Origin of the vibrational shift of CO chemisorbed on Pt(111)

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. D. F.Ogle ee, M. A. Van Ho e, and G. A. Somo jai, Su . Sci. 173,251 (1987). 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