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Bonding of Methyl Phosphonate to TiO2(110)† C. L. Pang,‡,§,| M. Watkins,‡ G. Cabailh,‡,§ S. Ferrero,| L. T. Ngo,|,⊥ Q. Chen,‡,§ D. S. Humphrey,‡,§ A. L. Shluger,‡ and G. Thornton*,‡,§ London Centre for Nanotechnology, UniVersity College London, London WC1H 0AJ, United Kingdom; Chemistry Department, UniVersity College London, London WC1H 0AJ, United Kingdom; Department of Chemistry, UniVersity of Manchester, Manchester, M13 9PL, United Kingdom; and Department of Chemistry, Box 351700, UniVersity of Washington, Seattle, Washington 98195-1700 ReceiVed: March 2, 2010; ReVised Manuscript ReceiVed: April 14, 2010
We have used scanning tunneling microscopy (STM), noncontact atomic force microscopy (NC-AFM), low energy electron diffraction (LEED), and ab initio calculations to study adsorbates resulting from exposure of rutile TiO2(110)1 × 1 to methyl phosphonic acid (CH3PdO(OH)2). At low exposures, adsorbates appear on the 5-fold coordinated Ti (Ti5c) rows. As the coverage of adsorbates approaches 0.5 ML, STM images show an ordered 2 × 1 overlayer consistent with LEED. We propose that the phosphonic acid is deprotonated with the resulting phosphonate bridging across two adjacent Ti5c atoms in the [001] direction. This bridging conformation would lead to the observed 2 × 1 overlayer and is analogous to that found for a range of carboxylates adsorbed on TiO2(110). 1. Introduction The adsorption of organic molecules onto oxide surfaces has received a great deal of attention recently due to the role that these systems can play in emerging technologies such as novel solar cells and molecular electronics.1-3 Organic phosphonic acids have been studied intensively of late due to the strong bonds they make with metal and metal oxide substrates. This adhesive property can be exploited in corrosion protection of surfaces, such as those of aluminum,4-6 and is important in the decontamination of chemical agents such as organo-phosphorus compounds in aqueous solution (sarin and pesticides).7 Phosphonic acid groups are also employed extensively to graft molecules with other functionalities to target surfaces.8-11 Despite these applications, adsorbates formed by exposure to phosphonic acids have received much less attention than carboxylates, for example. The latter have been studied extensively on single crystal substrates, including those of TiO2(110).12-17 There have, however, been a number of studies of adsorption onto powders resulting from exposure to phosphonic acid or related compounds such as dimethyl methylphosphonate.7 These include TiO2 powders. Here, we present scanning tunneling microscopy (STM) and noncontact atomic force microscopy (NCAFM) studies of the adsorption of methyl phosphonic acid (MPA) on rutile TiO2(110), and the results of complementary computations using density functional methodology. Figure 1 shows a schematic depiction of the MPA molecule. The functional group consists of a phosphorus atom connected to an O atom with a double bond and to two OH groups via single bonds. Figure 2 shows a high resolution STM image of the TiO2(110) surface together with a ball model of the structure. The key features are the 5-fold coordinated Ti (Ti5c) rows running in the [001] direction, which alternate with bridging-O †
Part of the “D. Wayne Goodman Festschrift”. * To whom correspondence should be addressed. Telephone: +44 20 7679 7979. Fax: +44 20 7679 0595. E-mail:
[email protected]. ‡ London Centre for Nanotechnology, University College London. § Chemistry Department, University College London. | University of Manchester. ⊥ University of Washington.
Figure 1. Schematic representation of (a) the MPA molecule and three adsorption modes of the MPA molecule on TiO2(110): (b) monodentate; (c) bidentate with single proton transfer; and (d) bidentate with double proton transfer. The bidentate bonding involves adjacent Ti5c atoms in the [001] azimuth. The colors of atoms are as follows: yellow, P; red, O; gray, C; green, H; with blue and red intersections representing Ti atoms and O atoms, respectively.
