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

PHYSICAL REVIEW BVOLUME 52, NUMBER 16 Qrigin of the vibrational shift of CQ chemisorbed on Pt(111) 15 OCTOBER 1995-II F.Illas, S.Zurita, and J.Rubio Departament de Quimica Fisica, Facultat de Quimica, Universitat de Barcelona, C/Marti iFranques 1, 08028 Barcelona, Spain A. M. Marquez Departamento de Quimica Fisica, Facultad de Quimica, Universidad de Sevilla, 41012Sevilla, Spain (Received 21 February 1995;revised manuscript received 6June 1995) Ab iriitio self-consistent field and complete active space self-consistent field cluster-model wave functions have been obtained for aCO-Pt4 cluster model simulating the atop interaction of CO on Pt(111). The origin of the vibrational shift between free and chemisorbed CO has been investigated by means of the constrained space orbital variation method. This analysis shows that the vibrational shift is the result of several e8'ects. First, there is alarge positive shift due to Pauli repulsion, and second various negative contributions; these are substrate polarization, o. donation, and ~back donation, respectively. This theoretical analysis shows that the mechanism suggested by Blyholder is, in fact, the one responsible for the observed. vibrational shift. I. INTRODUCTION Due to its direct relationship to industrial catalytic processes involving CO reactions on Pt-based catalysts, chemisorption of CO on Pt(111)has been one of the most extensively studied systems in surface science. Now, it is well established that CO chemisorbs nondissociatively on Pt(111)leading to regular structures where the metal surface is almost perfect. 'Avariety of experimental techniques show that, at low coverages, CO is chemisorbed mainly at atop sites with the molecular axis perpendicular to the surface and in aC-down orientation. When the coverage is increased, two different species are observed. These species have been assigned as chemisorbed CO above the atop and bridge sites of the Pt(111)surface. This assignment has been confirmed through quantitative analysis of the low-energy electron diffraction (LEED) pattern of the c(4X2) phase. ' Electronic energy-loss spectroscopy vibrational rneasurements for the CO/Pt(111) system at very low exposure show two peaks at 465 and 2100 cm ', which are assigned to the C-Pt and C-O stretching modes. When the CO exposure is increased, two new bands at 350 and 1870 cm 'appear. These two new bands are assigned to the corresponding C-Pt and C-O vibrational modes of bridge chemisorbed CO. 'This is in agreement with the quantitative LEED analyses mentioned above. 'Acommon feature of the two vibrational bands assigned to the C-0 stretching mode is that they are shifted with respect to the internal normal mode of free CO, which is 2170 cm '.'In fact, the appearance of these vibrational shifts is precisely used as aguide to determine adsorption sites. "Thus, it is customary to assign the peaks in the =2130— 2000-cm 'region to atop sites, the =2000— 1800-cm 'region to bridge sites, and the ones appearing at =1880— 1650 cm 'to hollow sites. "' Here we must point out that, although this approach has been widely used to assign adsorption sites, its applicability has been questioned recently. '' The first attempt to explain the origin of the CO stretching mode vibrational shift in terms of amechanism of CO bonding to metal surfaces was given as early as 1964 by Blyholder. 'According to this mechanism, also known as cr donation — ~back donation mechanism, bonding occurs because of acharge transfer from the 5o orbital of CO to the unoccupied metal orbitals followed by acharge transfer, or back donation, from the d„metal orbitals to the 2m* unoccupied level of CO. The validity of the Blyholder mechanism has been theoretically proven in awide number of different systems. This includes metal-carbonyl complexes, small metal-CO molecules, and CO on metal surfaces. 'An often ignored important point is that for late transition metals such as Cu, or for d' metal-carbonyl complexes, the only important mechanjsm js precjsely the back donafjon. Adetailed analysis of the different contributions to the vibration shift for CO on Cu(100) and Pd(100) has been reported by Bagus and co-workers. These authors have used anew theoretical method of analysis, the constrained space orbital variation method, to show that there are two main physical contributions to the vibrational shift of chemisorbed CO. The constrained space orbital variation (CSOV) method allowed Bagus and co-workers to show that there is alarge positive shift due to the Pauli repulsion between the frozen electronic densities of the chemisorbed molecule and that of the sur0163-1829/95/52(16)/12372(8)/$06. 