PHYSICAL REVIEW BVOLUME 52, NUMBER 16
Q igin o he ib a ional shi o CQ chemiso bed on P (111)
15 OCTOBER 1995-II
F.Illas, S.Zu i a, and J.Rubio
Depa amen de Quimica Fisica, Facul a de Quimica, Uni e si a de Ba celona, C/Ma i iF anques 1,
08028 Ba celona, Spain
A. M. Ma quez
Depa amen o de Quimica Fisica, Facul ad de Quimica, Uni e sidad de Se illa, 41012Se illa, Spain
(Recei ed 21 Feb ua y 1995; e ised manusc ip ecei ed 6June 1995)
Ab i ii io sel -consis en ield and comple e ac i e space sel -consis en ield clus e -model wa e unc-
ions ha e been ob ained o aCO-P 4 clus e model simula ing he a op in e ac ion o CO on P (111).
The o igin o he ib a ional shi be ween ee and chemiso bed CO has been in es iga ed by means o
he cons ained space o bi al a ia ion me hod. This analysis shows ha he ib a ional shi is he e-
sul o se e al e8'ec s. Fi s , he e is ala ge posi i e shi due o Pauli epulsion, and second a ious neg-
a i e con ibu ions; hese a e subs a e pola iza ion, o. dona ion, and ~back dona ion, espec i ely. This
heo e ical analysis shows ha he mechanism sugges ed by Blyholde is, in ac , he one esponsible o
he obse ed. ib a ional shi .
I. INTRODUCTION
Due o i s di ec ela ionship o indus ial ca aly ic
p ocesses in ol ing CO eac ions on P -based ca alys s,
chemiso p ion o CO on P (111)has been one o he mos
ex ensi ely s udied sys ems in su ace science. Now, i is
well es ablished ha CO chemiso bs nondissocia i ely on
P (111)leading o egula s uc u es whe e he me al su -
ace is almos pe ec . 'A a ie y o expe imen al ech-
niques show ha , a low co e ages, CO is chemiso bed
mainly a a op si es wi h he molecula axis pe pendicu-
la o he su ace and in aC-down o ien a ion. When
he co e age is inc eased, wo di e en species a e ob-
se ed. These species ha e been assigned as chemiso bed
CO abo e he a op and b idge si es o he P (111)su ace.
This assignmen has been con i med h ough quan i a i e
analysis o he low-ene gy elec on di ac ion (LEED)
pa e n o he c(4X2) phase. '
Elec onic ene gy-loss spec oscopy ib a ional nea-
su emen s o he CO/P (111) sys em a e y low expo-
su e show wo peaks a 465 and 2100 cm ', which a e as-
signed o he C-P and C-O s e ching modes. When he
CO exposu e is inc eased, wo new bands a 350 and 1870
cm 'appea . These wo new bands a e assigned o he
co esponding C-P and C-O ib a ional modes o b idge
chemiso bed CO. 'This is in ag eemen wi h he quan i-
a i e LEED analyses men ioned abo e. 'Acommon
ea u e o he wo ib a ional bands assigned o he C-0
s e ching mode is ha hey a e shi ed wi h espec o
he in e nal no mal mode o ee CO, which is 2170
cm '.'In ac , he appea ance o hese ib a ional
shi s is p ecisely used as aguide o de e mine adso p ion
si es. "Thus, i is cus oma y o assign he peaks in he
=2130—
2000-cm ' egion o a op si es, he
=2000—
1800-cm ' egion o b idge si es, and he ones
appea ing a =1880—
1650 cm ' o hollow si es. "'
He e we mus poin ou ha , al hough his app oach has
been widely used o assign adso p ion si es, i s applicabil-
i y has been ques ioned ecen ly. ''
The i s a emp o explain he o igin o he CO
s e ching mode ib a ional shi in e ms o amecha-
nism o CO bonding o me al su aces was gi en as ea ly
as 1964 by Blyholde . 'Acco ding o his mechanism,
also known as c dona ion —
~back dona ion mechanism,
bonding occu s because o acha ge ans e om he 5o
o bi al o CO o he unoccupied me al o bi als ollowed
by acha ge ans e , o back dona ion, om he d„me al
o bi als o he 2m* unoccupied le el o CO. The alidi y
o he Blyholde mechanism has been heo e ically p o -
en in awide numbe o di e en sys ems. This includes
me al-ca bonyl complexes, small me al-CO molecules,
and CO on me al su aces. 'An o en igno ed impo -
an poin is ha o la e ansi ion me als such as Cu, o
o d' me al-ca bonyl complexes, he only impo an
mechanjsm js p ecjsely he back dona jon. Ade-
ailed analysis o he di e en con ibu ions o he ib a-
ion shi o CO on Cu(100) and Pd(100) has been epo -
ed by Bagus and co-wo ke s. These au ho s ha e
used anew heo e ical me hod o analysis, he con-
s ained space o bi al a ia ion me hod, o show
ha he e a e wo main physical con ibu ions o he i-
b a ional shi o chemiso bed CO. The cons ained
space o bi al a ia ion (CSOV) me hod allowed Bagus
and co-wo ke s o show ha he e is ala ge posi i e shi
due o he Pauli epulsion be ween he ozen elec onic
densi ies o he chemiso bed molecule and ha o he su -
0163-1829/95/52(16)/12372(8)/$06. 00 52 12 372 1995 The Ame ican Physical Socie y
52 ORIGIN OF THE VIBRATIONAL SHIFT OF CO. ..12 373
ace known as a"wall e ec ."This e ec is almos can-
celed by ala ge nega i e shi due o he dona ion om
me al d o he CO 2~ o bi als; his is p ecisely he back
dona ion mechanism.