(Ob) rows. In STM, the Ti5c rows usually appear bright, whereas in NC-AFM the Ob rows usually appear bright.18-22 The other significant features are the defects, which appear as bright spots between the bright rows in STM (and as depressions in the NCAFM). These defects have been denoted as type-A defects,19 and recent work shows that they consist of bridging oxygen vacancies (Ob-vac) and bridging hydroxyl (OHb).20-22 Here, we show experimentally that MPA adsorbs strongly to the TiO2 surface and, at coverages approaching half a monolayer (where 1 ML is defined as the density of primitive surface unit cells), this leads to a 2 × 1 overlayer similar to that observed for many carboxylic acids.12-16 An interpretation of these data, supported by density functional theory calculations, is that the
10.1021/jp1018923 2010 American Chemical Society Published on Web 05/12/2010
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Figure 2. TiO2(110) surface. (a) 75 Å2 STM image of as-prepared TiO2(110) recorded at 1.5 V and 0.1 nA. Bright rows correspond to 5-fold coordinated Ti rows, and dark rows correspond to bridging-O rows. Type-A defects can be seen between the bright rows and are assigned as Ob-vac and OHb. (b) Stick model of TiO2(110). Blue and red intersections represent Ti atoms and O atoms, respectively. Red spheres denote bridging-O. An Ob-vac and an OHb are shown.
MPA molecules adsorb dissociatively, forming bidentate methyl phosphonate anions which bridge across two Ti5c sites along the [001] direction. 2. Methods Experimental. The experiments were performed in Manchester and London, employing an Omicron STM/AFM apparatus equipped with a digital demodulator (Nanosurf) and an Omicron variable temperature scanning tunneling microscope. Both microscopes were operated under a base pressure of 1 × 10-10 mbar and at room temperature. STM images were recorded in the constant current mode using tungsten tips held at ground potential with the sample biased positively (empty states regime) in the range 1.2-1.5 V, with the tunneling current in the range 0.5-1.1 nA. NC-AFM images were recorded using a silicon cantilever (Nanosensors) with a constant frequency shift (∆f) of approximately -30 Hz. The resonant frequency of the cantilever was ∼70 kHz, and the spring constant was ∼2.75 N m-1. The rutile crystals (Pi-Kem) were slightly reduced and transparent blue. Sample preparation was carried out by Ar+ ion bombardment (1 keV) and annealing to ∼1000 K in vacuum. A home-built doser was used to evaporate the MPA (Tevaporation ) 106 °C). It consists of a tungsten heating filament wrapped around a glass dosing tube which houses the solid MPA. In both microscopes, the doser was attached to a preparation chamber via a hand valve so that the preparation chamber could be baked with the doser detached. The doser was thoroughly degassed above the power used for evaporation. We tested the efficacy of the doser by depositing 5 s to 30 min MPA onto the TiO2(110) surface: C-H vibrations were detected in high resolution electron energy loss spectroscopy, while phosphorus and carbon were detected in Auger electron spectroscopy. These features were not detected unless the sample was placed in lineof-sight to the doser.
Pang et al. Computational. Calculations were performed using the density functional theory within two different computational schemes: Calculations on small (2 × 1) unit cells were performed using the VASP code23 using the PW91 density functional,24 a planewave basis set with effective energy cutoff of 500 eV (350 eV for molecular dynamics), a projector augmented wave representation25 of core electrons (Ti 3s and 3p electrons were treated as valence), and a 5 × 5 × 1 Monkhorst-Pack k-point mesh for integrations over the Brillouin zone. STM images were simulated using the Tersoff-Hamann approximation26 including occupied states within 0.5 eV of the valence band edge for occupied states images and unoccupied states within 0.5 eV of the conduction band edge for empty states images. Images shown are electon density isosurfaces of 1.0 × 10-6 |e|/Å3. They correspond to pseudo constant-current images. For static calculations, simulation cells containing up to five layers of TiO2 substrate were included, where a layer is composed of O-Ti-O units. Ab initio molecular dynamics simulations were carried out on a three layer TiO2 substrate within the microcanonical ensemble using a 1.0 fs integration time step. The simulations were started from a configuration close to a local minimum and