00 52 12 372 1995 The American Physical Society 52 ORIGIN OF THE VIBRATIONAL SHIFT OF CO. ..12 373 face known as a"wall effect."This effect is almost canceled by alarge negative shift due to the donation from metal dto the CO 2~ orbitals; this is precisely the back donation mechanism. In spite of the large body of theoretical evidence in favor of the validity of the donation — back donation mechanism in carbonyl complexes or in CO above surface cluster models, some authors have claimed that the frequency and intensity of the CO stretching modes in metal carbonyl can be explained without recourse to this bonding mechanism. ''We must point out that these works were published well before the theoretical analyses of Bagus and co-workers and, hence, were not aware of the theoretical proof of the Blyholder mechanism, at least for the case of CO on Cu(100). However, in arecent theoretical cluster model study Ohnishi and Watari argue that the Blyholder mechanism does not hold for CO on Pt(111). These authors report avibrational frequency of 1830 cm 'for CO interaction with an atop Pt atom of a cluster model simulating the Pt(111). The vibrational shift with respect to the calculated free CO is not reported, but their value represents ashift of — 340 cm 'with respect to the experimental vibrational frequency of free CO. According to the usual assignments, this vibrational frequency is too low for CO interacting at the atop site. Regardless of this large vibrational shift Ohnishi and Watari state that because the CO 2'* level lies above the Fermi level, the back donation mechanism cannot contribute to the CO-Pt bonding. Asimilar conclusion is reached from theoretical model studies by Volphilhac, Baba, and Achard where the CO-Pt interaction is found to be weak and involving only the 5' orbital of CO. In this work, we will report an ab initio cluster-model study of the interaction of CO at the atop site of aPt(111) surface model. We will be especially concerned with the origin of the vibrational shift of the CO internal stretching mode. An analysis of the results using the CSOV method allows us to identify the leading mechanisms of these vibrational shifts. We will unambiguously show that the mechanisms for this vibrational shift are consistent with the Blyholder model and, also, with previous studies for CO interacting with other metal surfaces. II. SURFACE CLUSTER MODEL AND COMPUTATIONAL DETAILS In this work we use aPt4 cluster model to simulate the atop interaction of CO with the onefold atop site of the Pt(111) surface. Our model contains only one surface atom and three atoms in the second layer with the geometry fixed at the bulk value (Fig. 1). The symmetry point group of the surface cluster model is C3,.Because of the limitations of such asurface model it is not possible to obtain accurate results for some properties as the interaction energy. However, local properties such as equilibrium geometries or vibrational frequencies are usually well reproduced by small cluster models. More important than obtaining accurate values for these quantities is the proper understanding of the adsorbate-surface chemical bond. Here, the cluster-model approach is especially well suited considering that high-quality ab inicl . FIG. 1. Schematic representation of the CO-Pt4 cluster model of CO above the atop site of the Pt(111)surface. tio wave functions can be obtained and analyzed (see Ref. 34, and references therein). Ab initio calculations for transition-metal clusters, even for asmall Pt4 model, may be rather involved. This is not only due to computational requirements, which today should not be aproblem, but because of the existence of d open shells, which lead to avery large number of electronic states in asmall energy range (=0.2eV). Away to solve the problem is the use of pseudopotentials to describe the inner cores of the Pt atoms. However, if the 51 6s' electrons of each Pt atom are explicitly included we will still have the same problem