In spi e o he la ge body o heo e ical e idence in
a o o he alidi y o he dona ion —
back dona ion
mechanism in ca bonyl complexes o in CO abo e su ace
clus e models, some au ho s ha e claimed ha he e-
quency and in ensi y o he CO s e ching modes in me al
ca bonyl can be explained wi hou ecou se o his bond-
ing mechanism. ''We mus poin ou ha hese wo ks
we e published well be o e he heo e ical analyses o
Bagus and co-wo ke s and, hence, we e no awa e o he
heo e ical p oo o he Blyholde mechanism, a leas o
he case o CO on Cu(100). Howe e , in a ecen heo e -
ical clus e model s udy Ohnishi and Wa a i a gue ha
he Blyholde mechanism does no hold o CO on
P (111). These au ho s epo a ib a ional equency o
1830 cm ' o CO in e ac ion wi h an a op P a om o a
clus e model simula ing he P (111). The ib a ional
shi wi h espec o he calcula ed ee CO is no epo -
ed, bu hei alue ep esen s ashi o —
340 cm 'wi h
espec o he expe imen al ib a ional equency o ee
CO. Acco ding o he usual assignmen s, his ib a ional
equency is oo low o CO in e ac ing a he a op si e.
Rega dless o his la ge ib a ional shi Ohnishi and
Wa a i s a e ha because he CO 2'* le el lies abo e he
Fe mi le el, he back dona ion mechanism canno con-
ibu e o he CO-P bonding. Asimila conclusion is
eached om heo e ical model s udies by Volphilhac,
Baba, and Acha d whe e he CO-P in e ac ion is ound
o be weak and in ol ing only he 5' o bi al o CO.
In his wo k, we will epo an ab ini io clus e -model
s udy o he in e ac ion o CO a he a op si e o aP (111)
su ace model. We will be especially conce ned wi h he
o igin o he ib a ional shi o he CO in e nal s e ch-
ing mode. An analysis o he esul s using he CSOV
me hod allows us o iden i y he leading mechanisms o
hese ib a ional shi s. We will unambiguously show
ha he mechanisms o his ib a ional shi a e con-
sis en wi h he Blyholde model and, also, wi h p e ious
s udies o CO in e ac ing wi h o he me al su aces.
II. SURFACE CLUSTER MODEL AND
COMPUTATIONAL DETAILS
In his wo k we use aP 4 clus e model o simula e he
a op in e ac ion o CO wi h he one old a op si e o he
P (111) su ace. Ou model con ains only one su ace
a om and h ee a oms in he second laye wi h he
geome y ixed a he bulk alue (Fig. 1). The symme y
poin g oup o he su ace clus e model is C3,.Because
o he limi a ions o such asu ace model i is no possi-
ble o ob ain accu a e esul s o some p ope ies as he
in e ac ion ene gy. Howe e , local p ope ies such as
equilib ium geome ies o ib a ional equencies a e usu-
ally well ep oduced by small clus e models. Mo e im-
po an han ob aining accu a e alues o hese quan i-
ies is he p ope unde s anding o he adso ba e-su ace
chemical bond. He e, he clus e -model app oach is
especially well sui ed conside ing ha high-quali y ab ini-
cl .
FIG. 1. Schema ic ep esen a ion o he CO-P 4 clus e mod-
el o CO abo e he a op si e o he P (111)su ace.
io wa e unc ions can be ob ained and analyzed (see Re .
34, and e e ences he ein).
Ab ini io calcula ions o ansi ion-me al clus e s, e en
o asmall P 4 model, may be a he in ol ed. This is
no only due o compu a ional equi emen s, which oday
should no be ap oblem, bu because o he exis ence o d
open shells, which lead o a e y la ge numbe o elec-
onic s a es in asmall ene gy ange (=0.2eV). Away
o sol e he p oblem is he use o pseudopo en ials o de-
sc ibe he inne co es o he P a oms. Howe e , i he
51 6s' elec ons o each P a om a e explici ly included
we will s ill ha e he same p oblem wi h he numbe o
low-lying elec onic s a es. The e o e, we ha e decided
o include he Sd 6s' elec on o he a op P a om only.
The es o P clus e a oms a e ea ed as one-elec on
pseudoa oms and he inne co es (including an a e aged
dshell) a e ep esen ed by a ecen ly de eloped one-
elec on pseudopo en ial. The use o his mixed pseudo-
po en ial app oach pe mi s us o ake in o accoun he in-
e ac ion o he CO o bi als wi h he 5d o bi als o he
a op P a om, which a e a he local, and enables amod-
es desc ip ion o he so conduc ion band.
