J. Phys. Chem. B 2001, 105, 10001-10006
10001
Density Functional Study of Formate Decomposition on NiO(111) Surface Toshiko Miura,† Hisayoshi Kobayashi,*,† and Kazunari Domen‡ Department of Chemistry and Bioscience, Kurashiki UniVersity of Science and the Arts, 2640 Tsurajima, Nishinoura, Kurashiki, 712-8505 Japan, and Chemical Resources Laboratory,§ Tokyo Institute of Technology, 259 Nagatsuda, Midori-ku, Yokohama 227, Japan ReceiVed: January 16, 2001; In Final Form: May 11, 2001
The mechanism of formate decomposition on a NiO(111) surface is investigated using the density functional method and (NiO)x cluster models. The reaction consists of three steps: (1) configuration change from bidentate to monodentate, (2) HCOO rotation around the CO axis, and (3) H atom transfer from the formate to the surface O atom. The bidentate form is more stable by 21 kJ/mol than the monodentate one, and the energy barrier measured from the former is 25 kJ/mol, which is consistent with the recent experimental finding that the mutual conversion is an equilibrium reaction. There is no essential reaction barrier during the HCOO rotation about the CO axis. The migration of H atoms from formate to the surface O atom is the rate-limiting step, and the activation energy is estimated to be 73 kJ/mol. The product is the surface OH groups and adsorbed CO2 molecule, which is consistent with the recent experimental stidies.
Introduction
Method of Calculation and Models
Characterization of reaction intermediates formed on metal and metal oxide surfaces gives crucial information on the mechanisms of surface reactions and catalysis.1 Adsorption and decomposition of formic acid is one of the reactions most extensively investigated. It is well-known that formic acid is easily dissociated into acidic proton and formate anion, and formate is a stable and commonly observable surface species such as in methanol oxidation and water-gas shift reactions. Among metals and metal oxides investigated so far, Ni and NiO surfaces have been used most frequently: Ni(100),2,3 Ni(110),4-10 Ni(111),11 NiO(100),12-14 and NiO(111).14-21 The reaction mechanism is rather complicated. The dehydrogenation and dehydration compete with each other and the relative ratio depends on various reaction conditions, such as catalyst materials, surface conditions, temperature, gas pressure, and so on. Large amounts of experimental data have been accumulated, and only a few theoretical calculations have been carried out for formate adsorption to Cu,22 TiO2,23 ZnO,24 and MgO,25 and the reaction mechanism is not yet clear. Recently Domen and co-workers published a series of papers on infrared reflection absorption spectroscopy (IRAS) and timeresolved sum-frequency generation (SFG) vibrational spectroscopy for adsorption and decomposition of formate on Ni(110)8-10 and NiO(111)16-21 surfaces. They revealed that picosecond laser pulse irradiation converts the more stable formate in a bidentate configuration to the less stable one in a monodentate configuration, prior to decomposition.21 The rate-determining step is considered to be the C-H bond fission in both systems, whereas the detailed parts of the mechanisms are different. In this article, we apply the density functional theory (DFT) calculation to the energetic and structural changes during the adsorption and decomposition of formate on the NiO(111) surface.
