Assessment of Hybrid Density Functionals for the Adsorption of

Article pubs.acs.org/JPCA

Assessment of Hybrid Density Functionals for the Adsorption of Carbon Monoxide on Platinum Model Clusters Thomas M. Soini,† Alexander Genest,‡ and Notker Rösch*,†,‡ †

Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, Connexis #16-16, Singapore 138632, Singapore

‡

ABSTRACT: We examined computationally the adsorption of CO on various sites of (111) facets of the model clusters Pt79 and Pt225 with the semilocal exchange−correlation functionals PBE, TPSS, and M06L as well as their corresponding hybrid DFT variants PBE0, TPSSh, and M06. The adsorption of CO molecules on Pt(111) is a well-known challenge for the Kohn−Sham DFT approach because one has to treat adequately the electronic structure of the metallic moiety and simultaneously control the self-interaction in the adsorbate. Indeed, in the context of the so-called CO puzzle, hybrid DFT methods do not appear to be beneficial. (LUMO).9−11 The relative strength of these two synergetic interactions depends on the local topology of the adsorption site and the electronic structure of the metal.4 Back-bonding is most pronounced at μ3-type hollow sites (fcc-, hcp-type) due to the larger overlap between 2π* and d levels.10,11 The selfinteraction error,12 an inherent defect of all semilocal XC methods, causes the partially occupied 2π* MOs to lie too low in energy, enhancing back-bonding. In consequence, this attractive self-interaction artifact is strongest at hollow sites, thus rationalizing the unphysical preference for CO adsorption at fcc-hollow sites of Pt(111) (and other metal surfaces) by semilocal DFT methods. However, back-bonding occurs to some extent at all types of adsorption sites, which explains the generally overestimated adsorption energies with semilocal XC approximations.4,5,13−15 Once this failure of semilocal XC approximations was recognized, a number of theoretical studies examined various related aspects, e.g., models of the adsorption sites,14,16,17 the influence of relativistic effects,14,18,19 and the effect of empirical self-interaction corrections acting on the 2π* MOs.14,17 Also hybrid DFT methods like B3LYP20 and PBE021 were applied4,14−16 to describe the CO adsorption on Pt(111) as these functionals provide a partial self-interaction correction. However, while rectifying the energies of the 2π* MOs, the exact-exchange (EXX) term of hybrid functionals significantly deteriorates the description of the density of states and the multireference character within the metal moiety.4,22 Yet, though suffering from self-interaction, semilocal DFT methods like TPSS can provide quite an accurate description of transition metal systems.23

1. INTRODUCTION Describing the correct preference for the adsorption site of CO molecules on the Pt(111) surface is a well-known challenge to Kohn−Sham DFT methods as common semilocal exchange− correlation (XC) functionals fail. 1−5 The resulting CO adsorption energies of Pt(111) not only are too large by at least 40 kJ/mol3−5 but are also unable to reproduce the correct adsorption site preference on this surface (“CO puzzle”).1 Experiments found the CO molecule to adsorb on a top site position (μ1, denoted as “t”),6−8 semilocal XC methods yield an fcc-hollow μ3-type (“f”) adsorption complex as preferred (Figure 1). 1,2,4,5 This generic failure of all semilocal exchange−correlation approximations can be understood in the context of the Blyholder model,9 which describes CO bonding to transition metals via σ-donation from the CO 5σ molecular orbital (MO) to the metal surface, and “backbonding” from the metal to the unoccupied CO 2π* orbitals

Figure 1. Positions of the top (t), fcc-hollow (f), and bridge (b) adsorption sites on the (111) facets of the model clusters Pt79 (top) and Pt225 (bottom). © XXXX American Chemical Society

Received: February 23, 2015 Revised: April 3, 2015

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DOI: 10.1021/acs.jpca.5b01803 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Table 1. CO Adsorption Energiesa Eads (kJ/mol) per Molecule Obtained with the Assessed Functionals at the Different Adsorption Sites on the (111) Facets of Examined Cluster Models

In a recent study22 we found the hybrid functional TPSSh24 to yield a very good description of late transition metal clusters due to its smaller fraction (10%) of EXX compared to the amount of EXX in B3LYP (20%) and PBE0 (25%). Motivated by these results, we address in the present work the question whether TPSSh provides a sufficiently strong SI correction for rectifying the site preference of adsorption. To this end we examined the CO adsorption on (111) facets of Pt model clusters using TPSSh and two other hybrid DFT methods (PBE0, M06) and their semilocal counterparts (TPSS, PBE, M06L). We compared the generalized-gradient approximation (GGA) PBE25 and its nonempirical hybrid version PBE0,21 the meta-GGA TPSS,26 and its one-parameter hybrid variant TPSSh, as well as the hybrid meta-GGA functional M0627 and its local reparametrization M06L.28 We also briefly discuss scalar relativistic effects.