The en-elec on pseudopo en ial o he a op P a om
has been cons uc ed ollowing he nonempi ical o mal-
ism o Du and and co-wo ke s. The di e en s, p, d,
and po en ials ha e been ob ained om an all-elec on
ela i is ic sel -consis en ield (SCF) calcula ion ca ied
ou in a e y la ge basis se o Sla e - ype o bi als o he
12 374 F.ILLAS, S.ZURITA, J.RUBIO, AND A. M. MARQUEZ 52
P a om. The spo en ial has been cons uc ed o ma ch
he ela i is ic all-elec on 6s o bi al o he P a om in he
5d 6s'( D) con igu a ion. The ppo en ial is ob ained in
asimila way bu om an a omic calcula ion in he
5d 6p'( F). Fo he dpo en ial we ha e ollowed a
di e en app oach and used amix u e o he po en ials
ex ac ed om ela i is ic SCF calcula ions in he
5d 6s'( D) and he 5d' ('S) elec onic s a e. The mix-
u e be ween hese wo dpo en ials has been ca ied ou
o ep oduce a bes he Ha ee-Fock limi ene gy
di e ences co esponding o he Sd 6s'( D},Sd 6s (F),
and Sd' ('S) mul iple s. This p ocedu e is simila o ha
sugges ed by Fe nandez Pacios bu he e he di e en
weigh gi en o each po en ial is op imized. Finally, he
po en ial has been ob ained om acalcula ion o he
'con igu a ion o P +. This p ocedu e enables one o
ob ain an po en ial ac ing in he egion o he 5d a om-
ic o bi als. The one-elec on pseudopo en ial is con-
s uc ed in asimila manne bu con ains asphe ically
a e aged dhole. This pseudopo en ial has been p e ious-
ly used in as udy o P 3 and P 4 ba e clus e s and o he
P H and P H+ dia omic molecules. '
Fo he en-elec on a op P a om we use aGaussian-
ype o bi al (GTO) basis se con aining 6s, 4p, and 6d
p imi i e GTO scon ac ed o 3s, 2p, and 3d; his is ab-
b e ia ed as (6s4p6d/3s2p3d). Fo he one-elec on P
pseudoa oms we use a(5s3p /2s Ip )basis se . Fo CO we
use he iple ze a plus pola iza ion con ac ion o he
Dunning (10s,6p, ld }p imi i e se . He e we mus poin
ou ha esul s ob ained wi h he abo e desc ibed basis
se a e almos unchanged when la ge basis se s,
(7s7p6d2 /SsSp4d2 )and (6s3p/4s2p), a e employed
o desc ibe he clus e P a oms.
Using he abo e-men ioned pseudopo en ials and basis
se s we ha e ob ained ab ini io Ha ee-Fock, SCF, and
mul icon igu a ional Ha ee-Fock sel -consis en ield
wa e unc ions o he P 4-CO supe sys em. Fo he
mul icon igu a ional case he comple e ac i e space sel -
consis en ield (CASSCF) me hod was used.
We ha e conside ed always aC-down in e ac ion and a
e ical o ien a ion; he symme y poin g oup o he su-
pe sys em is again C3,.In o de o unde s and he non-
dyna nical co ela ion con ibu ion o he ib a ional e-
quency o ee and chemiso bed CO, se e al CASSCF
wa e unc ions we e used. In each case, we ha e op i-
mized bo h C-P and C-0 in e nuclea dis ances and cal-
cula ed he ib a ional equencies co esponding o he
no mal mode pe pendicula o he su ace, he us a ed
ansla ion, and he in e nal CO s e ching. The high-
and low- equency sepa a ion me hod has been used o
ob ain he wo ib a ional equencies a he equilib ium
geome ies. The calcula ed alues o hese wo di e en
ib a ional modes di e by one o de o magni ude, hus
jus i ying he p esen uncoupled app oach. The ib a-
ional equencies ha e been ob ained om acubic
analysis o apolynomial i o se en poin s a ound he
minimum o he co esponding ene gy cu e. In o de o
iden i y he o igin o he C-0 ib a ional shi we ha e
ca ied ou an analysis o he ib a ional equency using
CSOV me hod
All calcula ions ha e been ca ied ou on alocally
modi ied e sion o HONDO8. 5package ' unning on
IBM RISC-6000 wo ks a ion.