The gradient corrected and the hybrid DF methods were employed in this calculation. The used functionals were the Slater26 and Becke exchange27 and the Lee-Yang-Parr correlation functionals28 (BLYP). In addition to them, the HartreeFock exchange and the Vosko-Wilk-Nusair correlation functionals29 were used for the hybrid method (B3LYP).30 The Gaussian 94/98 programs were used throughout the work.31 Los Alamos model core potentials (MCP)32 and corresponding basis sets were used for Ni atoms as implemented in these programs.31 Two MCP sets are implemented in Gaussian 94/98 programs: one is a large core (1s to 3p) and small valence (3d4s4p) (abbreviated as SV) basis set, and the other is a small core (1s to 2p) and large valence (3s3p3d4s4p) (abbreviated as LV) basis set. For calculations with a (NiO)4 cluster, we first obtained the outline of the reaction profile using the SV set, and then both the energy and structure are reevaluated with the LV set at points for the local minima and transition states (TSs) and other important points on the reaction paths. For H, C, and O atoms, Dunning-Huzinaga’s full double-ζ (D95) basis sets33 were used. For the harmonic frequency calculations, the allelectron 6-311G and 6-311G** basis sets were used as well as the LV set. NiO(111) is a polar surface, and a cleaved and nonreconstructed surface is not stable. According to Freund et al.,34,35 the surface is reconstructed to a (2 x 2) structure, and the trigonal pyramid-like (111) facets are repeated. This reconstruction, however, is sensitive to the atmosphere. In our experiments, the formate adsorbed surface is kept reconstructed in a vacuum, whereas it is restored to the (1 x 1) structure with formic acid in the gas phase.19 In normal or reconstructed surfaces, O atoms have a greater possibility to occupy the outer layer atom or the apex sites of the facet. However, it seems to be unlikely that formate is stably adsorbed to the O-terminated site, and the active sites of the reaction are assumed to be Ni-terminated sites, which are also created on the surface in the minority. All the clusters used in calculations, (NiO)4, Ni7O8, and (NiO)19,
†
Kurashiki University of Science and the Arts. Tokyo Institute of Technology. § Former Research Laboratory of Resources Utilization. ‡
10.1021/jp0101662 CCC: $20.00 © 2001 American Chemical Society Published on Web 09/22/2001
10002 J. Phys. Chem. B, Vol. 105, No. 41, 2001
Miura et al. TABLE 1: Energy Dependency on Spin Multiplicity for (NiO)4 and HCOO-(NiO)4-H relative energy, eV spin multiplicity basis set 1 3 5 7 9 11
(NiO)4 SV LV 5.0 3.5 2.4 1.2 0 3.1
2.6 2.0 1.4 0.8 0 2.0
HCOO(NiO)4-Ha SV LV NCb NCb 0.07 (0.06c) 0.9 0 2.8
NCb NCb NCb 0.3 0 1.9
Ni7O8 11 13 15
0.82 0 0.69
a Bidentate configuration with parallel orientation is used. b “NC” means that SCF is not converged. c HCOO and H moieties are optimized for the quintet state of HCOO-(NiO)4-H. For other spin states, the optimized structure for the nonet state is used intact.
and structure are reevaluated with the LV set at points for the local minima, transition states (TSs), and other important points on the reaction paths. To confirm our results, we additionally used larger clusters of Ni7O8 and (NiO)19 as well as a NiO diatom. Results and Discussion
Figure 1. Model for a reconstructed p(2 x 2) NiO(111) surface. Top layer Ni atoms occupy the three coordination number (3CN) sites, and the third layer Ni atoms have six coordination number (6CN). Illustrated structure is used as (NiO)19 cluster.
represent the local geometry of the Ni-terminated (111) facet. Figure 1 shows this site with a (NiO)19 cluster. It is well-known that adsorbed formic acid is easily dissociated into formate anion and proton at temperatures above 200 K.17 The proton binds to the surface O atom and forms an O-H bond, and formate binds to the Ni atom. We concentrate our analysis on the mechanism of single molecule decomposition, where the proton or the OH bond does not affect the decomposition of formate. On the other hand, it is much better to treat a neutral cluster rather than an anionic cluster such as [HCOO(NiO)4]-. To satisfy above requirements, the proton is bound to the O atom at the opposite end of the (NiO)x cluster throughout the reaction. Formate is adsorbed on the Ni atom in the bidentate configuration (forming the two Ni-O bonds). According to ref 21, before decomposition, the bidentate formate is transferred to the monodentate configuration where one of the Ni-O bonds is broken. Based on our recent experimental finding, a threestep reaction profile is constructed. (1) Formate is adsorbed on a Ni atom of a (NiO)xH cluster with bidentate configuration and then transformed to a monodentate configuration. (2) The monodentate formate is rotated around the CO axis so that the H atom could approach to the surface O atom. (3) The H atom migrates from the formate to the surface O atom, and CO2 is produced. Throughout this work, the formate and proton are optimized, and the (NiO)x moiety is maintained with a crystalline Ni-O distance of 2.09 Å. The sum of energies of (NiO)x cluster and HCOOH is taken as a reference, and the stabilization is denoted by negative values. Using the cubic (NiO)4 cluster, we first obtained the outline of the reaction profile using the SV set, and then both the energy
