Computational Studies of the Interactions of Oxygen with

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J. Phys. Chem. B 2001, 105, 9943-9952

9943

Computational Studies of the Interactions of Oxygen with Platinum Clusters Tao Li and Perla B. Balbuena* Department of Chemical Engineering, Swearingen Engineering Center, UniVersity of South Carolina, Columbia, South Carolina 29208 ReceiVed: May 14, 2001; In Final Form: August 2, 2001

Density functional theory is used to compute electronic and thermodynamic interactions between atomic and molecular oxygen and small Ptn clusters (n ) 2-6). Binding energies, vibrational frequencies, and charge distributions are reported. Two states are identified for the adsorption of molecular oxygen: the superoxo species (O2δ-) and the peroxo species (O22δ-) formed by charge transfer from the metal cluster to the O2 molecule. An analysis of the adsorbed O2 dissociation on Pt clusters illustrates the dependence of the activation barrier for dissociation on the metal cluster size.

Introduction The reduction of oxygen on a metal surface, one of the primary reactions taking place in proton-exchange membrane fuel cells,1,2 has been widely studied in electrochemistry.3 Platinum has been reported as the most active electrocatalyst for oxygen reduction in an acid electrolyte medium, and the adsorption of oxygen on the metal surface has been identified as a fundamental step of its reduction mechanism.4 Oxygen adsorption has been investigated with several experimental techniques, including low-energy electron diffraction (LEED),5,6 molecular beam scattering,7 thermal desorption,8 high resolution including electron energy loss spectroscopy (EELS),9,10 and Auger electron spectroscopy (AES).5,11 However, some experimental results are controversial. For example, some debate still exists regarding the magnitude of the adsorption energy and whether gas-phase adsorption can be characterized as molecular or atomic. Experiments carried out on low-index Pt surfaces have shown that oxygen adsorbs both dissociatively and molecularly on the Pt(111) surface.8-10 Adsorbed molecular oxygen is found at temperatures lower than 150 K, and the dissociation of the adsorbed oxygen takes place at higher temperatures. Molecular beam and surface scattering techniques7 have been used to determine the desorption barrier for atomic oxygen that was found to be strongly dependent on coverage. LEED and EELS experiments5,12 suggested that atomic oxygen would prefer the 3-fold hollow sites of the Pt(111) surface in agreement with findings from the transmission channel technique.13 Vibrational data5,10 indicated the existence of a peroxo species (O22δ-), which has a single O-O bond. Single vibrational frequencies were characterized for the adsorbed-atomic and subsurface species.9 Temperature-programmed thermal desorption spectroscopy (TPDS), EELS, and LEED studies of oxygen adsorption on Pt(111) yielded two types of adsorbates: a 2-fold coordinated species (superoxo) and a 1-fold coordinated species (peroxo). The superoxo species was reported in the low-coverage region.9 Theoretical studies of transition-metal clusters yield important detailed information about adsorption and reaction properties.14 * To whom correspondence should be addressed. E-mail: balbuena@ engr.sc.edu.

The cluster model has been widely used for the study of chemisorption and reactions on transition-metal surfaces because of the local character of the interaction between the admolecule and the adsorbent.15,16 Quantum mechanical studies of Pt clusters and their interactions with oxygen are scarce, however. Rubio and Illas17 have studied the adsorption properties and bonding nature of atomic oxygen on the 3-fold hollow (111) sites of Pt9 and Pt25 clusters using several ab initio techniques. Ab initio local-spin-density calculations18 for the adsorption of O2 on a Pt(111) four-layer slab have identified two distinct molecular precursors for the dissociation of oxygen. One is in a paramagnetic superoxo state, and it is formed at the bridge site in a flat top-bridge-top geometry. The second precursor is in a nonmagnetic peroxo state and is located at the hollow site in a slightly canted top-hollow-bridge configuration. The extended Huckel19 and semiempirical models20 have also been used to examine the chemisorption of molecular oxygen on Pt(111) and -(100) surfaces. Current advances in nanofabrication techniques allow the preparation of nanoscale catalysts having potential improved performances. Such improvement is attributed to large surface areas and to the possibility of reaching alternative reaction paths that cannot be achieved with macroscopic catalysts. However, fabrication techniques cannot yet yield a fine control on sizes and shapes. For instance, platinum-ruthenium nanoparticles fabricated using a variety of procedures21-27 show substantial differences in surface composition, morphology, and, therefore, their catalytic activity. Dispersions of platinum on activated carbon yield clusters of a wide range of sizes and shapes.24,25,28 Scanning tunneling microscopy (STM) has revealed the existence of single platinum atoms, platinum dimers, and platinum trimers on highly oriented pyrolytic graphite.28 Recent studies have demonstrated that the activity of Pt clusters varies greatly with the cluster size and the type of reaction, and probably an optimum cluster size exists for each particular reaction. Therefore, the study of reactivity on small clusters is important in order to elucidate the mechanisms of adsorption and reaction and to determine cluster size and shape effects on reactivity. In this work, we perform a systematic density functional theory (DFT) study of the electronic structure and properties of small Ptn clusters (n ) 2-6) and their interactions with atomic and

10.1021/jp0118219 CCC: $20.00 © 2001 American Chemical Society Published on Web 09/15/2001