III. RESULTS AND DISCUSSION
The elec onic s uc u e o he P 4 ba e clus e i sel is
acomplica ed na e because o he a ious possible spin
and space coupling be ween he a op P a om d-hole and
he elec onic s uc u e a ising om he 6s "conduc ion-
band" elec ons. In he C3, poin g oup he ou
conduc ion-band elec ons lead o an a,eelec onic
con igu a ion wi h he open-shell elec ons coupled o a
Az e m. The a op P do bi als a e spli in o e+e+a,
symme y species due o he symme y lowe ing om
sphe ic symme y o he C3„poin g oup. The e o e, he
delec onic con igu a ion becomes ei he e e ai(3i)
o eeai( E) and coupling wi h he s-band elec ons
aie eaie (E). Upon in e ac ion wi h CO he ele an
low-lying elec onic s a es a e he same p o ided CO is a
closed-shell molecule. A he SCF le els hese elec onic
s a es a e sepa a ed by =0.15 eV o P 4 and by =0.40
eV o P 4-CO. Fo he P 4-CO sys em he lowes elec-
onic s a e is Ewi h an e' open shell and is he one
chosen in his wo k o ep esen he a op in e ac ion o
CO wi h P (111). Ade ailed desc ip ion o he esul s
conce ning he emaining elec onic s a es o bo h P 4
and P 4-CO will be epo ed elsewhe e.
The C-P and C-0 dis ances and he wo ib a ional
modes, us a ed ansla ion and in e nal CO s e ching,
o he Eelec onic g ound s a e ha e been ob ained a
he SCF and CASSCF le els, whe e we ha e indeed con-
side ed se e al ac i e spaces. In he CASSCF me hod,
he wa e unc ion is uni ocally de e mined once he
numbe o ac i e elec on and ac i e o bi als is speci ied.
Fo P 4-CO he i s CAS, he ea e e e ed o as CAS1,
con ains 9elec ons in 8ac i e o bi als. The ac i e o bi -
als a e all o esymme y and co espond (app oxima ely)
o he do bi als o he P a op a om, he 1m and 2~* o
CO, and he eopen shell. The second CAS, CA2, in-
ol es 9elec ons in 10 o bi als. I is he same as CAS1
bu adds ano he i ual o bi al o dcha ac e wi h an
ex a node. Finally, we ha e conside ed a hi d CAS,
CAS3, which in ol ed 7elec ons in 8o bi als. In his
case, we conside as ac i e o bi als hose domina ed by
he So.,1~, 6o.*,and 2~* o bi als o CO plus he eopen
she11 mainly o clus e s-band cha ac e . Amo e de ailed
desc ip ion o each o he abo e desc ibed ac i e spaces is
schema ically gi en in Fig. 2. In all CASSCF calcula-
ions he con ibu ion o he SCF con igu a ion o he
inal CASSCF wa e unc ion is always la ge han 94%.
This is aclea indica ion o he adequacy o he SCF ap-
p oach o desc ibe he CO-P 4 in e ac ion.
Resul s o he P -C and C-0 dis ances and o he i-
b a ional equency co esponding o he us a ed
ansla ion a e epo ed in Table I. The SCF and
di e en CASSCF alues o he C-P dis ance a e e y
close and a e o he o de o he expe imen al alue. In
ac , he calcula ed alues a e o =2.0A o be compa ed
wi h 1.85+0.1Aas epo ed by Ogle ee, Van Ho e, and
Somo jai. 'The SCF and CASSCF ca1cula ed C-0 dis-
52 ORIGIN OF THE VIBRATIONAL SHI j. OF CO. ..12 375
CAS1 CAS2 CAS3
9
ac i e
elec ons
9
ac i e
elec ons
7
ac i e
elec ons
i uals 8
o bi als 10
o bi als 8
o bi als
a op P dinac i e ac i e inac i e
Kco
Open shell
(P 4s-band)
a op P
co
ac i e
inac i e
ac i e
ac i e
ac i e
inac i e
ac i e
ac i e
ac i e
ac i e
ac i e
inac i e
FIG. 2. Schema ic ep esen a ion o he
elec onic s uc u e o he P 4-CO sys em
showing he dominan cha ac e o each o bi -
al. The di e en comple e ac i e spaces used
in he CASSCF calcula ions a e also indica ed.
CO ac i e ac i e ac i e
co inac i e inac i e ac i e
ances a e also close o he expe imen al alue. Fo he
SCF we ha e ob ained an op imum dis ance o 1.10 A
whe eas he di e en CASSCF calcula ions lead o alues
o 1.12—
1.13 Aand he expe imen al alue is 1.15+0.05
A.'Simila esul s we e ob ained in he local densi y
unc ional (LDF) s udy o Ohnishi and Wa a i who e-
po aC-P dis ance o 2.09 Aand aC-0 dis ance o 1.13
A. Hence, bo h he SCF (o CASSCF) and he LDF ap-
p oach lead o equilib ium geome ies ha a e close o
he expe imen al alues. In e es ingly enough he clus e
equilib ium geome ies a e close o hose epo ed o he
simple P -CO sys em by ei he Smi h and Ca e (1.99
and 1.13 A, using gene alized alence bond and dissocia-
ion consis en con igu a ion in e ac ion me hods )o
Roszak and Balasub amanian (1.90 and 1.15 A, om el-
a i is ic CASSCF ollowed by mul i e e ence
con igu a ion in e ac ion calcula ions ).