Electronic Structure of the (NiO)4 and HCOO-(NiO)4-H Clusters. The electronic structure of the (NiO)4 cluster is examined for various spin multiplicities. Table 1 shows the relative energy measured from the lowest spin states. The nonet state (S ) 4) is found to be the energetically lowest state for both the free (NiO)4 cluster and the adsorbed cluster of HCOO(NiO)4-H. The nonet state of (NiO)4 corresponds to the triplet state (S ) 1) per each NiO moiety. The energy increases as the spin multiplicity decreases or increases from the nonet state. Energy dependence on spin multiplicity is also examined for the bidentate configuration of adsorbed formate and proton. The quintet state (S ) 2) is stabilized as low as the nonet state with the SV basis set, but it cannot be confirmed due to no SCF convergence with the LV basis set calculation. At any rate, the nonet state is the lowest state again, and the following reactions are investigated on this spin state. Configuration Change from Bidentate Form to Monodentate Form. Two optimized structures are obtained for the bidentate configuration, and they are referred to as perpendicular and parallel orientations, as shown in Figure 2a,b. The calculated adsorption energies are 127 and 121 kJ/mol, and the perpendicular orientation is slightly more stable. A monodentate configuration, in which one of the Ni-O bonds is broken, is obtained as shown in Figure 2c. The monodentate configuration is less stable than the bidentate ones by 15-21 kJ/mol. The corresponding trasnsition states (TSs) are shown in Figure 3. TS1 is the TS from the perpendicular orientation of bidentate to the monodentate. As expected, the transformation includes increase of one Ni-O bond length and the rotation of molecular plane about the another Ni-O bond. TS2 is the TS from the parallel orientation of bidentate to the monodentate, and the structural change is simply increase of the Ni-O bond length. The activation energies measured from the corresponding local minima are 25 and 26 kJ/mol, respectively. These results are in good agreement with our recent experimental results.21 The temperature jump of ca. 300 K caused by the irradiation of picosecond near-infrared (1.06 µm) laser pulses revealed the
Study of Formate Decomposition
J. Phys. Chem. B, Vol. 105, No. 41, 2001 10003
Figure 3. Two TS structures between the bidentate and monodentate configurations. TS1 and TS2 locate on the reaction path from the perpendicular and parallel orientations, respectively, toward the monodentate.
Figure 2. Two bidentate (perpendicular and parallel orientations) and one monodentate configurations of adsorbed formate. (a) Perpendicular orientation where the formate plane is perpendicular to the Cs symmetry plane and (b) parallel orientation where the formate plane coincides with the Cs symmetry plane. (c) Monodentate configuration, which has a single Ni-O bond. The parallel bidentate and monodentate configurations are separated by an energy barrier.
irradiation induced transformation between the bidentate and monodentate configurations. The former is more stable by 19 kJ/mol, and the two configurations are separated by a small barrier. The calculated small energy difference between the bidentate and monodentate and the relatively low barrier (not estimated by our measurements) are consistent with our current understanding that the two configurations must coexist and can be converted mutually.21 The optimized structures for HCOO and H groups with the (NiO)4 cluster are reproduced with the (NiO)19 cluster shown in Figure 1, and the energies are estimated by single-point calculations. (The H atom is bonded to the bottom layer O atom on the right side with the same local geometry.) The hybrid DF method and the SV basis set are used instead of the pure gradient corrected DF method and the LV basis set due to the convergence problem. The stabilization energies are calculated to be 183, 160, and 132 kJ/mol, for the perpendicular and parallel orientations of bidentate and for monodentate, respectively. Although the stabilization energies are larger, the order is the same as the result of the (NiO)4 cluster. A possibility of so-called bridged configuration is also examined. When the formate molecular plane is rotated by 60° about the O-Ni axis in Figure 2c, the formate O atom is directed toward the Ni atom in “the third layer”, as shown in Figure 4a. The optimization leads to a bridged configuration with a larger adsorption energy of 197 kJ/mol, and the structure is shown in Figure 4(b). However, this is an artifact due to smallness of
Figure 4. Possibility of a bridged configuration. With the (NiO)4 cluster, the opposite orientation of the monodentate configuration (a) leads to a bridged configuration (b). With a larger Ni7O8 cluster, the opposite orientation (c) leads to the bidentate configuration (d), whereas the “normal” orientation leads to the monodentate configuration (e).