resulted in an average temperature of 249 K after an equilibration period of 5 ps. This was sufficiently close to the experimental temperature that no temperature rescaling was applied. The CP2K program suite,27 which uses local Gaussian basis functions for most operations, was used to calculate the energies of larger (4 × 2) supercells, allowing isolated molecules and surface reconstructions to be investigated. For computational expedience, only three layers of TiO2 were considered. The PBE density functional28 was used with Gaussian basis sets of DZVP quality for geometry optimization,29 GTH pseudopotentials,30,31 and the auxiliary plane-wave basis, used to calculate the hartree energy, had a 4000 eV energy cutoff. Single point calculations at optimized geometries were carried out using a larger TZV2P29 quality Gaussian basis set on all atoms except the Ti ions to remove remaining errors due to basis set superposition error (BSSE), which were already rather small with the DZVP basis sets (∼50 meV). 3. Results a. STM Images after Low Exposure to MPA. Figure 3a shows an STM image following a low exposure to the MPA. Bright spots are shown clearly lying on the bright rows with ∼0.08 ML coverage. Between the bright rows, type-A defects can be observed, indicating that the bright rows correspond to Ti5c.12,18-22 Figure 3b shows an STM image taken following a longer exposure to MPA. The bright spots have ∼0.2 ML coverage. In these images, the apparent height of the spots above the rows is ∼1 Å. Figure 4a and b shows an STM and a NC-AFM image, respectively, of the surface following further exposure to MPA. The STM image has ∼0.3 ML coverage of bright spots. In patches, the bright spots are well-packed such that the nearest distance between neighboring spots in the [001] direction is 6 and 6.5 Å in the [11j0] direction. This is equivalent to two unit cell distances in the [001] direction and to one TiO2(110) unit cell distance in the [11j0] direction, suggesting that, in parts, the overlayer has a 2 × 1 structure. b. Saturation Coverage of MPA. Figure 5 shows two STM images following further exposure to MPA. A 2 × 1 overlayer is clearly observable, which essentially covers the entire surface, giving a coverage of ∼0.5 ML. The corrugation of the saturated
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Figure 4. Images of 0.3 ML MP on TiO2(110). (a) 220 Å2 STM image recorded at 1.2 V and 1.0 nA. (b) 200 Å × 130 Å NC-AFM image of the same surface. Expanded areas are shown in the insets, 57 Å2.
Figure 3. STM images of TiO2(110) recorded following low exposure to MPA. (a) 0.08 ML methyl phosphonate (MP), 75 Å2, recorded at 1.2 V and 1.1 nA. One type-A defect is highlighted by a circle, and two MP adsorbates by squares. (b) 0.20 ML MP, 130 Å2, recorded at 1.4 V and 1.0 nA.
overlayer is approximately 0.4 and 0.6 Å in the [001] and [11j0] directions, respectively. Figure 6 shows the associated low energy electron diffraction (LEED) pattern. The LEED beams from the TiO2(110)1 × 1 substrate are marked with a solid rectangle, whereas the additional 2 × 1 superstructure is indicated with a dashed rectangle. c. Density Functional Theory (DFT) Calculations. Calculations of 2 × 1 supercells containing a molecule of MPA, corresponding to the full 0.5 ML coverage observed experimentally, show that the molecule binds in a bidentate manner to the surface, forming two oxygen-titanium bonds. This bonding is strong, with the adsorption energies calculated to be -2.54 and -2.33 eV for simulations including three and five layers of the TiO2 substrate, respectively. Configurations with the MPA monodentate (Figure 1b) or bidentate to a single surface Ti5c ion relaxed toward the bidentate adsorption structures (Figure 1c, d) and were high in energy. The calculated geometry for the most stable structure (shown in Figure 7) has Ti-O, MPA(O)-H, and surface O-H distances of 1.91, 1.71, and 1.01 Å, respectively. The two protons originally forming the MPA hydroxyl groups are donated to surface bridging oxygen sites, but remain close to the donor molecule and in a geometry indicating a significant hydrogen-bonding interaction between the surface OH groups and the MPA oxygen. However,