The ib a ional equency o he us a ed ansla ion
calcula ed a SCF o CASSCF le els is e y simila bu is
qui e di 'e en om ha co esponding o he P -CO sys-
em. In ac , he p esen alue o =300 cm 'con as s
wi h ha epo ed by Smi h and Ca e o 600 cm
This di e ence seems o indica e ha al hough he bond-
ing geome y o P -CO is close o ha o P „-CO, he ex-
is ence o ame al "sband" leads o signi ican di e ences
in he con ibu ion o each dis inc physical e ec in-
ol ed in he bonding mechanism o CO wi h asingle P
a oin o wi h aP su ace. The p esen alue (=300
cm ')is also lowe han he =494 cm 'densi y-
unc ional heo y esul epo ed by Ohnishi and
TABLE I. Calcula ed SCF and CASSCF alues o he C-P ,
d(C-P ), and C-O, d(C-0) dis ances and o he ib a ional mode
0
o CO pe pendicula o he su ace, P -Su . Dis ances a e in A
and equencies in cm '. CAS1, CAS2, and CAS3 ep esen he
di e en ac i e spaces used in he CASSCF calcula ions. A
de6ni ion o he di e en ac i e spaces is gi en in he ex .
Wa e
unc ion d(C-P ) P -Su
d{C-0)
1.989
2.006
1.989
2.001
1.85+0.05'
SCF
CAS1
CAS2
CAS3
Exp l.
'Re e ence 1.
Re e ences 4and 5.
1.100
1.124
1.129
1.135
1.15+0.05'
310
287
295
295
465'
Wa a i, which indeed is ema kably close o he expe i-
men al EELS alue o he peak assigned o he a op si e
(465 cm '). On he o he hand, ou alue ag ees wi h
he peak ha is expe imen ally assigned o he b idge CO
(384 cm '). Usually, he ab ini io clus e -model ap-
p oach leads o a he accu a e ib a ional equencies
o he ib a ional model pe pendicula o he su ace. In
a ecen wo k, Bagus and Illas ha e used an Ag4 model o
ep esen NO in e ac ing abo e a h ee old hollow si e o
he Ag(111) su ace and ound e y good ag eemen be-
ween expe imen al (=230 cm ') and calcula ed (=205
cm ') alues. The p esen di Fe ence be ween he cal-
cula ed and expe imen al alues o his ib a ional mode
12 376 F.ILLAS, S. ZURITA, J.RUBIO, AND A. M. MARQUEZ
TABLE II. Vib a ional equency o ee and chemiso bed
CO and o he ib a ional shi (in cm '). CAS1, CAS2,
CAS3, and CAS4 ep esen he di e en ac i e spaces used in
he CASSCF calcula ions. Ade ini ion o he di e en ac i e
spaces is gi en in he ex .
Wa e
unc ion Chemiso bed Shi
2370
2251
2177
2180
SCF 2445 —
75
CAS1 2319 =—
69
CAS2 2319 a
CAS3 2197 a
CAS4 2176
Expe imen al 2170 —
60
'Re e ence 13.
Re e ences 4and 5.
'No displayed CASSCF o ee and chemiso bed CO no com-
pa able (see ex ).
2110'
may be due o limi a ions o he su ace clus e model, o
adso ba e-adso ba e in e ac ions o may e en indica e
ha he expe imen al assignmen s ha e o be e ised (see
Re s. 13 and 14). The las poin may be es ed by sui able
clus e -model calcula ions o CO in e ac ing wi h bo h
a op and b idge si es and is cu en ly being in es iga ed
in ou labo a o y.
Now, le us u n ou a en ion o he main poin o he
p esen wo k, which conce ns he in e nal CQ ib a ional
mode. Asumma y o esul s o his equency is epo -
ed in Table II whe e we ha e added he co esponding
calcula ed and. expe imen al alues o ee CQ. He e, we
mus poin ou ha he compa ison be ween he calcula -
ed ib a ional equency o he s e ching mode, cQ o
ee and chemiso bed CO is s aigh o wa d o he SCF
calcula ions. Howe e , i is a he in ol ed when
CASSCF wa e unc ions a e conside ed. This is because
e en i he e is aone- o-one co espondence be ween he
ac i e o bi als in CQ and in CQ-P 4, in he la e hese
ac i e o bi als a e mixed wi h P 4 o bi als and he
amoun o nondynamical co ela ion in oduced by
CASSCF in ee and chemiso bed CQ is no he same.
Fi s o all, we will b ieAy commen on he esul s con-
ce ning he cQ o ee CO. F om he esul s on Table II
we see ha , compa ed o he expe imen al alue, he SCF
calcula ed cQ is oo la ge by 275 cm '. In oduc ion o
co ela ion in he mbond by conside ing he lm and 2m
molecula o bi als o CO (4 elec ons in 4o bi als in he
CASSCF) educes he di 'e ence o 149 cm '. This CAS
is o be compa ed wi h CAS1 o CQ-P 4, and o alesse
ex en also o CAS2. Adding he 5o. and 6o* o he ac-
i e space, 6elec ons in 6o bi als, educes he di e ence
be ween he expe imen al and calcula ed alue o 27
cm '. The esul om his CAS is o be oughly comm-
pa ed wi h he one ob ained om CAS3 o he supe sys-
em. Finally, conside ing all alence molecula o bi als
as ac i e, 10 elec ons in 8o bi als, leads o a alue ha
di6'e s om he expe imen al one by 6cm 'only. F om
he p eceding discussion i is clea ha he di e ence be-
ween he expe imen al and he SCF calcula ed alue o
he cQ is due o nondynamical co ela ion. This e6'ec
should be a he simila o ee and chemiso bed CQ and
i is expec ed o be la ge in he la e case i he ~back
dona ion mechanism is impo an . The e o e, i is possi-
ble o compa e SCF ib a ional equencies o ee and
chemiso bed CQ and in es iga e he o igin o he ib a-
ional shi .