with the number of low-lying electronic states. Therefore, we have decided to include the Sd 6s' electron of the atop Pt atom only. The rest of Pt cluster atoms are treated as one-electron pseudoatoms and the inner cores (including an averaged dshell) are represented by a recently developed oneelectron pseudopotential. The use of this mixed pseudopotential approach permits us to take into account the interaction of the CO orbitals with the 5d orbitals of the atop Pt atom, which are rather local, and enables amodest description of the sor conduction band. The ten-electron pseudopotential for the atop Pt atom has been constructed following the nonempirical formalism of Durand and co-workers. The different s, p, d, and fpotentials have been obtained from an all-electron relativistic self-consistent field (SCF) calculation carried out in avery large basis set of Slater-type orbitals for the 12 374 F.ILLAS, S.ZURITA, J.RUBIO, AND A. M. MARQUEZ 52 Pt atom. The spotential has been constructed to match the relativistic all-electron 6s orbital of the Pt atom in the 5d 6s'( D) configuration. The ppotential is obtained in asimilar way but from an atomic calculation in the 5d 6p'( F). For the dpotential we have followed a different approach and used amixture of the potentials extracted from relativistic SCF calculations in the 5d 6s'( D) and the 5d' ('S) electronic state. The mixture between these two dpotentials has been carried out to reproduce at best the Hartree-Fock limit energy differences corresponding to the Sd 6s'( D},Sd 6s (F), and Sd' ('S) multiplets. This procedure is similar to that suggested by Fernandez Pacios but here the different weight given to each potential is optimized. Finally, the fpotential has been obtained from acalculation for the f'configuration of Pt +. This procedure enables one to obtain an fpotential acting in the region of the 5d atomic orbitals. The one-electron pseudopotential is constructed in asimilar manner but contains aspherically averaged dhole. This pseudopotential has been previously used in astudy of Pt3 and Pt4 bare clusters and of the PtH and PtH+ diatomic molecules. ' For the ten-electron atop Pt atom we use aGaussiantype orbital (GTO) basis set containing 6s, 4p, and 6d primitive GTO scontracted to 3s, 2p, and 3d; this is abbreviated as (6s4p6d/3s2p3d). For the one-electron Pt pseudoatoms we use a(5s3p /2s Ip )basis set. For CO we use the triple zeta plus polarization contraction of the Dunning (10s,6p, ld }primitive set. Here we must point out that results obtained with the above described basis set are almost unchanged when larger basis sets, (7s7p6d2f /SsSp4d2f )and (6s3p/4s2p), are employed to describe the cluster Pt atoms. Using the above-mentioned pseudopotentials and basis sets we have obtained ab initio Hartree-Fock, SCF, and multiconfigurational Hartree-Fock self-consistent field wave functions for the Pt4-CO supersystem. For the multiconfigurational case the complete active space selfconsistent field (CASSCF) method was used. We have considered always aC-down interaction and a vertical orientation; the symmetry point group of the supersystem is again C3,.In order to understand the nondynarnical correlation contribution to the vibrational frequency of free and chemisorbed CO, several CASSCF wave functions were used. In each case, we have optimized both C-Pt and C-0 internuclear distances and calculated the vibrational frequencies corresponding to the normal mode perpendicular to the surface, the frustrated translation, and the internal CO stretching. The highand low-frequency separation method has been used to obtain the two vibrational frequencies at the equilibrium geometries. The calculated values for these two different vibrational modes differ by one order of magnitude, thus justifying the present uncoupled approach. The vibrational frequencies have been obtained from acubic analysis of apolynomial fit to seven points around the minimum of the corresponding energy curve. In order to identify the origin of the C-0 vibrational shift we have carried out an analysis of the vibrational frequency using CSOV method All calculations have been carried out on alocally modified version of HONDO8. 