9944 J. Phys. Chem. B, Vol. 105, No. 41, 2001 molecular oxygen. The objective is to identify the evolution of electronic, geometric, and thermodynamic properties of O2 and Ptn upon O2 adsorption and dissociation on Ptn clusters. Methodology DFT as implemented in Gaussian9429 has been used for all of the calculations. We employed the functional B3PW91, which uses a combination of B330 exchange functionals and PW9131,32 correlation functionals. For Pt, the electrons from the 5s2, 5p6, 5d9, and 6s1 shells were treated explicitly using the Gaussian (3s2p2d) basis set. The 1s to 4f core electrons were described by the Los Alamos National Laboratory (LANL2DZ) using effective core pseudopotentials of double-ξ type.33 For oxygen and hydrogen atoms, we used the polarized basis set 6-311G(d). The presence of a polarization d shell can ensure a possible charge transfer from the substrate to the adsorbate. Full geometry optimizations have been performed via the Berny algorithm in redundant internal coordinates.34 The thresholds for convergence are 0.00045 and 0.0003 au for the maximum component of force and the root mean square (rms) of the forces, respectively. The self-consistency of the noninteractive wave function was performed with a requested convergence on the density matrix of 10-8 and 10-6 for the rms and maximum density matrix error between iterations, respectively. These settings provide correct energies of at least five decimal figures and geometries of approximately three decimal figures within the level of theory. Results and Discussion Bare Ptn Clusters. Table 1 lists the calculated geometries, absolute energies, multiplicities, binding energies per atom, vertical ionization potentials, and electron affinities for bare Pt clusters. Some experimental results are included for the smallest clusters. The corresponding structures are illustrated in Figure 1. Binding energies per atom for a Ptn cluster are calculated according to the following equation:

EB(Ptn) ) [E(Ptn) - n(EPt)]/n The calculated ground state for the Pt atom is 3D with the 5d96s1 configuration, in agreement with experimental results,35,36 whereas the calculated 5d10 configuration is 0.58 eV higher in energy than the ground state. The calculated ground state for Pt2 is a triplet, the singlet energy being 0.6 eV above it. From STM studies, the average bond length of a Pt dimer on graphite is 2.45 Å,37 slightly longer than the calculated Pt-Pt bond length of 2.41 Å. The calculated binding energy is -1.15 eV/atom, comparatively lower than the -1.65 eV/atom average experimental value (Table 1). Figure 1a depicts the three lowest-energy states found for Pt3. The most stable structure corresponds to a singlet equilateral triangle geometry. Our result is in agreement with B3LYP38 and with complete active space multiconfiguration selfconsistent field (CAS-MCSCF)39 calculations, but it differs from the reports of generalized valence bond configuration interaction (GVB-CI) calculations40 that yielded an 3A1 Jahn-Teller distorted isosceles triangle ground state. As pointed out by Majumdar et al.,39 this difference may be attributed to the lack of sufficient higher-order correlation effects in the GVB-CI results. The STM-detected Pt trimers are linear chains and equilateral triangles.37 The average STM bond length is 2.60 Å, longer than our calculated 2.50 Å bond length. For Pt4 clusters, there are three stable structures: rhombus, square, and tetrahedron as shown in Figure 1b. The most stable

Li and Balbuena geometry (Table 1) is the tetrahedral, in agreement with a previous eight valence electrons effective core potential (DFT/ ECP) result.41 Our results indicate that all of the Pt4 structures exhibit Jahn-Teller deformations. The rhombus energy is 0.96 eV above the energy of the tetrahedral structure, and the square configuration energy is also 0.55 eV above it. The calculated binding energy for the tetrahedral geometry is -2.17 eV/atom, which is lower than the -2.36 eV/atom DFT/ECP value.41 Figure 1c depicts three stable structures obtained for Pt5 clusters. The ground-state structure is the square-based pyramid, where a Jahn-Teller distortion is also observed. The energy differences among the structures are small (Table 1); the trigonal-bipyramid energy is 0.63 eV above the energy of the ground-state square-based pyramid, and the planar isosceles trapezium structure is also 0.7 eV above it. A recent CASMCSCF42 reported as the ground state of Pt5 a distorted tetragonal-pyramid structure in the 1B2 state. The same study found this structure, along with regular (undistorted) squarebipyramid, planar, and trigonal-bipyramid structures, as the lowest-lying electronic state of the Pt5 cluster. We also investigated one Pt6 structure as described in Table 1 and Figure 1d. As the cluster size increases, the calculated average bond length (Table 1) starts to be comparable to the reported bulk Pt-Pt distance of 2.77 Å.43 The binding energy per atom also increases with the cluster size (Table 1), although it is still far from the cohesive energy of bulk Pt (6.14 eV).44 Both the vertical electron affinities (EA) and the vertical ionization potentials (IP) show oscillations as a function of the cluster size, which arise from changes in the n cluster electronic structure after the addition of one atom to the n - 1 atom cluster.45 As the cluster size increases, we observe a reduction in the IP and an increase in EA values, whereas (EA + IP)/2 tends to be a constant value of about 5 eV. These reactivity indexes are discussed in a later section in relation to O2 dissociation. We have tested the amount of spin contamination in our UHF calculations. It was found that the expectation values of the spin operator S2 corresponded to the exact theoretical value for a pure spin state for all of the ground-state Ptn clusters except for Pt4 (tetrahedron) and Pt5 (square-based pyramid), where highspin contamination was detected. In such cases, our results indicate that DFT predicts other clusters, with energies only slightly above the ground state, which are geometrically and electronically closer to the ground states obtained by MCSCF methods.42 The ground-state cluster Mulliken populations (Table 2) indicate that the Pt atoms adopt mainly the s1d9 configuration, regardless of the cluster size and electronic configuration. Overall, the d and p orbital populations are enhanced when the cluster size increases, which indicates the increased involvement of these orbitals in the Pt-Pt bonding. The 6s populations decrease with the increase in cluster size, and such electron redistribution contributes to the lengthening of the Pt-Pt bond.42 For Pt4, the charges are transferred from atoms 1 and 3 to atoms 2 and 4, and these transfers are due to the asymmetric geometry of the tetrahedral cluster, creating a small dipole because of the Jahn-Teller distortion. The bond between atoms 2 and 4 is comparatively shorter than any other bond in the cluster, while the bond between atoms 1 and 3 is the longest. The optimized square-based pyramid Pt5 also shows a distorted structure, and charges are transferred from atoms 1 and 4 to atoms 2, 3, and 5, resulting in a dipole moment of 0.442 D. Ptn-O Interactions. Optimization of PtO leads to a lowlying triplet state. The equilibrium geometry gives a Pt-O bond