The SCF ib a ional shi be ween ee and chem-
iso bed CO is o —
75 cm and he expe imen al ib a-
ional shi is o —
60 cm .This esul seems o indica e
hai he di6'e en ial mechanisms a e al eady con ained in
he SCF wa e unc ion. The absolu e alue o he SCF
calcula ed cQ is oo la ge and again, explici conside a-
ion o nondynamical co ela ion e6'ec s h ough ei he
CAS1, CAS2, and CAS3 la gely imp o es he absolu e
alue o he cQ o he chemiso bed molecule. Howe e ,
o he easons men ioned abo e, i is almos impossible
o de ine an app op ia e ib a ional shi o he CASSCF
calcula ions. Resul s om CAS1 o ee and chem-
iso bed CO a e p obably compa able because he cQ is
educed om he SCF alue by 126 and 119 cm '. As
commen ed abo e, CAS2 and CAS3 in oduce di6'e en
amoun s o elec onic co ela ion in ee and chemiso bed
CQ and i is no clea how o de ine an app op ia e ib a-
ional shi . Howe e , he CASSCF alues a e use ul be-
cause hey clea ly indica e he o igin o he di6'e ence be-
ween he SCF calcula ed and he expe imen al alues.
Fo chemiso bed CQ, bo h CAS2 and CAS3 calcula ed
equencies a e in a he good ag eemen wi h expe i-
men al hough compa ison wi h espec o ee CQ can-
no be done and he o igin o he ib a ional shi canno
be unde s ood. On he o he hand, he SCF alues pe -
mi adi ec compa ison and show he exis ence o a i-
b a ional shi owa ds he igh di ec ion.
In o de o p o e ha he SCF ib a ional shi is no
o ui ous we will now in es iga e he di6'e en physical
con ibu ions o his shi . This analysis is possible
hanks o he CSQV me hod, which pe mi s aclea sepa-
a ion be ween di6'e en physical e ec s. The CSOV
analysis s a s by cons uc ing a ozen o bi al (FO) wa e
unc ion om he supe posi ion o he elec onic densi ies
o ee CQ and P 4. This FQ wa e unc ion is ob ained
by placing CO a he equilib ium posi ion abo e he P 4
model. Howe e , in o de o compu e he ib a ional e-
quency o he CO in e nal mode, we cons uc ase ies o
FQ wa e unc ions using se e al CO dis ances bu keep-
ing he CQ cen e o mass ixed a he equilib ium posi-
ion. The expec a ion alue o he ene gy a each CO dis-
ance compu ed om his FO wa e unc ion pe mi s us
o ob ain a i s es ima e o he cQ mode in which none
o he possible bonding mechanisms is allowed. A his
FO s ep he ib a ional equency o CO is 399 cm
la ge han ha o ee CQ also calcula ed a he SCF le -
el. This la ge posi i e shi has also been ound o CO
on Cu„clus e s ep esen ing he Cu(100) su ace 'and
o CO abo e clus e models ep esen ing MgO(100) o
NO abo e clus e models simula ing he Cu20(111) su -
ace. ''This shi has been in e p e ed as a"wall"
e ec . I is agene al e ec and, consequen ly, he same
in e p e a ion holds he e o CO on P (111). In he nex
CSQV s ep we in oduce he subs a e pola iza ion by al-
lowing he P 4 o bi als o a y bu using only i s own i -

52 ORIGIN OF THE VIBRATIONAL SHIFT OF CO. ..12 377
500
V
O
0
O
C
O
250—
-250—
ea ~aa ~assess
~aa aaa asa aa
~seas eases ~
s'ad'a/as' ~
~aa saa saa ~sI
paaaapaaaai
~~~'a a4"a
PsPaPaPa. 'saasaaasaaj
ssea aaaaaaa
-500 III I I
FO pol P 4 don P 4 pol CO don CO SCF
cso s ep
FIGa 3. Di e en physical con ibu ions o he ib a ional
shi be ween ee and chemiso bed CO as ob ained om he
CSOV decomposi ion. FO, pol P 4, don P 4, pol CO, and don
CO s and o he V(P 4,P 4), V(P 4,all), V(CO;CO), and V(CO;all)
as speci ied in he ex ; SCF s ands o he uncons ained
Ha ee-Fock calcula ion.
ual space. To indica e his new a ia ion we use he
V(P 4:P 4), symbol, whe e he i s se in he pa en heses
holds o he o bi als ha a y and he second se shows
he o bi al space in which he a ia ion is ca ied ou .