Pt79

Pt225

siteb

PBEc

PBE0

TPSS

1t 2f Δ(2f−1t) 3be 5t 6f Δ(6f−5t)

156 168 12 176 134 154 20

180 196 16

151 (150)d 160 (160)d 9 174 127 146 19

TPSSh M06L 156 164 8

145 153 8

M06 159 176 17

128f 153f 25

Experimental result for Pt(111): 115 ± 15 kJ/mol; ref 45. bFor the designation of the adsorption sites, see Figure 1 and section 2. c Reference 17. dIn parentheses: results of all-electron scalar-relativistic calculations; see text. eFor PBE0, TPSSh, M06L, and M06, geometry optimization of CO adsorption at site 3b leads to an adsorption complex with CO at the hollow site near the facet edge. fSingle-point calculations at the corresponding TPSS geometry. a

2. COMPUTATIONAL DETAILS All calculations were carried out with the program PARAGAUSS,29 an implementation of the Gaussian-type orbital fitting-functions density functional method (LCGTO-FF-DF).30 We recently added modules to compute the EXX term and thus enabled hybrid DFT calculations, via our own implementation of electron repulsion integrals as well as an existing, highly optimized library.31 With dynamic load balancing, parallel execution can be very efficient.32 All calculations were carried out in spin-restricted fashion. Changes in the density matrix were converged to below 5 × 10−6, employing a fractional occupation number technique30 with an energy range of 0.01 eV. For computational efficiency, we calculated the model clusters by applying D4h symmetry constraints (C4v for a CO molecule in the gas phase). We employed the orbital basis set def2-TZVP,33 together with the corresponding pseudopotential for Pt.34 For calculating the Hartree potential, we used the appropriate auxiliary basis set35 to represent the electron density.30 In the all-electron scalar relativistic calculations,36,37 we employed a SARC-type basis for Pt,38 together with a wellestablished prescription for the auxiliary basis set.30 All adsorption energies were corrected for the basis set superposition error,39 invoking the counterpoise correction,40 which typically amounts to 7−8 and 10−11 kJ/mol for top and hollow sites, respectively, in line with the larger overlap at the latter sites. The numerical integration of XC terms was carried out with a superposition41 of atom-centered spherical Lebedevtype grids,42 each locally exact for spherical harmonics up to angular momentum L = 19. The radial grids contained 245, 134, and 117 radial shells for Pt, C, and O, respectively. The utility suite PARATOOLS43 was used to relax all atomic forces below 10−5 au. CO adsorption sites were modeled on the (111) facets of truncated octahedral clusters (Figure 1). On Pt79 we examined top (1t), fcc-hollow (2f), and μ2-bridge (3b) sites; on the model Pt225 we focused at top (5t) and fcc-hollow (6f) sites near the center of (111) facets.17