Interactions of Oxygen with Platinum Clusters

J. Phys. Chem. B, Vol. 105, No. 41, 2001 9945

TABLE 1: B3PW91/LANL2DZ Optimized Geometries, Energetic Properties, and Multiplicities (M) of Platinum Clustersa

cluster

M

geometry (Å, deg)

binding energy/atom (eV/atom)

energy (hartree) -119.11827

electron affinity (eV)

vertical ionization potential (eV)

1.50 (2.12)62

8.69 (8.98)35

2.41 (1.89)65

8.51 (8.68)66

2.05 (1.87)65

7.96

1.89

6.77

Pt

3

Pt2 Pt2

1 3

1-2 ) 2.358 1-2 ) 2.411 (2.45)37,63

-238.29905 -238.32116

-0.85 -1.15 (-1.44/-1.86,37 -1.5764)

Pt3 linear

3

1-2 ) 2.402; 1-3 ) 2.402; 3-1-2 ) 180.00

-357.51410

-1.45

Pt3 equilateral triangle

1

1-3 ) 2.499; 1-2 ) 2.498; 2-3 ) 2.498 (2.66)28; 1-2-3 ) 59.98

-357.56048

-1.87

Pt3 isosceles triangle

3

1-3 ) 2.528; 1-2 ) 2.591; 2-3 ) 2.527; 1-2-3 ) 59.19; 2-3-1 ) 61.67

-357.55161

-1.79

Pt4 rhombus

1

1-3 ) 2.557; 1-4 ) 2.557; 1-2 ) 2.495; 2-4 ) 2.557; 2-3 ) 2.559; 1-2-3 ) 60.77; 1-3-2 ) 58.40; 4-1-3 ) 121.49

-476.75683

-1.93

Pt4 tetrahedron

3

1-2 ) 2.611; 1-4 ) 2.611; 2-3 ) 2.611; 2-4 ) 2.596; 1-3 ) 2.743; 4-3 ) 2.611

-476.79228

-2.17

Pt4 square

1

1-3 ) 2.488; 1-4 ) 2.489; 2-3 ) 2.489; 2-4 ) 2.489; 1-3-2 ) 90.10

-476.77210

-2.03

Pt5 planar, isosceles trapezium

3

1-2 ) 2.734; 1-3 ) 2.627; 1-4 ) 2.512; 1-5 ) 2.497; 2-3 ) 2.640; 3-5 ) 2.552; 2-4 ) 2.529; 5-1-3 ) 59.7; 3-1-2 ) 58.90; 2-1-4 ) 65.70

-595.98372

-2.14

Pt5 square-based pyramid

3

1-4 ) 2.603; 1-3 ) 2.594; 3-2 ) 2.612; 2-4 ) 2.594; 1-5 ) 2.628; 3-5 ) 2.685; 2-5 ) 2.685; 4-5 ) 2.627; 1-2 ) 3.678; 3-4 ) 3.677; 4-1-3 ) 90.10; 1-5-4 ) 59.40;

-596.00942

-2.28

2.35

6.97

Pt5 trigonal bipyramid

1

1-2 ) 2.493; 1-3 ) 2.642; 1-4 ) 2.642; 1-5 ) 2.840; 3-4 ) 4.221; 4-5 ) 2.628; 3-5 ) 2.628; 2-4 ) 2.642; 2-5 ) 2.840; 2-3 ) 2.642; 1-3-5 ) 65.21; 1-2-5 ) 63.96; 1-4-2 ) 56.32

-595.98617

-2.15

2.72

6.67

Pt6

1

1-3 ) 2.674; 1-4 ) 2.674; 2-3 ) 2.672; 2-4 ) 2.672; 1-5 ) 2.676; 1-6 ) 2.671; 3-5 ) 2.677; 4-5 ) 2.675; 4-6 ) 2.673; 2-6 ) 2.676; 2-5 ) 2.675; 3-1-6 ) 60.05; 3-2-6 ) 60.01; 5-3-6 ) 90.03

-715.21628

2.30

2.857

6.536

a

Experimental values are in parentheses. Atoms are numbered according to Figure 1.

length of 1.75 Å, which is much smaller than the value 2.11 Å suggested by a nearest-neighbor force constant model.9 Charge is transferred from Pt to O, and the charge on the oxygen atom is -0.37 au. Results from the Mulliken population analysis reveal that electrons are transferred from the metal d orbital to the adsorbate p orbital. The adsorption energy is calculated according to the formula

Eads ) -(EPtnO - EPtn - EO) where EPtnO is the total energy of the substrate/adsorbate system, EPtn is the energy of the bare metal cluster, and EO is the energy of the oxygen molecule. The calculated PtO adsorption energy is 3.67 eV.

The ground state for the interaction of atomic oxygen with Pt2 is a triplet, with an isosceles triangular structure (Figure 2a) and a stretched equilibrium Pt-Pt distance of 2.69 Å as compared to the Pt-Pt bond length for the bare cluster (2.41 Å; Table 1). The Pt-O bond length is 1.89 Å, slightly longer than that of PtO. The calculated bridge-site adsorption energy for Pt2O is 3.67 eV. Experimental studies tend to agree that atomic adsorption takes place at 3-fold hollow sites, but the reported adsorption energies range from 2.16 to 5.20 eV.7,10,46,47 This variation in energies is attributed to coverage dependence. The adsorbed oxygen in Figure 2a bears a negative Mulliken charge of -0.53 au, indicating an electron flow from the metal atoms to the adsorbate as observed in PtO.

9946 J. Phys. Chem. B, Vol. 105, No. 41, 2001

Li and Balbuena

Figure 1. B3PW91/LANL-2DZ optimized geometries of (a) Pt3 clusters, (b) Pt4 clusters, (c) Pt5 clusters, and (d) Pt6 cluster. The geometric and energetic parameters for these clusters are reported in Table 1. The ground states are the singlet equilateral triangle for Pt3, the triplet tetrahedron for Pt4, and the triplet square-based pyramid for Pt5.