5package 'running on IBM RISC-6000 workstation. III. RESULTS AND DISCUSSION The electronic structure of the Pt4 bare cluster itself is acomplicated rnatter because of the various possible spin and space coupling between the atop Pt atom d-hole and the electronic structure arising from the 6s "conductionband" electrons. In the C3, point group the four conduction-band electrons lead to an a,eelectronic configuration with the open-shell electrons coupled to a Azterm. The atop Pt dorbitals are split into e+e+a, symmetry species due to the symmetry lowering from spheric symmetry to the C3„point group. Therefore, the delectronic configuration becomes either e e ai(3i) or eeai( E) and coupling with the s-band electrons aie eaie (E). Upon interaction with CO the relevant low-lying electronic states are the same provided CO is a closed-shell molecule. At the SCF levels these electronic states are separated by =0.15 eV for Pt4 and by =0.40 eV for Pt4-CO. For the Pt4-CO system the lowest electronic state is Ewith an e' open shell and is the one chosen in this work to represent the atop interaction of CO with Pt(111). Adetailed description of the results concerning the remaining electronic states for both Pt4 and Pt4-CO will be reported elsewhere. The C-Pt and C-0 distances and the two vibrational modes, frustrated translation and internal CO stretching, for the Eelectronic ground state have been obtained at the SCF and CASSCF levels, where we have indeed considered several active spaces. In the CASSCF method, the wave function is univocally determined once the number of active electron and active orbitals is specified. For Pt4-CO the first CAS, hereafter referred to as CAS1, contains 9electrons in 8active orbitals. The active orbitals are all of esymmetry and correspond (approximately) to the dorbitals of the Pt atop atom, the 1m and 2~* of CO, and the eopen shell. The second CAS, CA2, involves 9electrons in 10 orbitals. It is the same as CAS1 but adds another virtual orbital of dcharacter with an extra node. Finally, we have considered athird CAS, CAS3, which involved 7electrons in 8orbitals. In this case, we consider as active orbitals those dominated by the So.,1~, 6o.*,and 2~* orbitals of CO plus the eopen she11 mainly of cluster s-band character. Amore detailed description of each of the above described active spaces is schematically given in Fig. 2. In all CASSCF calculations the contribution of the SCF configuration to the final CASSCF wave function is always larger than 94%. This is aclear indication of the adequacy of the SCF approach to describe the CO-Pt4 interaction. Results for the Pt-C and C-0 distances and for the vibrational frequency corresponding to the frustrated translation are reported in Table I. The SCF and different CASSCF values for the C-Pt distance are very close and are of the order of the experimental value. In fact, the calculated values are of =2.0Ato be compared with 1.85+0.1Aas reported by Ogletree, Van Hove, and Somorjai. 'The SCF and CASSCF ca1culated C-0 dis- 52 ORIGIN OF THE VIBRATIONAL SHIvj. OF CO. ..12 375 CAS1 CAS2 CAS3 9 active electrons 9 active electrons 7 active electrons virtuals 8 orbitals 10 orbitals 8 orbitals atop Pt dinactive active inactive Kco Open shell (Pt 4s-band) atop Pt co active inactive active active active inactive active active active active active inactive FIG. 2. Schematic representation of the electronic structure of the Pt4-CO system showing the dominant character of each orbital. The different complete active spaces used in the CASSCF calculations are also indicated. CO active active active co inactive inactive active tances are also close to the experimental value. For the SCF we have obtained an optimum distance of 1.10 A whereas the different CASSCF calculations lead to values of 1.12— 1.13 Aand the experimental value is 1.15+0.05 A.'Similar results were obtained in the local density functional (LDF) study of Ohnishi and Watari who report aC-Pt distance of 2.09 Aand aC-0 distance of 1.13 A. Hence, both the SCF (or CASSCF) and the LDF approach lead to equilibrium geometries that are close to the experimental values. Interestingly enough the cluster equilibrium geometries are close to those reported for the simple Pt-CO system by either Smith and Carter (1.99 and 1.13 A, using generalized valence bond and dissociation consistent configuration interaction methods )or Roszak and Balasubramanian (1.90 and 1.15 A, from relativistic CASSCF followed by multireference configuration