the expectation that back-bonding is reduced in hybrid DFT methods due to the higher energy of the CO 2π* MOs. The present PBE0 results on Pt79 agree rather well with the corresponding slab model values: Eads(t) = 187 kJ/mol, Eads(f) = 193 kJ/mol.4 This agreement has to be considered with caution as the cluster results include an attractive influence of the neighboring facet edges.17,44 Both sets of results are notably too high compared to the experimental reference, Eads = 115 ± 15 kJ/mol.45,46 The M06 adsorption energies are considerably lower, Eads(1t) = 159 kJ/mol, Eads(2f) = 176 kJ/mol, than those obtained from PBE0 and only slightly higher than the PBE results. The smaller Eads values of M06 are surprising as the amount of EXX in this method (27%) is similar to that in PBE0 (25%). The lower M06 adsorption energies likely are related to its deviating description of the metallic moiety (section 3.2).22 The Eads values from the meta-GGA functionals TPSS [Eads(1t) = 151 kJ/mol, Eads(2f) = 160 kJ/mol] and M06L [Eads(1t) = 145 kJ/mol, Eads(2f) = 153 kJ/mol] are the smallest among the methods studied here. The TPSSh functional yields only slightly higher adsorption energies than TPSS, 156 kJ/mol (1t) and 164 kJ/mol (2f), in agreement with its relatively small amount of EXX (10%). In a previous study17 we noted the bridge site 3b on Pt79 to be strongly affected by the nearby facet edge.17 A CO molecule, initially adsorbed there, relaxed in most cases to the closest hollow position near the facet border. This attraction17 is also noticeable with PBE and TPSS, which still yield a stable minimum at this site. With TPSS a comparatively high adsorption energy results, 174 kJ/mol, which is similar to the previously reported PBE result, 176 kJ/mol.17 The adsorption behavior of CO on the site 3b of the cluster Pt79 suggests examining cluster effects also in the present study.17 Although the influence due to the smaller average nearest neighbor Pt−Pt distances is quite small at these cluster sizes,17 the undercoordinated atoms near the borders of the (111) facets affect the adsorption energies much more. To probe the effect of facet edges in the present context, we also explored adsorption at the larger (111) facets of the cluster model Pt225. In a previous study17 we identified the sites 5t and 6f of Pt225 (Figure 1) as reliable models of the corresponding adsorption sites on the extended Pt(111) surface. On this cluster model the preference for the 3b site vanishes as expected.17 Thus, bridge sites are considered irrelevant for the

3. RESULTS AND DISCUSSION 3.1. CO Adsorption Energies. The adsorption energies Eads obtained with six functionals for the sites 1t, 2f, and 3b on the cluster model Pt79 (Figure 1) are collected in Table 1. PBE0 yields relatively large adsorption energies: Eads(1t) = 180 kJ/ mol, Eads(2f) = 196 kJ/mol. These values are notably larger than the corresponding PBE results (Table 1), at variance with B


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Table 2. Pt−C and C−O Bond Lengths at the Different Adsorption Complexesa on the (111) Facets of the Structurally Relaxed Pt79 Cluster Model, C−O Bond Length of the Gas Phase CO Molecule, and Average Nearest Neighbor Pt−Pt Distance ⟨Pt−Pt⟩ of the Isolated Models (All Values in pm) Pt−C

Pt79

Pt225 C−O

Pt79

Pt225

⟨Pt−Pt⟩

1t 2fb 3bc 5t 6f 1t 2f 3b 5t 6f COgasd Pt79e Pt225e

PBE

PBE0

TPSS

TPSSh

M06L

M06

182.6 208.4 199.8 184.6 208.6−211.2 115.2 119.3 117.7 115.0 119.0 113.7 275.8 276.9

180.9 202.2−207.8

183.7 204.5−214.5 201.3 185.8 209.5−213.4 114.9 118.6 117.4 114.8 118.6 113.5 274.2 275.9

182.8 202.6−213.2

183.6 209.4

183.4 205.6−210.1

114.2 117.9

114.2 117.9

113.4 116.9

113.0 273.5

112.8 276.8

112.3 281.6

113.5 117.4

112.4 273.3

a See Figure 1 and section 2 for a designation of the adsorption sites. bThe adsorption geometry at the site 2f can exhibit anisotropies due to the mismatch between the overall cluster symmetry D4h and local symmetry constraints at the site. cBridge site 3b geometry unstable for PBE0, TPSSh, M06L, and M06. dExperimental reference for CO in the gas phase dC−O = 112.8 pm, ref 55. eExperimental reference for Pt−Pt distance in the extended bulk dPt−Pt = 277 pm, ref 56.