Full optimization of a Pt3 cluster of D3h symmetry interacting with an oxygen atom positioned at the hollow site above the cluster plane yielded a transition state (one imaginary frequency); its structure is shown in Figure 2b. This triplet Pt3O system has a lower C1 symmetry. The calculated Pt-Pt equilibrium bond length for the ground-state bare Pt3 cluster (2.50 Å; Table 1) becomes elongated after the adsorption of atomic oxygen, as it was observed in the Pt2O cluster. The PtPt bonds in Pt3O stretch to values between 2.70 and 2.77 Å, indicating a weakening of the metal-metal interaction upon oxygen adsorption. The calculated Pt-O bond lengths (2.02.03 Å) are all smaller than the sum of Pauling’s covalent radii of Pt and O (2.11 Å), indicating a very strong Pt-O covalent bond. These Pt-O bond lengths are in the same order as those found in organometallic compounds.48 The adsorbed oxygen atom is 1.24 Å away from the Pt3 cluster plane, in agreement with reported LDA/VWN49 and B3PW91/SBK50 calculations. The calculated Pt-O characteristic stretching frequency (no scale factor has been applied), ν ) 484 cm-1, is in the range of the experimental values of ν ) 4715,10,13 and 480 cm-1.9 After

adsorption, the charge distributions and orbital populations on each of the three Pt atoms (Table 3) change according to its interaction with the adsorbate. The s-, p-, and d-shell populations of the Pt atoms all decreased with respect to those in the bare cluster, with the d population showing the largest change. Correspondingly, the p population of the oxygen atom increases in the adsorbed state. The population analysis shows the direction of the electron flow, which is also reflected on the Mulliken charges. A bridge-site optimized singlet structure (Figure 2c) is a Pt3O local minimum. The Pt-O vibrational frequency is 583 cm -1 with an adsorption energy of 3.17 eV. This energy is 0.5 eV lower than that in Pt2O, showing the variation of reactivity of Ptn with the cluster size. The oxygen atom bears a charge of -0.61 au, the charges of the two nearest platinum atoms are both 0.29 au, and the charge on the third Pt atom that does not interact with oxygen is only 0.03 au. The Pt-Pt bond is stretched to 3.08 Å. Ptn-O2 Interactions. Adsorption. Several possible coordination modes for O2 adsorption on Pt have been proposed: the

Interactions of Oxygen with Platinum Clusters

J. Phys. Chem. B, Vol. 105, No. 41, 2001 9947

TABLE 2: Mulliken Population (B3PW91/LANL2DZ) on Metal Atoms for Ground-State Pt Clustersa species Pt2

Pt3

Pt4

Pt5

Pt6

a

Pt1 charges s p d charges s p d charges s p d charges s p d charges s p d

Pt2

Pt3

Pt4

Pt5

Pt6

0 0 2.99 2.99 6.07 6.07 8.93 8.93 0 0 0 2.76 2.76 2.76 6.13 6.13 6.13 9.12 9.12 9.12 0.002 -0.002 0.002 -0.002 2.70 2.72 2.70 2.72 6.15 6.18 6.15 6.18 9.15 9.10 9.15 9.10 0.024 -0.012 -0.012 0.024 -0.023 2.71 2.72 2.72 2.71 2.68 6.22 6.21 6.21 6.22 6.32 9.04 9.08 9.08 9.04 9.03 0 0 0 0 0 0 2.58 2.58 2.58 2.58 2.58 2.58 6.27 6.27 6.27 6.27 6.27 6.27 9.16 9.16 9.16 9.16 9.16 9.16

Atoms are numbered according to Figure 1.

Figure 2. B3PW91/LANL-2DZ/6-311G* optimized geometries of (a) triplet Pt2O adsorption on the bridge site, (b) Pt3O adsorption on the hollow site, and (c) Pt3O adsorption on the bridge site. The structure in b is a transition state. The structure in c is a singlet. Atomic charges are underlined.

Griffiths model51 where both oxygen atoms are bonded to the same substrate atom, the Pauling model52 where O2 is connected to a Pt atom through a single bond, and the Yeager model53 where O2 is adsorbed at a bridge site. Full geometry optimization has been performed for these adsorption geometries, yielding the adsorption energy, the adsorption height (h), the O-O bond length, and the vibrational frequency. Height h is defined as

TABLE 3: Net Atomic Charges and Atomic Orbital Populations from Mulliken Analyses for Pt3 (B3PW91/LANL2DZ)a species Pt3

O

O/Pt3b

O/Pt3c

O charges s p d charges s p d charges s p d charges s p d

0 3.99 4.00 0.00 -0.546 4.00 4.53 0.01 -0.606 4.00 4.59 0.01

Pt1

Pt2

Pt3

0 2.76 6.13 9.12

0 2.76 6.13 9.12

0 2.76 6.13 9.12

0.177 2.68 6.12 9.02 0.030 2.73 6.10 9.13

0.171 2.69 6.12 9.02 0.288 2.72 6.18 8.81

0.199 2.70 6.12 8.99 0.288 2.72 6.18 8.81

a Atom numbers are according to Figure 1a. For O atom (B3PW91/ 6-311G*) and Pt3O (B3PW91/LANL2DZ+6-311G*), atoms are numbered according to parts b and c of Figure 2. b Corresponds to structure in Figure 2b. c Corresponds to structure in Figure 2c.

