Validation of Density Functionals for Adsorption Energies on

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Validation of Density Functionals for Adsorption Energies on Transition Metal Surfaces Kaining Duanmu, and Donald G. Truhlar J. Chem. Theory Comput., Just Accepted Manuscript • Publication Date (Web): 16 Dec 2016 Downloaded from http://pubs.acs.org on December 17, 2016

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Journal of Chemical Theory and Computation

revised for JCTC – 12/14/2016

Validation of Density Functionals for Adsorption Energies on Transition Metal Surfaces Kaining Duanmu† and Donald G. Truhlar* Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-043, USA ABSTRACT. The quantitative prediction of adsorption energies of radicals and

molecules on surfaces is essential for the design and understanding of heterogeneous catalytic processes. A recent paper by Wellendorff et al. collected an experimental database of 39 reaction energies involving adsorption energies on transition metal surfaces that can be used as benchmarks for testing quantum mechanical electronic structure methods, and we compared the experimental data to Kohn-Sham density functional calculations with six exchange-correlation functionals. In this paper, we rearranged the data into two categories: open-shell radical adsorption reactions and closed-shell molecular adsorption reactions. We recalculated the adsorption energies with PBE and we also calculated them with three functionals, M06-L, GAM, and MN15-L, that were not studied in the Wellendorff et al. paper; and we compared our results to the benchmark data. Of the nine functionals that have been compared to the databases, we find that BEEF-vdW, GAM, and RPBE perform best for the open-shell radical adsorption reactions, and MN15-L performs best for the closed-shell molecular adsorption, followed by BEEF-vdW and M06-L.

Keywords adsorption energies, catalysis, density functional theory, transition-metal surfaces

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1. Introduction The use of accurate computational methods for modeling the interaction between transition metal surfaces and adsorbates is essential for theoretical work on heterogeneous catalysis; however the validation of computational methods is difficult for two reasons. First, the experimental thermodynamic data available for surface–adsorbate systems is not large, and there are uncertainties in the measurement of the adsorption energies due to possible surface defects and the interpretation of the experimental results. Second, there are uncertainties in the structures of systems that have been studied experimentally, for example, the structures of the metal surfaces, the adsorption sites, and the adsorbate coverage ratio. A recent paper1 by Wellendorff et al. compiled an experimental database of 39 reliably measured adsorption energies on well-characterized surfaces of ten transition metals. The adsorption energies cover a wide range of values and are usable as benchmarks. This database was then compared to Kohn-Sham density functional theory (DFT)2 calculations with six exchange-correlation functionals, namely LSDA (using the exchange approximation of Gáspár and the local uniform electron gas approximation of Perdew and Wang for correlation, which combination may be denoted GPWL,3 • Perdew and Wang's 1991 generalized gradient approximation (GGA), labeled PW91,4 • the Perdew-Burke-Ernzerhof GGA, labeled PBE,5 • the empirical PBE GGA for solids, labeled PBEsol,6 • Hammer et al.'s revised PBE GGA, labeled RPBE,7 and • the Bayesian error estimation with van der Waals correlation functional, labeled BEEF-vdW.8 The database was divided in two sub-databases: chemisorptions with strong covalent bonds and physical adsorptions with large van der Waals contributions. Because chemical and van der Waals interactions are not always unambiguously distinguishable, and because we want to separate bond-breaking energies from adsorption energies, in the present work we use a different partition of the database based on the character of the adsorbates, in particular we distinguish open-shell radical adsorption processes and closed-shell molecular adsorption processes. We recalculated the adsorption energies with PBE, and we also applied three previously untested functionals, namely • the Minnesota 2006 local functional (M06-L),9 • the gradient approximation for molecules (GAM) functional,10 and • the Minnesota nonseparable 2015 local functional (MN15-L).11


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2. Computational Details The adsorption energies are calculated using MN-VFM,12 which is a locally-modified version of the VASP13,14 code. The projector augmented wave (PAW)15,16 method is used to treat the core. For C, O, and N, the 1s electrons are frozen, and valence electrons are explicit. For I, the core electrons are frozen, and 5s and 5p electrons are explicit. For transition metals the valence s and d electrons and semicore p electrons are treated as valence electrons (the PAW potentials for this treatment are labeled “pv” in VASP); e.g., the 3p, 3d, and 4s electrons of Co, Ni, and Cu are treated explicitly, and the other electrons are frozen. Spinpolarized calculations are used for the ferromagnetic metals Ni and Co and for open-shell adsorbates. We employed the following computational parameters that are the same as used in the previous1 study. First we optimize the lattice constant for each bulk metal. Then we model the metal surfaces as 4-layer metal slabs with at least 10 Å vacuum layer. Each layer of the slab contains either 2 × 2 unit cells or 3 × 3 unit cells. The bottom two metal layers are fixed in their bulk geometry, while the top two layers and the adsorbate, if any, are fully optimized. The electron temperature is set to 0.05 eV. The cut-off energies for plane-wave and the Monkhorst-Pack k points are shown in Table 1. First (step 1) the geometry of each species is optimized with the force convergence criterion for optimization set to be 0.025 eV/Å along all directions of the relaxing atom and with the first set of conditions (see Table 1); it was found that calculations performed this way are accurate enough for geometry optimization.1 In some cases, though, the forces are very difficult to converge near the equilibrium geometries (where the potential energy surface is very flat), and we simply require that the geometries are reasonable and the energies are converged to 10-4 eV. After the geometry optimization, the energies are calculated with the parameters labeled as step 2 in Table 1. Table 1. Computational Parameters in Adsorption Energy Calculations. 2 × 2 slab