the radial distribution function of the hydroxyl protons and the oxygen of MPA not bound to the surface, obtained from a molecular dynamics simulation, has a bimodal distribution (Figure 8a) indicating that protons transfer back and forth between the molecule and surface at the simulation temperature (∼249 K). We anticipate that this should have a significant influence on the OH stretching mode, which should be observable using infrared spectroscopy. Simulated STM images of the full 0.5 ML overlayer were calculated using the Tersoff-Hamann approximation.26 States within 0.5 eV of the valence or conduction band edge for filled or empty state images, respectively, were included in the integral. The simulated images of complete monolayers show that the molecules appear as large blobs centered upon the methyl group of the acid (Figure 7 plotted as isosurfaces of electron density, 1 × 10-6 |e| · Å-3). The appearance of the molecule is not expected to depend significantly on the applied bias voltage due to the presence of energy levels with significant molecular character at both the valence and conduction band edges (Figure 9) and the molecular image appears largely topological: the methyl group of the molecule is raised above the surface and is the principle component of the image. The simulated images show a smaller spatial extent in the [11j0] direction than the experimental images. This is due to the molecule being fairly flexible: ab initio molecular dynamics simulations show that the MPA methyl group undergoes large oscillations in the [11j0] direction (see Figure 8b), with the angle formed by the P-C bond and the surface normal fluctuating by almost 30°. There will also be a contribution to the width discrepancy from the absence of finite tip size in the Tersoff-Hamann approximation. The spatial extent of the
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Figure 7. Adsorption geometry and simulated STM images of the MPA molecule at saturation (0.5 ML) coverage on TiO2(110). The side view is looking along the [001] direction, which is the vertical direction in the plan view. To obtain the STM images, the Tersoff-Hamann approximation is used with the DOS integrated over states within 0.5 eV of the valence band edge (left and blue) or conduction band edge (right and red) and the electron density isosurfaces plotted are 1 × 10-6 |e| · Å-3. The colors in the models are as in Figure 1.
Figure 5. STM images of 0.5 ML MP on TiO2(110) recorded with 1.5 V and 0.8 nA. (a) 350 Å2 image. (b) 140 Å2 image. In (b), the solid rectangle in the inset indicates the 2 × 1 unit cell of MP anions.
Figure 8. (a) Radial distribution function showing the distance between the hydroxyl protons of the MPA and (black circles) the TiO2(110) bridging oxygens or (red squares) the oxygen of MPA not bound to the surface. (b) Angle made by the P-C bond of the molecule and the surface normal as a function of time during a molecular dynamics simulation. The models are shown in side view looking along the [001] azimuth. The colors in the models are as in Figure 1.
Figure 6. LEED pattern (46 eV) of 0.5 ML MP on TiO2(110). The solid rectangle indicates the 1 × 1 substrate unit cell, and the dashed rectangle shows the 2 × 1 MP unit cell.
methyl group is likely to obscure the neighboring bridging oxygen row, making direct observation of the proposed hydroxyl groups using scanning probe techniques unfeasible.
To investigate the behavior of MPA at lower coverage, calculations were performed using a larger 4 × 2 supercell. This cell can accommodate a single molecule separated from its periodic images by ∼6 Å and offers surface bridging oxygen sites for the protons distant from the molecular ion. For this “isolated” molecule, we find that it is still most preferable for the MPA molecule to donate both of its protons to neighboring bridging oxygen sites: a top view of the adsorbed molecule is shown in Figure 10a. The adsorption energy of this isolated molecule is slightly greater than that of molecules adsorbed within complete overlayers. The energy difference is +0.41 eV per molecule and is overestimated due to the absence of dispersion interactions in our treatment.32 The inclusion of an empirical van der Waals correction32,33 reduced this energy difference to +0.27 eV. The slightly reduced binding energy per molecule at full 0.5 ML coverage indicates that ordered layers should only form when isolated surface sites have already
Bonding of Methyl Phosphonate to TiO2(110)
Figure 9. Projected density of states for the monolayer adsorbed MPA molecules. Note the presence of molecular DOS near both the conduction and valence band edges. The energy zero is the top of the valence band.
Figure 10. Configurations of the isolated MPA molecule on TiO2(110), showing the relative energies of different proton positions.