interaction calculations ). The vibrational frequency for the frustrated translation calculated at SCF or CASSCF levels is very similar but is quite diff'erent from that corresponding to the Pt-CO system. In fact, the present value of =300 cm 'contrasts with that reported by Smith and Carter of 600 cm This difference seems to indicate that although the bonding geometry of Pt-CO is close to that of Pt„-CO, the existence of ametal "sband" leads to significant differences in the contribution of each distinct physical effect involved in the bonding mechanism of CO with asingle Pt atoin or with aPt surface. The present value (=300 cm ')is also lower than the =494 cm 'densityfunctional theory result reported by Ohnishi and TABLE I. Calculated SCF and CASSCF values for the C-Pt, d(C-Pt), and C-O, d(C-0) distances and for the vibrational mode 0 of CO perpendicular to the surface, vPt-Surf. Distances are in A and frequencies in cm '. CAS1, CAS2, and CAS3 represent the different active spaces used in the CASSCF calculations. A de6nition ofthe different active spaces is given in the text. Wave function d(C-Pt) vPt-Surf d{C-0) 1.989 2.006 1.989 2.001 1.85+0.05' SCF CAS1 CAS2 CAS3 Exptl. 'Reference 1. References 4and 5. 1.100 1.124 1.129 1.135 1.15+0.05' 310 287 295 295 465' Watari, which indeed is remarkably close to the experimental EELS value for the peak assigned to the atop site (465 cm '). On the other hand, our value agrees with the peak that is experimentally assigned to the bridge CO (384 cm '). Usually, the ab initio cluster-model approach leads to rather accurate vibrational frequencies for the vibrational model perpendicular to the surface. In arecent work, Bagus and Illas have used an Ag4 model to represent NO interacting above athreefold hollow site of the Ag(111) surface and found very good agreement between experimental (=230 cm ') and calculated (=205 cm ') values. The present difFerence between the calculated and experimental values for this vibrational mode 12 376 F.ILLAS, S. ZURITA, J.RUBIO, AND A. M. MARQUEZ TABLE II. Vibrational frequency for free and chemisorbed CO and for the vibrational shift (in cm '). CAS1, CAS2, CAS3, and CAS4 represent the different active spaces used in the CASSCF calculations. Adefinition of the different active spaces is given in the text. Wave function Chemisorbed Shift 2370 2251 2177 2180 SCF 2445 — 75 CAS1 2319 =— 69 CAS2 2319 a CAS3 2197 a CAS4 2176 Experimental 2170 — 60 'Reference 13. References 4and 5. 'Not displayed CASSCF of free and chemisorbed CO not comparable (see text). 2110' may be due to limitations of the surface cluster model, to adsorbate-adsorbate interactions or may even indicate that the experimental assignments have to be revised (see Refs. 13 and 14). The last point may be tested by suitable cluster-model calculations for CO interacting with both atop and bridge sites and is currently being investigated in our laboratory. Now, let us turn our attention to the main point of the present work, which concerns the internal CQ vibrational mode. Asummary of results for this frequency is reported in Table II where we have added the corresponding calculated and. experimental values for free CQ. Here, we must point out that the comparison between the calculated vibrational frequency for the stretching mode, vcQ for free and chemisorbed CO is straightforward for the SCF calculations. However, it is rather involved when CASSCF wave functions are considered. This is because even if there is aone-to-one correspondence between the active orbitals in CQ and in CQ-Pt4, in the latter these active orbitals are mixed with Pt4 orbitals and the amount of nondynamical correlation introduced by CASSCF in free and chemisorbed CQ is not the same. First of all, we will brieAy comment on the results concerning the vcQ for free CO. From the results on Table II we see that, compared to the experimental value, the SCF calculated vcQ is too large by 275 cm '. Introduction of correlation in the mbond by considering the lm and 2m molecular orbitals of CO (4 electrons in 4orbitals in the CASSCF) reduces the dift'erence to 149 cm '. This CAS is to be compared with CAS1 for CQ-Pt4, and to alesser extent also to CAS2. Adding the 5o. and 6o* to the active space, 6electrons in 6orbitals, reduces the difference between the experimental and calculated value to 27 