3 × 3 slab

molecules

Step 1

680 eV (50 Ry) 680 eV (50 Ry) 680 eV (50 Ry) 6×6×1 4×4×1 Γ point

Step 2

816 eV (60 Ry) 816 eV (60 Ry) 816 eV (60 Ry) 8×8×1 6×6×1 Γ point

Experimental reaction enthalpies contain contributions from zero point energy and thermal vibrations and rotations. In Ref. 1, the reaction enthalpies were converted to reaction energies (differences in Born-Oppenheimer potential energies) by correcting for thermal contributions and using zero-point energies calculated with PBE, and we use these vibrationless reaction energies for comparison to DFT.



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The database contains both dissociative and non-dissociative adsorption reactions. For dissociative adsorption reactions, Ref. 1 considered the total reaction, including both dissociation of the adsorbate and adsorption of the radicals.1 For example, the reaction O2 + Ni(100) → 2O/Ni(100) includes a dissociation reaction O2 → 2O and an adsorption reaction O + Ni(100) → O/Ni(100). In the present work, we study the pure adsorption process, which in this case is O + Ni(100) → O/Ni(100) To generate the energies for the new adsorption reactions, we need to use dissociation energies of the small molecules. Table 2 shows these energies. In this table the reference data for S1-S4 are experimental data from refs 17, 18, 19; the S1, S2, S4 data are calculated by using handbook data18 for the enthalpy of dissociation at 0 K and NIST data17 for the anharmonic zero point energy. The S3 data is calculated using the enthalpy of dissociation at 0 K18 and spectroscopic constants19 from the handbook. The reference data for S5 and S6 are from our own CCSD(T)-F12b20,21 calculations with the all-electron cc-pVQZ22 basis set for C and H and the effective-core-potential basis set cc-pVQZ-PP23 for I. The CCSD(T)-F12b calculations are performed with Molpro. For the DFT calcuations in Table 2, we used MG3S basis sets24 for C and H, and def2-TZVP basis set25 with the SDD effective core potential26 for I. These calculations are performed with a locally-modified version of Gaussian 09,27 in particular with MNGFM6.7.28 Table 2. Dissociation Energies (kcal/mol) of Small Molecules. No. reaction S1 S2 S3 S4 S5 S6

ref.

O2 → O + O H2 → H + H I2 → I + I NO → N + O CH2I2 → CH + H + 2I CH3I → CH3 + I

120.8 109.5 35.9 152.7 239.0 65.2

PBE M06-L GAM MN15-L 143.4 104.5 50.8 171.8 247.7 67.1

123.7 103.6 47.9 150.8 240.0 64.5

131.5 105.8 55.0 152.0 249.7 68.0

A more complicated example is the reaction NO + Ni(100) → N/Ni(100) + O/Ni(100) which contains two separate adsorption reactions N + Ni(100) → N/Ni(100) and O + Ni(100) → O/Ni(100)


120.6 109.8 38.7 152.6 227.7 59.1

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with the latter one being already considered in O2 adsorption, which allows us to use algebra to calculate the adsorption energy of N + Ni(100) → N/Ni(100) and add it to the database. Similar algebra was used to obtain pure radical adsorption energies from two adsorption data for alkyl iodides. Table 2 shows the molecular dissociation energies of the dissociative adsorption reactions studied in Ref. 1 and the present work, and Table 3 shows how we treated these reactions differently than in Ref. 1. Table 3. Dissociative Adsorption Reactions Studied in Ref. 1 and in The Present Work. ref. 1

present work

O2 + M → 2O/M H2 + M → 2H/M NO + Ni(100) → N/Ni(100) + O/Ni(100) I2 + Pt(111) → 2I/Pt(111) CH2I2 + Pt(111) → CH/Pt(111) + H/Pt(111) + 2I/Pt(111) CH3I + Pt(111) → CH3/Pt(111) + I/Pt(111)

O + M→ O/Ma H + M→ H/M N + Ni(100) → N/Ni(100) I + Pt(111)→ I/Pt(111) CH + Pt(111)→ CH/Pt(111) CH3 + Pt(111)→ CH3/Pt(111)

a

M stands for a metal surface.