the shortest Pt-O distance for the Pauling coordination, and it is the vertical distance from the O-O axis to the substrate for the other two coordination modes. Our calculations yielded a triplet 1-fold Pauling model as the most stable PtO2 interaction, illustrated in Figure 3a. The bond length of a free oxygen molecule in the gas phase is 1.208 Å,48 and the O-O vibrational frequency is 1580 cm-1.54 For the Pauling structure (Figure 3a), h ) 1.939 Å, which coincides with the Pt-O bond length for this case. The O-O bond stretches 0.04 Å with respect to the gas phase. The calculated adsorption energy is 0.73 eV. The O-O stretching frequency is ν ) 1342 cm-1, which indicates a weakening of the O-O bond strength. The oxygen atom bonded to Pt bears a charge of -0.19 au, and the Pt atom has a positive charge of 0.25 au, indicating a net electron flow from the metal atom to the adsorbate which results in the bond weakening of the adsorbed oxygen. For bridge-site adsorption (Yeager model), two negative ion precursor species have been identified experimentally.55-58 These adsorbed negative ions play an important role as intermediate species in surface reactions. One is the superoxo species (O2δ-) characterized by an O-O stretching frequency in the range of ν ) 870-875 cm-1.9,10 The other is the peroxo species (O22δ-) with a characteristic bond stretching frequency of 700-710 cm-1.9,10 For the superoxo species, the oxygenoxygen bond order is estimated to be 1.5, while a bond order of 1 is attributed to the peroxo species.55 Parts b-e of Figure 3 display the calculated structures for bridge-site adsorption of molecular oxygen on Pt2, Pt4 in rhomboidal geometry, and Pt5 in the triangular-bipyramid structure. In the initial configuration, all of the metal clusters were set in their B3PW91/LANL2DZ optimized geometries, and the molecular axis of the oxygen molecule was located at the bridge adsorption site with its axis parallel to the nearest Pt-Pt bond. Two states have been identified for the Yeager model in Pt2O2. Figure 3b shows a triplet optimized structure, where the axis of the O2 molecule is twisted with respect to the initial parallel configuration. The geometry is unsymmetrical; the O-O bond length (1.312 Å) is 0.1 Å stretched with respect to the gas phase, which falls close to the NEXAFS range of 1.37 ( 0.05 Å for the superoxo species.57 The average adsorption height h is 1.87 Å. Taking the energy of the ground-state Pt2 cluster

9948 J. Phys. Chem. B, Vol. 105, No. 41, 2001

Li and Balbuena

Figure 3. B3PW91/LANL-2DZ/6-311G* optimized geometries of (a) triplet PtO2, (b) triplet Pt2O2, superoxo, (c) singlet Pt2O2, peroxo, (d) singlet Pt4O2, superoxo, and (e) singlet Pt5O2, superoxo. Atomic charges are underlined.

as the reference, the calculated adsorption energy is 0.72 eV, which is in agreement with local-spin-density calculations18 that yielded a superoxo-like paramagnetic precursor formed at a bridge site. The calculated O-O stretching frequency for the structure in Figure 3b is ν ) 1027 cm-1. Using a correlation between the bond order and O-O vibrational frequencies in dioxygen complexes given by Steininger et al.,9 we estimate the bond order of adsorbed oxygen to be 1.4. This gives further support for the identification of the adsorbed O2 as being in the superoxo configuration. We also tested the amount of spin contamination for this configuration, and we found that the expectation value of the S2 operator is exactly equal to the theoretical value. To explain the unexpected value of the multiplicity for the state in Figure 3b, we observe that the superoxo structure is evidently a precursor to adsorption and dissociation on the bridge site, where only one of the oxygen atoms has been bonded to Pt (bond length 1.936 Å as compared to 2.139 Å for the other PtO distance), yielding for Pt2O2 the same multiplicity as that for Pt2 and O2. The second Pt2O2 state, a singlet, is shown in Figure 3c. As in Figure 3b, the oxygen molecule sits on the bridge site with its axis only slightly shifted from the initial parallel coordinate. The O-O bond length is 1.43 Å, and h is 1.83 Å. These values are in good agreement with characterizations of the peroxo species based on photoemission spectroscopy58 and local-spindensity calculations.18 The calculated adsorption energy is 0.64 eV, slightly lower than that of Figure 3b. The O-O stretching frequency is ν ) 784 cm-1. Using the correlation between bond order and O-O vibrational frequencies in dioxygen complexes,9 we estimate the bond order of the adsorbed oxygen to be around 1.0. Thus, we associate this new state of adsorbed O2 as being in the peroxo configuration. Therefore, our calculations support the existence of two distinct chemisorbed molecular precursor states for O2 on platinum clusters. The superoxo state is formed first when the oxygen molecule is approaching the metal cluster. With the molecule moving much closer to the surface, the O-O bond is

TABLE 4: Net Atomic Charges and Atomic Orbital Populations from Mulliken Analyses for Pt2 (B3PW91/ LANL2DZ), the O2 Molecule (B3PW91/6-311G*), and Pt2O2 (B3PW91/LANL2DZ+6-311G*), Superoxo Speciesa species Pt2

O2

Pt2O2

a

O3 charges s p d charges s p d charges s p d

0 3.93 4.04 0.03 -0.163 3.94 4.20 0.02

O4

0 3.93 4.04 0.03 -0.214 3.94 4.24 0.02

Pt1

Pt2

0 2.99 6.07 8.93

0 2.99 6.07 8.93

0.180 2.86 6.12 8.84

0.197 2.60 6.15 9.06

Atoms are numbered according to Figure 3b.

further stretched, and the adsorbed molecule evolves into a peroxo state, which will eventually dissociate into adsorbed atomic states. The peroxo state is supposed to be more stable than the superoxo state. Our calculations indicate that both species are chemisorbed with similar adsorption energies, the peroxo binding energy being slightly smaller than that of the superoxo state. The stability of the peroxo state is given by the activation energy for dissociation, which is discussed in a subsequent section. The distribution of the electronic population for the superoxo and peroxo states (Tables 4 and 5, respectively) provides new insights about the O-O bond elongation and weakening after adsorption. For comparison, populations for bare clusters are also included in the tables. The Mulliken charges indicate again the electron flow from the metal atoms to the adsorbate molecule; note the asymmetry in the charge distribution for the superoxo state (Table 4). All of the Pt atom p-orbital populations are higher, and only the Pt atom closest to the adsorbate (atom 1) shows a decrease in the d population, while the s population of both Pt atoms bears the most dramatic decrease. Correspond-