cm '. The result from this CAS is to be roughly commpared with the one obtained from CAS3 of the supersystem. Finally, considering all valence molecular orbitals as active, 10 electrons in 8orbitals, leads to avalue that di6'ers from the experimental one by 6cm 'only. From the preceding discussion it is clear that the difference between the experimental and the SCF calculated value of the vcQ is due to nondynamical correlation. This e6'ect should be rather similar for free and chemisorbed CQ and it is expected to be larger in the latter case if the ~back donation mechanism is important. Therefore, it is possible to compare SCF vibrational frequencies for free and chemisorbed CQ and investigate the origin of the vibrational shift. The SCF vibrational shift between free and chemisorbed CO is of — 75 cm and the experimental vibrational shift is of — 60 cm .This result seems to indicate thai the di6'erential mechanisms are already contained in the SCF wave function. The absolute value of the SCF calculated vcQ is too large and again, explicit consideration of nondynamical correlation e6'ects through either CAS1, CAS2, and CAS3 largely improves the absolute value of the vcQ for the chemisorbed molecule. However, for the reasons mentioned above, it is almost impossible to define an appropriate vibrational shift for the CASSCF calculations. Results from CAS1 for free and chemisorbed CO are probably comparable because the vcQ is reduced from the SCF value by 126 and 119 cm '. As commented above, CAS2 and CAS3 introduce di6'erent amounts of electronic correlation in free and chemisorbed CQ and it is not clear how to define an appropriate vibrational shift. However, the CASSCF values are useful because they clearly indicate the origin of the di6'erence between the SCF calculated and the experimental values. For chemisorbed CQ, both CAS2 and CAS3 calculated frequencies are in rather good agreement with experiment although comparison with respect to free CQ cannot be done and the origin of the vibrational shift cannot be understood. On the other hand, the SCF values permit adirect comparison and show the existence of avibrational shift towards the right direction. In order to prove that the SCF vibrational shift is not fortuitous we will now investigate the di6'erent physical contributions to this shift. This analysis is possible thanks to the CSQV method, which permits aclear separation between di6'erent physical effects. The CSOV analysis starts by constructing afrozen orbital (FO) wave function from the superposition of the electronic densities of free CQ and Pt4. This FQ wave function is obtained by placing CO at the equilibrium position above the Pt4 model. However, in order to compute the vibrational frequency for the CO internal mode, we construct aseries of FQ wave functions using several CO distances but keeping the CQ center of mass fixed at the equilibrium position. The expectation value of the energy at each CO distance computed from this FO wave function permits us to obtain afirst estimate of the vcQ mode in which none of the possible bonding mechanisms is allowed. At this FO step the vibrational frequency of CO is 399 cm larger than that of free CQ also calculated at the SCF level. This large positive shift has also been found for CO on Cu„clusters representing the Cu(100) surface 'and for CO above cluster models representing MgO(100) or NO above cluster models simulating the Cu20(111) surface. ''This shift has been interpreted as a"wall" effect. It is ageneral effect and, consequently, the same interpretation holds here for CO on Pt(111). In the next CSQV step we introduce the substrate polarization by allowing the Pt4 orbitals to vary but using only its own vir- 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 Pt4 don Pt4 pol CO don CO SCF csov step FIGa 3. Different physical contributions to the vibrational shift between free and chemisorbed CO as obtained from the CSOV decomposition. FO, pol Pt4, don Pt4, pol CO, and don CO stand for the V(Pt4,Pt4), V(Pt4,all), V(CO;CO), and V(CO;all) as specified in the text; SCF stands for the unconstrained Hartree-Fock calculation. tual space. To indicate this new variation we use the V(Pt4:Pt4), symbol, where the first set in the parentheses holds for the orbitals that vary and the second set shows the orbital space in which the variation