provide a correct description of CO adsorption which is dominated by self-interaction.1 We also briefly examined the claim18,19 that a scalar relativistic electronic structure description is able to adjust the CO adsorption preference on Pt(111) by correcting the energy of the Pt 6s level that contributes to the binding, mostly by interacting with the CO 5σ orbital.10,11 To this end, we carried out scalar-relativistic all-electron calculations on the Pt79 model with the second-order Douglas−Kroll−Hess approach,36,37 again applying a single-point strategy at the TPSS geometry (def2-TZVP level). The CO adsorption energies at both sites, 1t and 2f, were fully confirmed (Table 1). Our present results are consistent with those of earlier cluster model studies,14 but they do not support claims that the CO puzzle for Pt(111) may be solved by applying a relativistic DFT treatment. The agreement of the results from scalar-relativistic and pseudopotential treatments illustrates the accuracy of the latter for adsorption energies; note the deviating conclusions for cohesive energies of metals.48 3.2. Structural Aspects. Table 2 provides pertinent interatomic distances calculated with the cluster models Pt79(CO)8 and Pt225(CO)8. The Pt−C distances roughly correlate with the calculated bond strengths at each type of adsorption site. Due to bond competition, individual Pt−C distances are calculated ∼10% longer at the 2f site than at the 1t site. The PBE0 functional yields the shortest Pt−C distances, 205.9 pm on average. The other functionals follow with Pt−C ≈ 209 pm except for TPSS, which yields a slightly larger average Pt−C distance of ∼211 pm. As noted earlier,17 the 3b bridging site of Pt79 exhibits quite a peculiar behavior. Upon structure relaxation, the CO adsorbate often is found to move to the adjacent hollow hcp site, near the facet edge. Only the functionals PBE and TPSS yield stable adsorption structures at site 3b. The C−O distances reflect the amount of back-bonding as the C−O bond is weakened, hence elongated, by the population of the antibonding 2π* orbitals.10 The ordering C−O(1t) < C−O(3b) < C−O(2f) reflects the stronger backbonding at hollow-type sites.4 Hybrid DFT methods yield less elongated C−O bonds compared to their semilocal counter-

question about the site preference on Pt225; hence adsorption energies were only examined for the aforementioned sites 5t and 6f. In our earlier work the PBE adsorption energy was calculated to decrease by 22 kJ/mol when going from the 1t site on Pt79 to the 5t site of Pt225 (Figure 1).17 A similar change, 24 kJ/mol, results with the TPSS functional. The corresponding change is smaller when going from 2f on Pt79 to 6f on Pt225: 14 kJ/mol for both PBE and TPSS. We also examined the 5t/6f pair on Pt255 with the TPSSh method, but we restricted these hybrid DFT studies to single-point calculations at the corresponding TPSS structures in view of the substantial computational effort. This single-point strategy works well already when applied to the smaller model Pt79 where Eads values at top and hollow sites are reproduced within 1 kJ/mol. For Pt225, the TPSSh adsorption energies were estimated at 128 kJ/mol (5t) and 153 kJ/mol (6f). With the larger cluster model Pt225, the adsorption energies are calculated smaller,17 reducing the deviation from the experimental reference compared to the case for Pt79 (Table 1). As in our earlier study,17 these results also suggest that the 1t site of Pt79 is slightly more affected by the attractive influence of the facet borders than the 2f site. We now quantify the site preferences by Δ(2f−1t) = Eads(2f) − Eads(1t) and Δ(6f−5t) = Eads(6f) − Eads(5t), which are calculated positive for all cases studied (Table 1). Yet, these values are expected to be negative for the extended surface Pt(111) as experimentally CO is found to adsorb at top sites.6−8 According to accurate computational results from many-body theory,5 the value Δ is estimated at about −8 kJ/ mol. Though TPSSh yields a relatively low preference, Δ(2f− 1t) = 8 kJ/mol on Pt79, the value Δ(6f−5t) increases to 25 kJ/ mol for Pt225. This latter value is even larger than the corresponding TPSS result, Δ(6f−5t) = 19 kJ/mol. This finding is at variance with the results of earlier plane-wave studies on slab models, where the EXX term in PBE0 was found to reduce the preference for the fcc-hollow site to ∼6 kJ/ mol.4,15 Finally, our results for M06L do not confirm earlier claims47 that this method provides a viable solution to the CO puzzle. The present results seem more in line with the expectation that a semilocal functional like M06L is unlikely to C