been occupied as interactions between neighboring MPA molecules are mildly repulsive. The slight energetic preference for the isolated environment is consistent with the lack of large ordered patches in the lower coverage experimental images Figures 3 and 4. We also considered the energies required to separate one or two protons from the adsorbed MP ion to more distant bridging oxygen sites. As already noted, the fully deprotonated MP ion with two neighboring protons is the most stable species (Figures 10a and 1d). A second configuration (Figures 10b and 1c) with one proton remaining on the MPA molecule is only 0.17 eV higher in energy, consistent with the observed proton transfer from surface to molecule in molecular dynamics. Moving one proton to a next nearest oxygen bridging site cost a modest 0.2-0.3 eV compared to the most stable configuration (Figure 10c, d). After the removal of the first proton, there was very little energy difference between the two configurations (Figure 10c, d), with a proton either on the methyl phosphonate (MP) ion or on a neighboring oxygen bridge site. To remove both protons to next-neighbor bridging oxygen sites was significantly more costly (Figure 10e); the configuration considered was 0.6 eV less stable than that when both protons neighbored the MP ion. 4. Discussion The 2 × 1 overlayer gives a strong intuitive indication of a bidentate bonding arrangement as seen in Figure 7, whereby
J. Phys. Chem. C, Vol. 114, No. 40, 2010 16987 the MP bridges two Ti5c species, adjacent in [001]. This is because the maximum packing density of such bridge-bonded MP anions would lead to a 2 × 1 arrangement. This is a similar situation to that seen for a series of carboxylates,12-16 where the carboxylic acids lose a proton and bond as carboxylate anions. A bidentate configuration has also been calculated for formic and acetic acid dissociatively adsorbed on rutile TiO2(011).34 However, the situation is more complicated for MPA. As seen in Figure 1, there are two ways in which MPA could form a bidentate arrangement by donating either one or two protons to the TiO2 surface. The analogy with the binding of carboxylic acids to the TiO2(110) surface suggests that MPA adsorbs dissociatively. This means that the bright spots, which increase in density with exposure, are MP species. DFT calculations support this, finding a dissociated state, with protons on neighboring bridging oxygen sites, as the most energetically favorable state at high molecular coverage. The above conclusions are consistent with adsorption studies on powders. Recently, Rusu and Yates also showed that, at temperatures above 214 K, dimethyl methylphosphonate adsorbs dissociatively in the bidentate configuration by losing a proton and a methyl group.7 Luschtinetz et al. also predicted the bidentate adsorption of phosphonic acid to be the most stable on both the anatase (101) and rutile (110) surfaces.35 Molecular dynamics simulations show that the overlayer is quite mobile, with protons transferring from bridging oxygen rows to MP ions and the methyl groups undergoing quite significant motion. The molecules should appear large and featureless due to the combined effect of the mobility of the adsorbed molecules observed during molecular dynamics simulations and the large spatial extent of the methyl group found in STM image simulations. This is in good qualitative agreement with the observed STM/AFM images. Unfortunately, this appears to rule out the observation of the proposed hydroxylated bridging oxygen rows using scanning probe techniques. Complementary information to provide confirmation of the proposed overlayer structure could be obtained from infrared spectroscopy. We anticipate significant red shifting and broadening of the OH vibrations due to the transfer of protons between the MP ion and surface, as observed in our molecular dynamics simulations. We are carrying out further calculations to investigate this fully and will report the results elsewhere. 5. Conclusions We have used STM and NC-AFM in combination with computational modeling to study the adsorption of methyl phosphonic acid on rutile TiO2(110) 1 × 1. Evidence is given for bidentate, bridging adsorption of the molecule as methyl phosphonate, following deprotonation of one or both OH groups. These anions attach themselves to two 5-fold coordinated sites so that, at saturation, a 2 × 1 ordered monolayer is formed. The overlayer is observed both with STM and in LEED. Acknowledgment. This work was funded by EPSRC (UK) and the EU. L.T.N.’s visit to Manchester was supported by a World University Network Fellowship. The authors would like to acknowledge a number of useful discussions with Morgan Alexander, Roger Newman, and Ioannis Liakos. Via membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC (EP/F067496), this work made use of the facilities of HPCx and HECToR, the UK’s national highperformance computing services. Finally, we wish to acknowledge use of the UCL Legion supercomputers.