is carried out. Since only Pt4 orbitals are varied in the Pt4 orbital space, it is clear that the new variational degree of freedom included in V(Pt4,'Pt4) accounts for substrate polarization in response to the fixed electronic density of CO. The contribution of this physical effect to the vco frequency is large (— 90 cm ') and contributes to adecrease of the initial wall effect (see Fig. 3). Next, we allow the Ptz molecular orbitals to use all the virtual space and this is indicated as V(Pt4', all). The V(Pt&,all) variation allows donation from the occupied Pt4 orbitals to the virtual (empty) orbitals of CO. In other words, the V(Pt4;all) CSOV step allows n. back donation to occur. The contribution of this effect to the vibrational shift is very large and negative (— 2S7 cm ') and arises essentially from mback donation. This will be clearly seen when discussing the variation on the population analysis accompanying each new variational degree of freedom (Fig. 4). Polarization of CO is introduced at the V(CO;CO} step and the contribution of this physical effect to the vibrational shift is small (— 8cm '}. Finally, we allow the CO orbitals to mix with the virtual orbitals of Pt~; V(CO;all). This last effect accounts precisely for the odonation and it is significant (— 72 crn ); this is again clear from the variation of the population analysis at this CSOV step (Fig. 2). There is asmall contribution (— 1S cm ') due to the effects not included in the previous variations owing to the mixing between the open shell orbital, mainly of Pt4 character, and the closed shells of CO, V(op;cl) and to possible couplings between the different mechanisms. 0.4 0 dd 0 CL OP O col I dd 0.2 0.0 0Pt4 variation ~Total CO variation Grr CO variation -0.2" -0.4—— pol Pt4 don Pt4 pol CO don CO mix (op-cl) SCF FIG. 4. Variations in the Mulliken population analysis corresponding to each step of the CSOV decomposition. The meaning of the different variations is as in Fig. 3and mix(op-cl) stands for the V(op;cl) variation. The fact that this final contribution is very small is indicative that all the important mechanisms have been included in the previous variations. To further illustrate that the mechanism responsible for the vc vibrational frequency shift is, in fact, that suggested by Blyholder, 'we represent in Fig. 4the variation in Mulliken population at each CSOV step. We must caution that Mulliken population analysis, although widely used, is not free of artifacts and can only provide a rough qualitative idea of the various charge transfers. Therefore, we represent the total changes in total population for both units, Pt4 and CO, and the variation on the mpopulation of CO at each CSOV step. Obviously, there are significant variations at the donation steps only. From Fig. 4it is clearly seen that at the V(Pt4;all) there is adecrease in Pt4 population that is accompanied by a similar increase on the CO electronic population. Moreover, the change on the CO population is almost exclusively of mcharacter. This is aclear indication of the mback donation from the substrate to the adsorbate. The other significant change occurs at V(CO;all) step and, in this case, Fig. 4reveals that donation from CO to Pt4 is only of o. character. Hence, Mulliken population analysis is in perfect agreement with the results obtained from frequency analysis and confirms the rightness of the Blyholder mechanism' to interpret the vibrational shift, and the chemical bond, of CO chemisorbed on Pt(111). To summarize the present discussion, the CSOV analyses described above show univocally that there are three important contributions to the vc shift. One of these contributions is always positive and is due to the initial Pauli repulsion, i.e.,the "wall" effect. The other two contributions are precisely the odonation and mback donation. Both are important, although the latter is larger; its importance might be even larger if nondynamical correlation is explicitly included through either configuration-interaction or CASSCF approaches. However, the SCF and CASSCF total ~population for free and chemisorbed CO is almost the same. Therefore, the increase in mpopulation of chemisorbed with respect to 12 378 F.ILLAS, S. ZURITA, J.RUBIO, AND A. M. MARQUEZ 52 free CO cannot be attributed to nondynamical correlation effects. The CASSCF results show