Interactions of Oxygen with Platinum Clusters

J. Phys. Chem. B, Vol. 105, No. 41, 2001 9949

TABLE 5: Net Atomic Charges and Atomic Orbital Populations from Mulliken Analyses for Pt2 (B3PW91/ LANL2DZ), the O2 Molecule (B3PW91/6-311G*), and Pt2O2 (B3PW91/LANL2DZ+6-311G*), Peroxo Speciesa species Pt2

O2

Pt2O2

a

O3 charges s p d charges s p d charges s p d

0 3.93 4.04 0.03 -0.319 3.97 4.34 0.02

O4

0 3.93 4.04 0.03 -0.319 3.97 4.34 0.02

Pt1

Pt2

0 2.99 6.07 8.93

0 2.99 6.07 8.93

0.319 2.60 6.13 8.95

0.319 2.60 6.13 8.95

TABLE 6: Net Atomic Charges and Atomic Orbital Populations from Mulliken Analyses for Pt4,a the O2 Molecule, and Pt4O2b species Pt4

O2

Pt4O2

Atoms are numbered according to Figure 3c.

ingly, the p-orbital population of each oxygen atom increases substantially. Hence, there is electron transfer mainly from the Pt s orbitals and from the d orbital corresponding to the Pt atom closest to oxygen to the p orbitals of the adsorbed dioxygen complex. The transferred electron occupies the orbital derived from the former antibonding πg orbital in molecular oxygen, which therefore causes Pt-O bond formation and O-O bond elongation and weakening. The total negative charge on the oxygen molecule increases for the optimized peroxo structure (Table 5) with respect to the superoxo state. Again, the Pt s populations decrease, while the p and d populations are all higher. Electrons are transferred from the Pt s orbitals to the p and s orbitals of the adsorbate atoms. The electron population transferred for the peroxo state almost doubles that of the superoxo species. Hence, transformation from the superoxo species to the peroxo species is due to this further electron transfer from the metal substrate to the oxygen molecule. The optimized Pt4O2 singlet structure is presented in Figure 3d. The axis of the oxygen molecule is slightly twisted from the configuration parallel to the Pt-Pt bond, as was observed in the superoxo Pt2O2. The oxygen molecule is about 1.91 Å away from the cluster surface, and its bond is stretched to 1.302 Å. The O-O stretching frequency is calculated to be ν ) 995 cm-1, corresponding to a bond order of 1.4.9 The adsorption energy is 0.72 eV, taking the singlet rhombus cluster as a reference. On the basis of h, O-O length, and ν, the adsorbed O2 can be characterized as the superoxo species. When the cluster structures before and after adsorption are compared, it is observed that the Pt-Pt bond stretches slightly from 2.55 to 2.62 Å. Thus, in agreement with the above analysis for Pt2O2, the Pt-Pt bond weakens upon adsorption. Table 6 shows the Pt4O2 net atomic charges and the atomic orbital populations from Mulliken analyses. The oxygen molecule bears a total charge of -0.28 au, and each Pt has a charge of 0.07 au. The s and p populations of each Pt are slightly higher than those in the bare cluster, while their d populations are lower. For the oxygen atoms, the p populations are all higher than those in the gas-phase molecule. Thus, on the one hand, electrons are transferring from the d level of the metal atoms to the antibonding orbital of the adsorbate. On the other hand, electrons are back transferred from the adsorbate orbitals to the substrate. Both interactions work to weaken the O-O bond. The results also strongly suggest that the unpaired d electrons of Pt directly participate in the newly formed Pt-O bond. Because of the electron back-donation from the molecule, the metal-metal bond will probably be strengthened instead of weakened. This

O5

O6

Pt1

Pt2

Pt3

charges -0.014 -0.014 0.014 s 2.71 2.71 2.66 p 6.26 6.26 6.09 d 9.04 9.04 9.24 charges 0 0 s 3.93 3.93 p 4.04 4.04 d 0.03 0.03 charges -0.133 -0.135 0.070 0.069 0.066 s 3.93 3.93 2.76 2.76 2.66 p 4.18 4.18 6.34 6.34 6.08 d 0.02 0.02 8.83 8.83 9.19

Pt4 0.014 2.66 6.09 9.24

0.066 2.66 6.08 9.19

a Atoms are numbered according to Figure 1b. bAtoms are numbered according to Figure 3d.

TABLE 7: Net Atomic Charges and Atomic Orbital Populations from Mulliken Analyses for Pt5 (B3PW91/ LANL2DZ),a the O2 Molecule (B3PW91/6-311G*), and Pt5O2 (B3PW91/LANL2DZ+6-311G*)b species Pt5

O2

Pt5O2

O5

O6

Pt1

charges 0.042 s 2.62 p 6.31 d 9.03 charges 0 0 s 3.93 3.93 p 4.04 4.04 d 0.03 0.03 charges -0.246 -0.246 0.147 s 3.95 3.95 2.62 p 4.28 4.28 6.40 d 0.02 0.02 8.83

Pt2

Pt3

Pt4

Pt5

0.042 -0.074 -0.074 0.063 2.62 2.77 2.77 2.58 6.31 6.16 6.16 6.18 9.03 9.15 9.15 9.18

0.147 2.62 6.40 8.83

0.079 2.64 6.13 9.15

0.079 2.64 6.13 9.15

0.039 2.72 6.18 9.06

a Atoms are numbered according to Figure 1c. b Atoms are numbered according to Figure 3e.

