237. [I0] J.K. NC.rskov and N.D. Lane. Phys, Ray. B21 ['19891 2136. M./, Stott and E. Zaremba, Phys, Rev. 1322 (1980) 1564. F1 I] J.K, N~rskov. Phys Ray. 1326 (1982) 2875. [12] O.K. Andersen, H.L. Skriver, H, Nohl and 13. Johansson. Pure Appl. Chem. 52 (1979) 93; O.K. Andersen, ~n: The electronic s~r~lcture of complex systems, N A T O Advanced SliMy lnstitme, W. T e ~ m e r m a n and P, Ph~rlscau. ed,,,, (Plenum, New York. 1982). [1311 The most comprehensive calculations arc those of M.J. Puska, R.M. Nieminea and M. Manninun, Phys, Ray. B24 (1980) 3037. [t4[ C, Umrig~r. [~1. Manninen and J.K. Norskov, to be published. [15] P. Norlunder. Ig. Ho]loway and J.K. Nerskov. Surf. Sci. t36 (1984) 59. [16"[ D.M. Ncwns, Phys. Ray. "/78 (1969) 1123, [171 B, Chakrabony, S. Hollo'~ray and J.K, Ncl~kov. Surf. Sol., in pr:ss.

[~18] Close to the metal atoms ~here is a third ¢onlribation to the interaction energy, uet included in cq. (2). describing the interaction with the metal cores [15~. This term can in some cases coatril.mt~ to energy differences along the surface, in particular on top of a surface I~tom. In most other ~ s e s it is negligible [15,17], [19J R. DiFoggio aaa R. Gomcr. Phys. Rev. B25 (1982) 3490. [20] M J, Pt~ka. R.M. Nierainen, M. Manniaen, B. Chakraborty. S Holloway and 2 K. Norskov, P h i . Ray. Lett. 51 (1983) 1081. [21] See, for example. P.H. Holloway, J. Vnc. ~ci. Tcchnol, 18 (1981) 653. [227 See, for example, G.C. 13~nd. Catalysis by Metals (Academic Prt~s, London, 1962). [23] S. Hoiloway, B.I. Lundqvist and J.K. Ngtrskov, Prec. of the 8131Int, Cony4". on catalysis (Berlin, BRD, 1984), [24./" See. lbr example, D,W, Goodman, R.D. Kelley, T.E. Madey ~,nd J.T. 'Yates. J. Carat. 63 (1980) 226; 12:.i. Ko and 19../, Madix, Surf. Sei. 109 (19801 22t, [25] See. for example, G* ErA. S.B. Laa and M- Weiss, Surf. Sei, 114 (1982) 527: G. Broddn. G. G',ffner and H.P. Bonzel, Surf. Sei. 84 (1979) 295. [26] D. Lachey. M. $urman and D.A. King, Vacuum 33 Ct 983) 867. [27] M. Grunze, F. Bozo, G. F_,'tl and M. Weiss, AppL Surf. Sci. I (1978) 241. [283 J.K. N~rskov, S. Holloway and N.D. Lang, Surf. Sei. 157 (1984) 65 [29] P J, Feibelmml and D,R. Hamma~n. Phys. Ray. Lett, 52 (1984) 6 l . [30] S. Andersson. P.-A. Kartsson and lvL Persson, Phys. Ray, Lett. 5I ~1983) 2378, and private communication, [31] Data from A, Ozaki and K. Ai'ta, in: Catalysis. J.R. Anderson and M. Bondcrt. ads. (Springer, Berlin, NewYork, 1981) Vol. 1. p~ 87, [32] Data from M.A. Vannicc, J. CataL ."t7 (1975) 449 and 462.