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The Journal of Physical Chemistry A parts. With the semilocal functionals, the C−O bond of adsorbates elongates by about 1.4 pm (1t) and 5.1−5.6 pm (2f) compared to the values calculated for CO in the gas phase. The corresponding changes obtained with the hybrid DFT methods are 1.1 pm and 5.0−4.6 pm, respectively. As judged by this criterion, back-bonding is reduced due to the EXX term, in consequence of the larger HOMO−LUMO gap of CO. The C−O distances of adsorbates on Pt225 (Figure 1) are slightly shortened, by less than 0.3 pm, compared to analogous sites on Pt79, whereas the dPt−C values increase by 1−2 pm. Both, the effect on the C−O bond lengths and the increased average nearest-neighbor distances ⟨Pt−Pt⟩ in Pt225, are the result of an increased bonding competition, which is larger in Pt225 than in the smaller system Pt79.44,49,50 For Pt79 the M06 functional yields ⟨Pt−Pt⟩ = 281.6 pm, which is notably larger than the experimental value, 277 pm, of bulk Pt. As clusters are expected to have shorter distances than the bulk, typically by 6−7 pm for systems of this size,51 this finding adds to the questionable results of M06 for transition metal clusters.22 To a minor extent this caveat also holds for M06L, 276.8 pm, so that its low value Δ(2f−1t) (section 3.1) is likely the result of a fortuitous error cancellation. 3.3. Electronic Structure Aspects. Finally, we analyze some aspects of the electronic structure as obtained with the functionals TPSS, TPSSh, and PBE0 for CO in the gas phase, the bare Pt79 cluster, and its adsorption complexes with CO located at the sites 1t and 2f. To this end we examine the Mulliken population based density of states (DOS) projections onto the s- and d-levels of the three Pt atoms in the center of the (111) facet of Pt79 (Figure 1) as well as onto the CO fragment MOs 4σ + 5σ, 1π, and 2π*. Figure 2 provides the PDOS plots for TPSS, TPSSh, and PBE0 for Pt79 and the two adsorption complexes as well as the orbital spectrum of CO in the gas phase. We briefly discuss the most relevant PDOS features (I)− (III) of the two adsorption complexes (Figure 2a,b) before addressing the differences in the electronic structures that result from the EXX term. (I) The remains of the 2π* MOs are mostly found as a broadened peak in the unoccupied region of the PDOS, at positive energies 2−6 eV. Some mixing with occupied metal levels is visible across the d-band; that mixing is notably stronger at the site 2f. Another local maximum of the 2π* PDOS is found to coincide with 1π-derived levels (II), which reflects back-bonding via a three-level interaction between Pt-d levels and the 1π and 2π* MOs.4,10,11,13,14 For adsorption at a hollow site, the 1π PDOS shows two distinct peaks, but only the lower lying one represents interactions with the 2π* MOs. The DOS projection onto the 4σ and 5σ MOs also exhibits two distinct peaks (III). For the higher lying one, a mixing with Pt s- and d-levels is visible in the top site adsorption complex, whereas at the site 2f this local maximum is very close to one of the 1π peaks. The lower 4σ + 5σ peak (IV) shows contributions from the Pt d-band as well as, in the case of CO adsorbed on 2f, a significant mixing from the Pt slevels, which is much smaller at the top-site. The EXX term increases the HOMO−LUMO gap, Δεgap, of an isolated CO molecule; the values are 7.4 eV (TPSS), 8.6 eV (TPSSh), and 10.1 eV (PBE0). TPSS describes Pt79 essentially as metallic (Δεgap ≈ 0). The hybrid DFT methods yield gaps of 0.2 eV (TPSSh) and 0.5 eV (PBE0). TPSS yields a vanishing gap Δεgap also for both adsorption complexes. For the 2f adsorption complex, slightly opened HOMO−LUMO gaps and somewhat downshifted HOMO levels are obtained with

Figure 2. Projected density of states (PDOS, arbitrary units) from TPSS, TPSSh, and PBE0 calculations on the MO energy spectrum of (a) the bare Pt79 cluster and an isolated CO molecule (top row), as well as of CO adsorption complexes on Pt79 at the sites (b) 1t and (c) 2f. All spectra were generated with a level broadening of 0.21 eV. The various panels show projections on the d and s orbitals of the three surface Pt atoms at the center of the (111) facet of Pt79 as well as 4σ + 5σ, 1π, and 2π* CO fragment MOs. All orbital energies (eV) with respect to the HOMO level of the corresponding Pt79 reference: Δε = ε − εHOMO(Pt79).