(NiO)4 cluster. As shown in Figure 1, the third layer Ni atoms are in the six coordination number (6CN) sites. We tried to confirm this point employing a Ni7O8 cluster. The energy dependence on the spin multiplicity for the free Ni7O8 cluster is also shown in Table 1. The multiplicity (2S + 1))13 is the lowest state, and the calculations for formate are carried out with this multiplicity. The optimization is started
10004 J. Phys. Chem. B, Vol. 105, No. 41, 2001
Figure 5. Energy changes along the whole reaction course consist of (a) conversion of bidentate to monodenate, (b) H-CdO rotation about the C-O bond, (c) C-H bond fission, and (d) desorption of CO2. The triangle and square plots indicate the results with the SV and LV basis sets, respectively. At the points where the LV results are plotted, both the SV and LV data are those for optimized structures. For other SV plots, the data are those for interpolated structures. Plots of the right end are the energy difference of (NiO)4-2H and CO2 relative to (NiO)4 and HCOOH.
with a structure of Figure 4c and leads to the bidentate configuration with parallel orientation as shown in Figure 4d. Adsorption energy is calculated to be 123 kJ/mol, and this value is almost same as the value of 121 kJ/mol for the (NiO)4 cluster. This means that the Ni atoms in the third layer and with the 6CN are not reactive to form the bridged configuration. The optimization started with a similar structure as Figure 2c leads to a monodentate configuration as shown in Figure 4e with a smaller adsorption energy of 117 kJ/mol. Thus the bridged configuration is not fulfilled unless two Ni atoms with the lower coordination number appear in the surface layer and in the next neighbor distance. We will not deal with this in the following discussion. HCOO Rotation around the CO Axis. The monodentate structure of formate is rotated by 180° about the CO axis so that the H atom in formate may approach the surface O atom adjacent to the Ni atom. The energy change during rotation is shown in Figure 5, as connected points in the second interval. For these intermediate structures, the HCOO moiety is assumed to be coplanar. The obtained flat curve indicates that the energy is almost constant and the coplanar restriction will not cause artificial influence on the energetics. The initial and final structures for rotation are shown in Figure 2c and Figure 6a, respectively, which are the result with the LV basis set, and the energy difference is only 2 kJ/mol. H Atom Transfer from the Formate to Surface O Atom. With the rotated structure, the distance between the H atom of formate and the surface O atom is reduced to 2.79 Å. The energy change for H atom migration is examined. Figure 5 indicates that the highest activation barrier is located in this step, although it is still below the reference energy level ((NiO)4 + HCOOH). Parts a and b of Figure 6 show the initial structure and TS3, respectively. The activation barrier for TS3 is estimated to be 73 kJ/mol. The experimentally estimated activation energies are 30 kJ/mol21 under catalytic conditions and 58 kJ/mol19 under vacuum. The latter value is well compared to the present calculation, since the calculation treats a single molecule decomposition. The difference is ca. 20% and the agreement is fairly good. The product of this step is adsorbed CO2 and two protons binding to the surface O atoms. The SV basis set calculation affords the structures shown in Figure 6c,d almost the same energies (-88.6 and -88.8 kJ/mol, respectively). With
Miura et al.
Figure 6. Structure and energy changes for the C-H bond fission. (a) The product for the rotation about C-O bond. This structure is the starting configuration for C-H bond fission. (b) The TS structure. (c) The optimized structure of the product of C-H bond fission with the SV basis set calculation but an intermediate configuration with the LV basis set calculation. (d) The product of C-H bond fission with the LV basis set calculation, for which the SV basis set affords a similar energy as (c).