Since only P 4 o bi als a e a ied in he P 4 o bi al space,
i is clea ha he new a ia ional deg ee o eedom in-
cluded in V(P 4,'P 4) accoun s o subs a e pola iza ion in
esponse o he ixed elec onic densi y o CO. The con-
ibu ion o his physical e ec o he co equency is
la ge (—
90 cm ') and con ibu es o adec ease o he in-
i ial wall e ec (see Fig. 3). Nex , we allow he P z molec-
ula o bi als o use all he i ual space and his is indi-
ca ed as V(P 4', all). The V(P &,all) a ia ion allows dona-
ion om he occupied P 4 o bi als o he i ual (emp y)
o bi als o CO. In o he wo ds, he V(P 4;all) CSOV s ep
allows n. back dona ion o occu . The con ibu ion o
his e ec o he ib a ional shi is e y la ge and nega-
i e (—
2S7 cm ') and a ises essen ially om mback
dona ion. This will be clea ly seen when discussing he
a ia ion on he popula ion analysis accompanying each
new a ia ional deg ee o eedom (Fig. 4). Pola iza ion
o CO is in oduced a he V(CO;CO} s ep and he con i-
bu ion o his physical e ec o he ib a ional shi is
small (—
8cm '}. Finally, we allow he CO o bi als o
mix wi h he i ual o bi als o P ~; V(CO;all). This las
e ec accoun s p ecisely o he odona ion and i is
signi ican (—
72 c n ); his is again clea om he a i-
a ion o he popula ion analysis a his CSOV s ep (Fig.
2). The e is asmall con ibu ion (—
1S cm ') due o he
e ec s no included in he p e ious a ia ions owing o
he mixing be ween he open shell o bi al, mainly o P 4
cha ac e , and he closed shells o CO, V(op;cl) and o
possible couplings be ween he di e en mechanisms.
0.4
0
dd
0
CL
OP
O
col
I
dd
0.2
0.0
0P 4 a ia ion
~To al CO a ia ion
G CO a ia ion
-0.2"
-0.4——
pol P 4 don P 4 pol CO don CO mix (op-cl) SCF
FIG. 4. Va ia ions in he Mulliken popula ion analysis co e-
sponding o each s ep o he CSOV decomposi ion. The mean-
ing o he di e en a ia ions is as in Fig. 3and mix(op-cl)
s ands o he V(op;cl) a ia ion.
The ac ha his inal con ibu ion is e y small is indi-
ca i e ha all he impo an mechanisms ha e been in-
cluded in he p e ious a ia ions.
To u he illus a e ha he mechanism esponsible
o he c ib a ional equency shi is, in ac , ha
sugges ed by Blyholde , 'we ep esen in Fig. 4 he a i-
a ion in Mulliken popula ion a each CSOV s ep. We
mus cau ion ha Mulliken popula ion analysis, al hough
widely used, is no ee o a i ac s and can only p o ide a
ough quali a i e idea o he a ious cha ge ans e s.
The e o e, we ep esen he o al changes in o al popula-
ion o bo h uni s, P 4 and CO, and he a ia ion on he
mpopula ion o CO a each CSOV s ep. Ob iously, he e
a e signi ican a ia ions a he dona ion s eps only.
F om Fig. 4i is clea ly seen ha a he V(P 4;all) he e is
adec ease in P 4 popula ion ha is accompanied by a
simila inc ease on he CO elec onic popula ion. Mo e-
o e , he change on he CO popula ion is almos ex-
clusi ely o mcha ac e . This is aclea indica ion o he
mback dona ion om he subs a e o he adso ba e. The
o he signi ican change occu s a V(CO;all) s ep and, in
his case, Fig. 4 e eals ha dona ion om CO o P 4 is
only o o. cha ac e . Hence, Mulliken popula ion
analysis is in pe ec ag eemen wi h he esul s ob ained
om equency analysis and con i ms he igh ness o he
Blyholde mechanism' o in e p e he ib a ional shi ,
and he chemical bond, o CO chemiso bed on P (111).
To summa ize he p esen discussion, he CSOV analy-
ses desc ibed abo e show uni ocally ha he e a e h ee
impo an con ibu ions o he c shi . One o hese
con ibu ions is always posi i e and is due o he ini ial
Pauli epulsion, i.e., he "wall" e ec . The o he wo
con ibu ions a e p ecisely he odona ion and mback
dona ion. Bo h a e impo an , al hough he la e is
la ge ; i s impo ance migh be e en la ge i nondynami-
cal co ela ion is explici ly included h ough ei he
con igu a ion-in e ac ion o CASSCF app oaches. How-
e e , he SCF and CASSCF o al ~popula ion o ee
and chemiso bed CO is almos he same. The e o e, he
inc ease in mpopula ion o chemiso bed wi h espec o
12 378 F.ILLAS, S. ZURITA, J.RUBIO, AND A. M. MARQUEZ 52
ee CO canno be a ibu ed o nondynamical co ela ion
e ec s. The CASSCF esul s show ha he SCF analysis
is co ec ; i.e., ha he main physical e ec s con ibu ing
o he ib a ional shi a e al eady included in he SCF
wa e unc ion. This is impo an because, as s a ed p e-
iously, compa ison be ween he calcula ed ee and
chemiso bed CO ib a ional equencies is essen ial o
unde s and he o igin o he ib a ional shi . This com-
pa ison can be done a he SCF le el and i is di icul , i
no impossible, a he CASSCF le el. He e, we mus
poin ou ha , a a iance o CO on Cu(100) o Pd(100),
he impo ance o he odona ion o CO on P (111) is
la ge. This is because bo h Cu and Pd ha e a illed 3do.