TPSSh, 0.3 eV, and PBE0, 0.6 eV. These results can be rationalized by the fact that adsorbates are able to reduce the metallic properties of finite clusters.52,53 However, if CO is adsorbed on the 1t site, slightly smaller Δεgap values and less negative HOMO energies are calculated with these two hybrid functionals as compared to the bare cluster. This behavior likely is related to the σ-bonding, which prevails at top sites (see below) and increases the electron density at the sites.9 Indeed, the total populations of the three surface atoms in the center of the (111) facet of Pt79 are increased by 1.5 e for CO adsorption at 1t, but only by 0.9−1.2 e in the 2f adsorption complex. This increased electronic charge raises the electrostatic potential and reduces the Δεgap value compared to the case for the 2f site, where more charge resides on the CO fragment reflecting the larger amount of back-bonding. D



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When analogous PDOS spectra from the functionals TPSS, TPSSh, and PBE0 are compared, the increasing amount of EXX broadens the Pt d-band, in agreement with earlier plane-wave results.4 Considering only the occupied Pt d-levels with a population >0.1, we find the main part of the occupied part of the d-band in Pt79 to extend over 7.5 eV (TPSS), 7.8 eV (TPSSh), and 8.2 eV (PBE0). Hybrid DFT methods yield a (slightly) reduced back-bonding as demonstrated by the integral over the occupied part of the 2π* PDOS, which is reduced from 0.43 e per CO fragment (TPSS) to 0.39 e (PBE0) in the 1t adsorption complex and, analogously, from 0.81 e to 0.78 e at the site 2f. In analogy, the mixing of the 1π*-levels at (II) appears reduced as the corresponding height in the PDOS increases by about 0.7 e (1t) and 3.5 e (for the lower 1π*-peak at 2f). One also notes the EXX-induced downward shifts of the PDOS features (II) and (III) as well as the corresponding upward shifts of the 2π*-derived levels (I) to be quite comparable to the changes of the orbital energies caused by the EXX term in a free CO molecule. Only in the case of the lower lying 4σ + 5σ peak (IV) of the 2f adsorption complex does the downshift with increasing amount of EXX appear to be more pronounced. Indeed, when going from TPSS to PBE0, the energy difference between the maxima (III) and (IV) of the 4σ + 5σ PDOS remains unchanged at 1t (within ∼0.1 eV), while it increases by ∼0.3 eV at the site 2f (Figures 2b,c). According to the extended Blyholder model10,11,54 these two peaks represent the bonding and nonbonding linear combinations of a three-orbital interaction; their increased spread seems to imply a stronger σ-bonding. This is in line with the observation that the EXX term increases the contribution of the Pt s and d-levels at (IV) of the 2f adsorption complex, from 3.6 e to 4.1 e (Pt-s) and from 2.9 e to 3.2 e (Pt-d), when going from TPSS to PBE0. Apart from the stabilization of the CO σ-levels at hollow sites, most effects of the EXX term (larger Δεgap values, d-band spread etc.) have been discussed before. Although only a qualitative argument, this new finding is consistent with the changes of the C−O distances (section 3.2).

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AUTHOR INFORMATION

Corresponding Author

*N. Rösch. E-mail: [email protected]. Phone: +49-89-289 13620. Fax: +49-89-289 13468. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Sven Krüger for numerous discussions. T.M.S. is grateful for support by the International Graduate School of Science and Engineering (IGSSE) of the Technische Universität München. The authors acknowledge a generous grant of computing resources by the Gauss Centre for Supercomputing (www.gauss-centre.eu), provided on the SuperMUC platform of Leibniz Supercomputing Centre Garching (www.lrz.de).

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REFERENCES

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4. CONCLUSION We compared three hybrid DFT functionals and their semilocal counterparts on the example of CO adsorption at top- and fcctype sites of the (111) facets of the model clusters Pt79 and Pt225. None of the examined methods was found to provide the top-site adsorption preference that one might expect in analogy to the Pt(111) surface, in agreement with recent plane-wave studies.4,15 This finding especially holds for the hybrid DFT method TPSSh, although this functional initially appeared promising due to its rather accurate description of the metal moiety22 and its rather low preference for the fcc-hollow site on the facets of the cluster model Pt79. The present findings underline the well-known fact21,24 that a specific fixed amount of exact exchange in hybrid functionals is not able to provide a uniformly accurate description of different systems or even, as in this case, different moieties of the same system. Comparing hybrid DFT methods with increased amount of exact exchange, it appears that, apart from eventual fortuitous error cancellations, e.g., by effects due to the basis set or the core− electron representation, no standard hybrid DFT method may be able to solve the CO puzzle. E


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Assessment of Hybrid Density Functionals for the Adsorption of

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