the LV basis set calculation, the structure shown in Figure 6c is an intermediate of a smaller stabilization energy of 64 kJ/ mol, and the structure shown in Figure 6d is the local minimum with a stabilization energy of 93 kJ/mol. In this structure, CO2 bends back to the opposite side against the O-H bond, and the energy is still stabilized by 29 kJ/mol. The stabilization energy, 93 kJ/mol, is subtracted by the sum of energy of a (NiO)4-2H cluster, where the two O-H bonds are formed, and the energy of free CO2. The difference, 27 kJ/mol, is ascribed to CO2 adsorption. The binding energy of two O-H bonds is estimated by the energy subtraction, i.e., E[(NiO)4] + E[(H2)] - E[(NiO)42H], and the value of 85 kJ/mol is obtained. Thus major part of the stabilization energy comes from the two O-H bonds. General Discussion and Comparison with Experimental Results. Figure 5 lists the energies of all structures examined in this work. The formate decomposition is divided into four steps: the bidentate to monodentate conversion, the rotation of H-CdO fragment about C-O axis, the migration of H atom from the H-C bond to the O-H bond, and the desorption of CO2 molecule. Along the course of reaction, not only the local minima and TSs but their intermediate structures are investigated using the SV basis set, and these energies are shown by a connected line (and triangle symbols). Structures and energies for the local minima and TSs are reevaluated using the LV basis set, and the results are plotted with square symbols. At first glance, the calculated relative energies are very similar between the two basis sets, which are different only for Ni atoms. One important difference is the relative energy between the TS1 and the monodentate configuration. With the SV basis set, the TS1 energy is lower than the monodentate one, which means that the two configurations are not separated. The LV basis set adequately stabilizes the monodentate configurations, and the two configurations are separated by an energy barrier. The second different point is the local minimum structures for the H atom migration, as mentioned. However, the more stable structure shown in Figure 6d is less important than configura-
Study of Formate Decomposition
J. Phys. Chem. B, Vol. 105, No. 41, 2001 10005
TABLE 2: Calculated Harmonic Frequencies for Bidentate and Monodentate Configurations after DCOOD Adsorptiona bidentate (perpendicular) ν(OD) ν(CD) νa(OCO) νs(OCO)
monodentate
LV
6-311G
6-311G**
exptlb
LV
6-311G
6-311G**
exptlb
2594 2243 1353 1200
2566 2218 1402 1208
2674 2145 1509 1291
2719 2160 1570d 1300
2594 2156 1501 1093
2566 2120 1525 1134
2674 2058 1633 1173
2640 2190 NOc 1267
a Unit is wavenumber. b Refs 19 and 21. c “NO” means “not observed”. d Not observed for vertical orientation used in the calculation but observed for tilted orientation in ref 17.
TABLE 3: Comparison of C-H Bond Lengths among Calculation Modelsa HCOO(NiO)4H: LV HCOO(NiO)4H: 6-311G HCOO(NiO)4H: 6-311G** HCOONiOH: LVb
bidentate
monodentate
difference
1.104 1.097 1.109 1.091
1.114 1.107 1.118 1.103
0.010 0.010 0.009 0.012
a Unit is angstrom. b Both bidentate and monodentate configurations have Cs symmetry. In the former, the H-C-Ni-O-H moiety is on the symmetry plane, and the molecule is coplanar for the latter.
tions on the surface, since the repulsive interactions between CO2 and the distant O and Ni atoms are expected with larger cluster models as shown in Figures 1 and 4c-e. So we would like to say that the use of the LV basis set, which has more flexible Ni orbitals, is required when the delicate energy difference is important, but the SV basis set works well for the geometries. The harmonic frequencies are evaluated for the bidentate configuration with perpendicular orientation and monodentate configuration. To compare with the experimental values, the atomic mass of hydrogen is replaced with that of deuterium. The optimization and frequency calculations with the 6-311G and 6-311G** basis set are added to check reliability of the used MCP basis sets and influence of the polarization functions. Table 2 shows these results as well as the available experimental data. Although all the calculated frequencies well reproduce with experimental values, the 6-311G** basis set definitely improves the agreement. Comparing the frequencies between the two configurations, the O-D stretching frequency is insensitive to the configurations. This may be ascribed to our calculation model in which the acidic proton is bound to the opposite side of the cluster to maintain neutrality. The C-D stretching frequency shifts to the opposite direction between