that the SCF analysis is correct; i.e.,that the main physical effects contributing to the vibrational shift are already included in the SCF wave function. This is important because, as stated previously, comparison between the calculated free and chemisorbed CO vibrational frequencies is essential to understand the origin of the vibrational shift. This comparison can be done at the SCF level and it is dificult, if not impossible, at the CASSCF level. Here, we must point out that, at variance of CO on Cu(100) of Pd(100), the importance of the odonation for CO on Pt(111) is large. This is because both Cu and Pd have afilled 3do. shell and, hence, cannot add more electrons to the dshell and the only possible o. donation involves mixing of CO orbitals to the cluster virtual orbitals, which represent the metal conduction band. Clearly, the open d-shell nature of the Pt atom permits abonding contribution through o. donation as well. Finally, we would like to point out that the above CSOV analyses of the vibrational frequency shift and of the Mulliken populations are consistent with aCSOV analysis of the interaction energy. At the FO step the CO-Pt4 is unbounded by +2.3eV. Substrate polarization reduces this repulsion in — 1.09 eV; m. back donation leads to afurther reduction by — 1.13 eV; CO polarization makes asmall contribution of — 0.12 eV but odonation contributes by — 0.81 eV. The final SCF interaction energy (— 0.9eV) difFers from the sum of the previous contribution (— 0.85) by 0.05 eV only. The basis set superposition error is of 0.06 eV only. These energetic contributions fully confirm the validity of the Blyholder mechanism for CO interacting with the Pt(111)surface. IV. CONCLUSIONS shift. The CSOV method allowed us to decompose this vibrational shift in its various physically meaningful contributions. As in the case of CO on other metal surfaces, two opposite effects have been identified. The first one is the "wall" effect originated by the Pauli repulsion between the two fixed electronic densities approaching each other. This is alarge positive contribution and it is overcome by the addition of several other effects, all working in the same direction. First, there is alarge contribution due to substrate polarization and next two contributions directly related to the odonation ~back donation mechanism, the latter being the largest although the former is also significant. This latter point is at variance of CO on other metal surfaces such as Cu(100) and Pd(100). This is simply because Pt has an incomplete Sd shell while both Cu(100} and Pd(100) have afilled 3d shell. The CSOV analysis unambiguously shows that the mechanism suggested by Blyholder does also hold for CO on Pt(111). Alast point concerns the theoretical results of Ohnishi and Watari. These authors have found arather low vibrational frequency for the stretching mode of chemisorbed CO. According to our analysis the origin of this low frequency must be the donation — back donation mechanism. In our opinion, analysis of the density of states for the Pt,3-CO cluster presented in Ref. 32 reveals that although the 2~* peak lies above the Fermi level it has aconsiderable area below the Fermi level, thus indicating the presence of mback donation. In conclusion, the vibrational shift between the free and chemisorbed CO is originated by alarge positive shift due to Pauli repulsion and two negative contributions due to o. donation and m. back donation, respectively. Our theoretical analysis univocally shows that the mechanism suggested by Blyholder' is, in fact, responsible for the observed vibrational shift. In this work we have used acluster-model approach to describe the atop interaction of CO with aPt(111}surface. In particular, we have analyzed the origin of the vibrational shift between free and chemisorbed CO. We have obtained SCF and CASSCF ab initio cluster-model wave functions, and determined the optimum geometry of chemisorbed CO and the vibrational frequencies for internal modes, which represent the normal coordinates for the motion of CO perpendicular to the surface and the CO stretching. Also, we have made use of constrained variations to analyze the origin of the vibrational ACKNOWLEDGMENTS We are grateful to NATO for the Collaborative Research Grant CGR-941191. 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