shell and, hence, canno add mo e elec ons o he dshell
and he only possible o. dona ion in ol es mixing o CO
o bi als o he clus e i ual o bi als, which ep esen he
me al conduc ion band. Clea ly, he open d-shell na u e
o he P a om pe mi s abonding con ibu ion h ough o.
dona ion as well.
Finally, we would like o poin ou ha he abo e
CSOV analyses o he ib a ional equency shi and o
he Mulliken popula ions a e consis en wi h aCSOV
analysis o he in e ac ion ene gy. A he FO s ep he
CO-P 4 is unbounded by +2.3eV. Subs a e pola iza ion
educes his epulsion in —
1.09 eV; m. back dona ion
leads o a u he educ ion by —
1.13 eV; CO pola iza-
ion makes asmall con ibu ion o —
0.12 eV bu odona-
ion con ibu es by —
0.81 eV. The inal SCF in e ac ion
ene gy (—
0.9eV) di Fe s om he sum o he p e ious
con ibu ion (—
0.85) by 0.05 eV only. The basis se su-
pe posi ion e o is o 0.06 eV only. These ene ge ic con-
ibu ions ully con i m he alidi y o he Blyholde
mechanism o CO in e ac ing wi h he P (111)su ace.
IV. CONCLUSIONS
shi . The CSOV me hod allowed us o decompose his
ib a ional shi in i s a ious physically meaning ul con-
ibu ions. As in he case o CO on o he me al su aces,
wo opposi e e ec s ha e been iden i ied. The i s one is
he "wall" e ec o igina ed by he Pauli epulsion be-
ween he wo ixed elec onic densi ies app oaching each
o he . This is ala ge posi i e con ibu ion and i is o e -
come by he addi ion o se e al o he e ec s, all wo king
in he same di ec ion. Fi s , he e is ala ge con ibu ion
due o subs a e pola iza ion and nex wo con ibu ions
di ec ly ela ed o he odona ion ~back dona ion mech-
anism, he la e being he la ges al hough he o me is
also signi ican . This la e poin is a a iance o CO on
o he me al su aces such as Cu(100) and Pd(100). This is
simply because P has an incomple e Sd shell while bo h
Cu(100} and Pd(100) ha e a illed 3d shell. The CSOV
analysis unambiguously shows ha he mechanism sug-
ges ed by Blyholde does also hold o CO on P (111).
Alas poin conce ns he heo e ical esul s o Ohnishi
and Wa a i. These au ho s ha e ound a a he low i-
b a ional equency o he s e ching mode o chem-
iso bed CO. Acco ding o ou analysis he o igin o his
low equency mus be he dona ion —
back dona ion
mechanism. In ou opinion, analysis o he densi y o
s a es o he P ,3-CO clus e p esen ed in Re . 32 e eals
ha al hough he 2~* peak lies abo e he Fe mi le el i
has aconside able a ea below he Fe mi le el, hus indi-
ca ing he p esence o mback dona ion.
In conclusion, he ib a ional shi be ween he ee
and chemiso bed CO is o igina ed by ala ge posi i e
shi due o Pauli epulsion and wo nega i e con ibu-
ions due o o. dona ion and m. back dona ion, espec i e-
ly. Ou heo e ical analysis uni ocally shows ha he
mechanism sugges ed by Blyholde ' is, in ac , esponsi-
ble o he obse ed ib a ional shi .
In his wo k we ha e used aclus e -model app oach o
desc ibe he a op in e ac ion o CO wi h aP (111}su -
ace. In pa icula , we ha e analyzed he o igin o he i-
b a ional shi be ween ee and chemiso bed CO. We
ha e ob ained SCF and CASSCF ab ini io clus e -model
wa e unc ions, and de e mined he op imum geome y
o chemiso bed CO and he ib a ional equencies o
in e nal modes, which ep esen he no mal coo dina es
o he mo ion o CO pe pendicula o he su ace and
he CO s e ching. Also, we ha e made use o con-
s ained a ia ions o analyze he o igin o he ib a ional
ACKNOWLEDGMENTS
We a e g a e ul o NATO o he Collabo a i e
Resea ch G an CGR-941191. Financial suppo was
p o ided by he "Comision In e minis e ial de Ciencia y
Tecnologia" o he Spanish "Minis e io de Educacion y
Ciencia" unde CICyT p ojec s PB92-0766-CO2-01 and
PB92-0662. The au ho s wish o hank he "Cen e de
Supe compu acio de Ca alunya, "CESCA, o pa o he
calcula ions.
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