trend of electron redistribution is different from that of the adsorption on Pt2, where only the s electrons of Pt play a key role in bonding. The interactions of Pt5 in trigonal-bipyramid structure (Figure 1c) with O2 yield the singlet optimized structure depicted in Figure 3e. Like in Pt2O2, the axis of the oxygen molecule is slightly twisted with respect to a configuration parallel to the nearest Pt-Pt bond. Thus, O2 adsorbs almost parallel to the platinum (1-2) bond at h ) 2.02 Å with an adsorption energy of 0.53 eV. The equilibrium O-O bond length is 1.34 Å, again in the range of NEXAFS measured values.57 Significant lengthening is observed for the Pt-Pt bond directly linked to the oxygen atoms; this lengthening is also found for smaller clusters. Using the calculated O-O vibrational frequency of 955 cm-1, the O-O bond order is estimated to be 1.4. On the basis of the calculated values of the O-O bond length, h, and the bond order, the Pt5O2 structure is also characterized as being in the superoxo state. The Pt5O2 net atomic charges and atomic orbital populations from Mulliken analyses are given in Table 7. Each of the O atoms bears a charge of -0.25 au, and the charge on each of the closest Pt atoms varies from 0.15 to 0.04 au. Again, the Pt p populations are slightly above those in the bare metal cluster, while d populations show the largest change. As observed in the smaller clusters, a major part of the electron transfer in Pt5O2 comes from the d orbital of Pt to the p orbital of oxygen. In agreement with the population analysis for Pt4O2, unpaired d electrons of Pt directly participate in the bonding of O adsorbed atoms. The electron transferred then fills the adsorbed oxygen

9950 J. Phys. Chem. B, Vol. 105, No. 41, 2001

Li and Balbuena

TABLE 8: PtnO Interactions, Summary complex

binding energiesa (eV)

∆νO-Ob (cm-1)

bond order

1.31 1.30 1.34 1.37,57,67 1.3958 (expt)

-0.18 -0.14 -0.25

∼1.5

1.43 1.40,57 1.4358 (expt)

-0.32

∼1.0

RO-O (Å)

Pt2O2 Pt4O2 Pt5O2 experiment and other calculated values

0.72 0.72 0.53 0.4-0.55,9 (expt)

653 685 725 71010 (expt)

Superoxo(O2δ-) 1.87 1.91 2.02 1.9218 (calculated, local-spin DFT)

Pt2O2 experiment and other calculated values

0.64 0.55,9 (expt)

896 87010 (expt)

Peroxo(O22δ-) 1.83 1.8118 (calculated, local spin DFT)

Ptn and O2

0

0

charge on oxygen atom

hO2-cluster (Å)

Molecular Oxygen ∞

∼2.0

1.2

Atomic Oxygen Pt3O experiment and other calculated values

-0.61c

3.17c 2.16-5.207,10,46,47 (expt)

a Bridge-site adsorption. b Vibrational shift with respect to gas-phase molecular oxygen. The experimental vibrational frequency of free O is 2 1580 cm-1, and our calculated value is 1680 cm-1. c Intermediate bridge/hollow site (Figure 2c).

second minimum becomes the most stable. The activation energy, calculated between the maximum and the first minimum, is estimated to be 0.7 eV at h ) 1.70 Å. The potential energy curve in Figure 4 is not based on full geometry optimizations, and cluster reconstruction is also neglected; therefore, this description of dissociation is only qualitative. To investigate the cluster size effect on the the activation energy for dissociation, we calculated the site dissociation energy according to a thermodynamic cycle:

Figure 4. Potential energy curve for O2 dissociation on Pt2, where the energy is relative to the gas-phase energy of O2. Each curve is calculated for a given value of h, the distance from O2 to Pt2. Coordinates used in the potential energy scan for O2 dissociation on Pt clusters are shown in the inset.

molecular orbital derived from the former antibonding πg orbital in molecular oxygen, and the O-O bond is elongated and weakened. Table 8 summarizes the findings for Ptn-O2 interactions. The calculated binding energies, frequency shift of the O-O bond of the adsorbate with respect to the gas-phase value, distance molecule cluster, and O-O bond length are all within the experimental range illustrating the identification of the superoxo and peroxo species. O2 Dissociation on Pt2. The geometry used for studying the dissociation of O2 on Ptn is illustrated in Figure 4 (inset). The Ptn structure is fixed according to the optimized ground-state structure (Table 1). Potential energy curves (B3LPW91/ LANL2DZ+6-311G*) for O2 dissociation on Pt2 calculated for several values of h (Figure 4) were obtained by varying the O-O distance, while the Pt2-O2 distance h is kept constant. When the oxygen molecule is far enough from the metal atoms (h ) 1.75 Å), a first minimum is observed corresponding to adsorbed molecular oxygen, slightly shifted to longer O-O distances than the gas-phase equilibrium bond length (1.208 Å). A second energy minimum corresponds to dissociated adsorbed oxygen which, at h ) 1.75 Å, is less stable than the adsorbed molecular oxygen state. As the molecule gets closer to the metal cluster, the double-well potential becomes clear; note that the

The site dissociation energy (DE, site) is calculated from this cycle using the gas-phase dissociation energy and the adsorption energies for the undissociated and dissociated species.

DE, site ) DE, gas phase + 2Eads(O) - Eads(O2) We have evaluated DE, site values for Pt2, Pt4, and two different geometries of Pt5 using the B3PW91/6-311G* calculated values for the O2 gas-phase dissociation energy (5.32 eV) and an average of the experimental adsorption energies Eads(O) reported for atomic oxygen on Pt (3.64 eV).7,10,46,47 The activation energy for dissociation (Ea) can then be calculated according to the Shustorovich bond-order conservation approximation.59

Ea )

(

)

1 Eads(O) + DE, site 2 2

Table 9 illustrates the variation of the activation energy as a function of cluster size and geometry. As discussed in relation to Table 1, as the cluster size increases, there is a reduction of IP from 8.51 eV for Pt2 and 6.77 eV for Pt4 to 6.97 eV for Pt5 (square-base pyramid) and 6.67 eV for Pt5 (trigonal bipyramid). The decrease of the ionization potential favors the electron transfer from the cluster to the adsorbate, which is also observed by the change of the cluster HOMO orbital energy that tends