the calculation and experiment. This is ascribed to the calculated C-H bond lengths. The optimized C-H bond lengths are shown in Table 3 for the LV, 6-311G, and 6-311G** basis sets with the (NiO)4 cluster and also for “adsorption” to the NiO diatom. We see that the monodentate configuration constantly gives the longer C-H bond length by ca. 0.01 Å, and the longer bond length “theoretically” results in the lower frequency. Since the difference in frequency observed experimentally is small (30 cm-1), we suspect that some unconsidered factors such as building-up charge and local electric field shift the relative position of frequencies. The symmetric OCO stretching reproduces the experimental shift. The asymmetric OCO stretching is not observed for the vertically oriented formate due to the surface selection rule, but the value of 1570 cm-1 is reported for the tilted orientation.17 In this work, the decomposition mechanism of formate adsorbed on the NiO(111) surface has been investigated using the DF method and cluster models. First, the formate is bound to the surface Ni atoms at the apex site of the trigonal facet. The bidentate configuration is easily converted to the mono-
dentate one since they are separated with a low-energy barrier. Then the H-CdO moiety in formate rotates about the C-O axis so that the formate H atom comes closer to the surface O atom. The H atom transfer is the rate-limiting step and produces the weakly adsorbed CO2 and the two O-H bonds. The calculated energy differences and harmonic frequencies relatively well reproduced the experimental results, although some discrepancy is seen in detail. We think that our present work has contributed to the understanding of the reaction profile. Acknowledgment. This work has been supported by CREST of JST (Japan Science and Technology). We are also grateful for financial support by a Grant-in Aid for Scientific Research on Priority Areas “Molecular Physical Chemistry” from the Ministry of Education, Science, Sports, and Culture. References and Notes (1) As a comprehensive textbook: Masel, R. I. Principles of Adsorption and Reactions on Solid Surfaces; John Wiley: New York, 1996. (2) Ko, E. I.; Madix, R. J. Appl. Surf. Sci. 1979, 3, 236. (3) Benziger, J. B.; Madix, R. J. Surf. Sci. 1979, 79, 394. (4) McCarty, J. G.; Falconer J. L.; Madix, R. J. J. Catal. 1973, 30, 235. (5) Falconer J. L.; Madix, R. J. Surf. Sci. 1974, 46, 473. (6) Falconer J. L.; Madix, R. J. Surf. Sci. 1975, 48, 393. (7) Madix, R. J.; Falconer J. L. Surf. Sci. 1975, 51, 547. (8) Yamataka, A.; Kubota, J.; Kondo, J. N.; Domen, K.; Hirose, C. J. Phys. Chem. 1996, 100, 18177. (9) Yamataka, A.; Kubota, J.; Kondo, J. N.; Hirose, C.; Domen, K. J. Phys. Chem. 1997, 101, 5177. (10) Yamataka, A.; Kubota, J.; Kondo, J. N.; Hirose, C.; Domen, K.; Wakabayashi, F.; Tamaru, K. J. Phys. Chem. 1998, B102, 4401. (11) Benziger, J. B.; Schoofs, G. R. J. Phys. Chem. 1984, 88, 4439. (12) Wulser, K.; Langell, M. A. Catal. Lett. 1992, 15, 39. (13) Troung, C. M.; Wu, M. C.; Goodman, D. W. J. Chem. Phys. 1993, 97, 9447. (14) Xu, C.; Goodman, D. W. Catal Today 1996, 28, 297. (15) Xu, C.; Goodman, D. W. J. Chem. Soc. Faraday Trans. 1995, 91, 3709. (16) Bandara, A.; Kubota, J.; Wada, A.; Domen, K.; Hirose, C. Surf. Sci. 1996, L580, 364. (17) Bandara, A.; Kubota, J.; Wada, A.; Domen, K.; Hirose, C. J. Phys. Chem. 1996, 100, 14962. (18) Kubota, J.; Bandara, A.; Wada, A.; Domen, K.; Hirose, C. Surf. Sci. 1996, 368, 361. (19) Bandara, A.; Kubota, J.; Wada, A.; Domen, K.; Hirose, C. J. Phys. Chem. 1997, B101, 361. (20) Matsumoto, T.; Bandara, A.; Kubota, J.; Hirose, C.; Domen, K. J. Phys. Chem. 1998, B102, 2979. (21) Bandara, A.; Kubota, J.; Onda, K.; Wada, A.; Kano, S. S.; Domen, K.; Hirose, C. J. Phys. Chem. 1998, B102, 5951. (22) Hu, Z.; Boyd, R. J. Chem. Phys. 2000, 112, 9562. (23) Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Gra¨tzel, M. J. Phys. Chem. 2000, B104, 1300. (24) Nakatsuji, H.; Yoshimoto, M.; Umemura, Y.; Takagi, S.; Hada, M. J. Phys. Chem. 1996, 100, 694. Yoshimoto, M.; Takagi, S.; Umemura, Y.; Hada, M. Nakatsuji, H. J. Catal. 1998, 173, 53. (25) Nakatsuji, H.; Yoshimoto, M.; Hada, M.; Domen, K.; Hirose, C. Surf. Sci. 1995, 336, 232; Lintuluoto, M.; Kanai, H.; Hada, M.; Nakatsuji, H. Surf. Sci. 1999, 429, 133. (26) Slater, J. C. Phys. ReV. 1951, 81, 385. (27) Becke, A. D. Phys. ReV. 1988, A38, 3098. (28) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (29) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200l. Wilk, L.; Vosko, S. H. J. Phys. C: Solid State Phys. 1982, 15, 2139.
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