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References and Notes (1) Gra¨tzel, M. Nature (London) 2001, 414, 338. (2) Grill, L.; Moresco, F. J. Phys.: Condens. Matter 2006, 18, S1887. (3) Nazin, G. V.; Qiu, X. H.; Ho, W. Phys. ReV. Lett. 2005, 95, 166103. (4) Liakos, I. L.; Newman, R. C.; McAlpine, E.; Alexander, M. R. Surf. Interface Anal. 2004, 36, 347. (5) Hector, L. G., Jr.; Opalka, S. M.; Nitowski, G. A.; Wieserman, L.; Siegel, D. J.; Yu, H.; Adams, J. B. Surf. Sci. 2001, 494, 1. (6) Liakos, I. L.; Newman, R. C.; McAlpine, E.; Alexander, M. R. Langmuir 2007, 23, 995. (7) Rusu, C. N.; Yates, J. T., Jr. J. Phys. Chem. B 2000, 104, 12292. (8) Cummins, D.; Boschloo, G.; Ryan, M.; Corr, D.; Nagaraja Rao, S.; Fitzmaurice, D. J. Phys. Chem. B 2000, 104, 11449. (9) Bae, E.; Choi, W.; Park, J.; Shin, H. S.; Kim, S. B.; Lee, J. S. J. Phys. Chem. B 2004, 108, 14093. (10) Pawsey, S.; Yach, K.; Reven, L. Langmuir 2002, 18, 5205. (11) Odobel, F.; Blart, E.; Lagre´e, M.; Villieras, M.; Boujtita, H.; El Murr, N.; Caramori, S.; Bignozzi, C. A. J. Mater. Chem. 2003, 13, 502. (12) Onishi, H.; Fukui, K.; Iwasawa, Y. Bull. Chem. Soc. Jpn. 1995, 68, 2447. (13) Sasahara, A.; Uetsuka, H.; Ishibashi, T.; Onishi, H. J. Phys. Chem. B 2003, 107, 13925. (14) Schnadt, J.; O’Shea, J. N.; Patthey, L.; Schiessling, J.; Krempaský, y J.; Shi, M.; Mårtensson, N.; Bru¨hwiler, P. A. Surf. Sci. 2003, 544, 74. (15) Sayago, D. I.; Polcik, M.; Lindsay, R.; Toomes, R. L.; Hoeft, J. T.; Kittel, M.; Woodruff, D. P. J. Phys. Chem. B 2004, 108, 14316. (16) Guo, Q.; Williams, E. M. Surf. Sci. 1999, 433, 322. (17) Pang, C. L.; Lindsay, R.; Thornton, G. Chem. Soc. ReV. 2008, 37, 2328.
Pang et al. (18) Diebold, U.; Anderson, J. F.; Ng, K.-O.; Vanderbilt, D. Phys. ReV. Lett. 1996, 77, 1322. (19) Diebold, U.; Lehman, J.; Mahmoud, T.; Kuhn, M.; Leonardelli, G.; Hebenstreit, W.; Schmid, M.; Varga, P. Surf. Sci. 1998, 411, 137. (20) Pang, C. L.; Bikondoa, O.; Humphrey, D. S.; Papageorgiou, A. C.; Cabailh, G.; Ithnin, R.; Chen, Q.; Muryn, C. A.; Onishi, H.; Thornton, G. Nanotechnology 2006, 17, 5397. (21) Pang, C. L.; Sasahara, A.; Onishi, H.; Chen, Q.; Thornton, G. Phys. ReV. B 2006, 74, 073411. (22) Lauritsen, J. V.; Foster, A. S.; Olesen, G. H.; Christensen, M. C.; Ku¨hnle, A.; Helveg, S.; Rostrup-Nielsen, J. R.; Clausen, B. S.; Reichling, M.; Besenbacher, F. Nanotechnology 2006, 17, 3436. (23) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (24) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (25) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (26) Tersoff, J.; Hamann, D. R. Phys. ReV. B 1985, 31, 805. (27) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Comput. Phys. Commun. 2005, 167, 103. (28) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (29) VandeVondele, J.; Hutter, J. J. Chem. Phys. 2007, 127, 114105. (30) Hartwigsen, C.; Goedecker, S.; Hutter, J. Phys. ReV. B 1998, 58, 3641. (31) Krack, M. Theor. Chem. Acc. 2005, 114, 145. (32) Grimme, S. J. Comput. Chem. 2006, 27, 1787. (33) The correction was applied a postieri without the geometry being self consistently relaxed with the new functional. (34) McGill, P. R.; Idriss, H. Surf. Sci. 2008, 602, 3688. (35) Luschtinetz, R.; Frenzel, J.; Milek, T.; Seifert, G. J. Phys. Chem. C 2009, 113, 5730.
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