Interactions of Oxygen with Platinum Clusters

J. Phys. Chem. B, Vol. 105, No. 41, 2001 9951 Conclusions

TABLE 9: Activation Energies for Dissociation of O2 on Ptn Clusters According to the Bond-Order Conservation Approximation59 on the Basis of Calculated (B3PW91/ LANL2DZ-6-311G*) Adsorption Energies for O2 on Ptn, Calculated (B3PW91/6-311G*) Values for the Gas-Phase Dissociation Energy of O2, and Average of Experimental Values7,10,46,47 for the Adsorption Energy of Atomic Oxygen on Pt cluster

Eads(O2) (eV)

DE,site (eV)

Ea (eV)

Pt2 superoxo Pt4 rhombus Pt5 trigonal bipyramid Pt5 square pyramid

0.71 0.72 0.53 0.83

-1.25 -1.24 -1.44 -1.14

0.28 0.29 0.19 0.34

The ground-state structures for Ptn clusters (n ) 4-6) are shown to be nonplanar, and most of them exhibit Jahn-Teller distortions. The population analysis indicates an increase of p-shell and d-shell populations and a decrease of the s-shell population with the increase of the cluster size. The calculated Pt-Pt bond lengths and bond strengths all increase monotonically with the cluster size. A bridge-site adsorption is found as the most stable structure for Pt3O. The adsorption energy for atomic oxygen shows a strong dependence on the metal cluster size and geometry. The bridge site is found to be the most favorable for the adsorption of O2 on Ptn. In the dimer complexes Pt2O2, we observe electron transfer from the Pt s orbitals to the oxygen p orbitals, whereas in PtnO2 (n > 2), the electron transfer to the adsorbate is from the Pt d and p orbitals. Two precursors for the dissociation of adsorbed molecular oxygen are identified: the superoxo and the peroxo. The superoxo state is formed first when the oxygen molecule is approaching the metal cluster. With the molecule moving much closer to the surface, the O-O bond is further stretched, and the adsorbed molecule evolves into a peroxo state, which will eventually dissociate into adsorbed atomic states. The potential energy curve for the dissociation of adsorbed oxygen shows a double well, corresponding to the molecular and adsorbed states. The first minimum is the most stable at adsorption distances relatively far from the metal cluster. As the molecule gets closer to the cluster, the second minimum becomes the most stable. A bond-order conservation approximation analysis illustrates the dependence of the activation energies for dissociation on the cluster size. The activation energies are reduced as the cluster IP decreases, facilitating the charge transfer to the adsorbate. A similar dissociating effect is observed upon application of an electric field in a direction consistent with the increase of the dipole moment of the adsorbate-cluster complex. The current work indicates that DFT methods are capable of describing the oxygen adsorption geometry and the changes in vibrational frequencies upon adsorption on Pt clusters. However, at least in some cases, we found that, in order to obtain a more accurate description of the Pt cluster ground states, a multireference treatment is required.

to become closer to the energy of the Πg* antibonding orbital in O2 (-6.16 eV).60,61 Thus, the cluster with highest IP shows the lowest activation energy for dissociation of adsorbed oxygen. The dissociation process in this study corresponds to an ideal isolated cluster-molecule. In practice, the activation energy is affected by the presence of other adsorbates, catalyst support, solvent environment, or an external applied electric field. To get insights into this last aspect, we investigated the effect of an external electric field (which could be that exerted by other ions and molecules) on the PtO2 structure in Figure 3a. A finite electric field generated by a dipole was added to the calculation as implemented in Gaussian94. The sign of the field was chosen so that a positive sign was in the direction parallel to the original dipole of the complex. The results are given in Table 10. The geometries were optimized under positive and negative fields. Under a positive field of moderate strength, the system becomes increasingly less stable, and there is a redistribution of charges where the Pt atom becomes less positive and where the O atom participating in the PtO bond becomes less negative. Consequently, the complex dipole moment decreases significantly, the Pt-O bond becomes elongated, and the O-O bond becomes shortened. When the field strength is sufficiently large (>10.3 × 107 V/cm), the system stabilizes on a structure closer to a separated Pt atom and O2 molecule. Under a negative field, the PtO2 complex becomes increasingly stable, resulting in an increase of the metal-oxygen charge transfer described in an earlier section. Therefore, the charge on Pt becomes more positive and that on the two oxygen atoms more negative. The PtO bond becomes shortened, whereas the O-O bond becomes elongated, thus favoring oxygen dissociation. At the strongest negative field tested (-10.3 × 107 V/cm), the complex dipole moment tripled the value at zero field.

Acknowledgment. This work is supported by the National Science Foundation (Career Award Grant CTS-9876065) and by the Army Research Office Grant DAAD19-00-1-0087. The use of computational facilities at the National Center for Supercomputing Applications (NCSA) at the University of

TABLE 10: Effect of an Applied Electric Field on PtO2:a Energies, Fully Optimized (B3PW91) Geometric Parameters, Atomic Mulliken Charges, and Dipole Moments structure parameter

atomic charge

field (V/cm)

energy (hartree)

Pt-O (Å)

O-O (Å)

Pt-O-O (deg)

Pt1 (au)

O2 (au)

O3 (au)

dipole moment (D)

0 5.14 × 106 25.7 × 106 5.14 × 107 10.3 × 107 -5.14 × 106 -25.7 × 106 -5.14 × 107 -10.3 × 107

-269.45076 -269.44998 -269.44766 -269.44657 -269.45100 -269.45161 -269.45578 -269.46266 -269.48189

1.939 1.938 1.945 1.958 2.004 1.936 1.933 1.930 1.930

1.248 1.247 1.240 1.232 1.215 1.249 1.256 1.264 1.279

115.54 115.48 115.55 116.19 118.54 115.54 115.85 116.16 118.49

0.245 0.233 0.183 0.119 -0.015 0.258 0.307 0.368 0.488

-0.186 -0.183 -0.168 -0.148 -0.107 -0.189 -0.204 -0.222 -0.255

-0.059 -0.051 -0.015 0.029 0.122 -0.068 -0.103 -0.146 -0.233

2.07 1.88 1.08 0.20 2.36 2.27 3.03 3.97 5.82

a

Structure is given in Figure 3a.

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