The other reactions studied in this paper are the same as in the previous work. We divide the reactions into two categories based on the adsorbates, and we show the full set of adsorbate coverages, adsorption sites, and reference energies in Table 4. Table 4. Adsorbate Coverages, Adsorption Sites and Reference Energies (kcal/mol). No. adsorption reaction open-shell radical adsorption reactions 1 N + Ni(100) → N/Ni(100) 2 H + Pt(111) → H/Pt(111) 3 H + Ni(111)→ H/Ni(111) 4 H + Ni(100) → H/Ni(100) 5 H + Rh(111) → H/Rh(111) 6 H + Pd(111) → H/Pd(111) 7 O + Ni(111) → O/Ni(111) 8 O + Ni(100) → O/Ni(100) 9 O + Pt(111) → O/Pt(111) 10 O + Rh(100) → O/Rh(100) 11 I + Pt(111) → I/Pt(111) 12 CH + Pt(111) → CH/Pt(111) 13 CH3 + Pt(111) → CH3/Pt(111)

adsorbate coverage

adsorption site

ref. energy

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/9 1/4 1/4 1/4 1/4

hollow hollow hollow hollow hollow hollow hollow hollow hollow hollow hollow hollow top

-100.4 -63.4 -66.7 -65.1 -63.4 -65.5 -118.4 -123.7 -85.3 -102.8 -55.4 -173.7 -59.8



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NO + Pt(111) → NO/Pt(111) NO + Pd(111) → NO/Pd(111) NO + Pd(100) → NO/Pd(100) H2O + 2/3 Pt(111)[1×1] + 1/3 O/Pt(111)[2×2] 17 → 2/9 {3(H2OˑˑˑOH)/Pt(111)[3×3]} closed-shell molecular adsorption reactions 18 CO + Ni(111) → CO/Ni(111) 19 CO + Pt(111) → CO/Pt(111) 20 CO + Pd(111) → CO/Pd(111) 21 CO + Pd(100) → CO/Pd(100) 22 CO + Rh(111) → CO/Rh(111) 23 CO + Ir(111) → CO/Ir(111) 24 CO + Cu(111) → CO/Cu(111) 25 CO + Ru(0001) → CO/Ru(0001) 26 CO + Co(0001) → CO/Co(0001) 27 NH3 + Cu(100) → NH3/Cu(100) 28 CH3I + Pt(111) → CH3I/Pt(111) 29 CH3OH + Pt(111) → CH3OH/Pt(111) 30 CH4 + Pt(111) → CH4/Pt(111) 31 C2H6 + Pt(111) → C2H6/Pt(111) 32 C3H8 + Pt(111) → C3H8/Pt(111) 33 C4H10 + Pt(111) → C4H10/Pt(111) 34 C6H6 + Pt(111) → C6H6/Pt(111) 35 C6H6 + Cu(111) → C6H6/Cu(111) 36 C6H6 + Ag(111) → C6H6/Ag(111) 37 C6H6 + Au(111) → C6H6/Au(111) 38 C6H10 + Pt(111) → C6H10/Pt(111) 39 H2O + Pt(111) → H2O/Pt(111) 14 15 16

1/4 1/4 1/4

hollow hollow hollow

-28.4 -43.5 -39.0

1/9

surface

-15.8

1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/4 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/4

hollow top hollow bridge top top top top top top hollow surface surface surface surface surface surface surface surface surface surface top

-29.6 -29.6 -34.4 -37.5 -33.9 -39.2 -13.6 -38.5 -28.4 -14.3 -20.1 -13.1 -3.3 -6.5 -9.3 -11.5 -38.7 -15.8 -14.6 -16.7 -29.4 -13.1

Reaction 17 29 is a complicated case, but since the final adsorbate (3(H2OˑˑˑOH) is an open-shell species, we decide to put it in the first category, and we calculate the energy of the adsorption reaction based on the reaction: H2O + 2/3 Pt(111)[1×1] + 1/3 O/Pt(111)[2×2] → 2/9 {3(H2OˑˑˑOH)/Pt(111)[3×3]} All of the other adsorption reactions in Table 4 can be written as: A + M → A/M, where A is the adsorbate and M is the metal surface, and the adsorption energy E is defined as: E = E(A/M) – [E(A) + E(M)]

(1)

There are 10 metals in Table 4; the Ni, Pt, Rh, Pd, Ir, Cu, Ag, and Au crystals have face-centered cubic structures, and the Ru and Co crystals have hexagonal close-packed structures. The adsorption coverage is fixed in the calculations by setting the ratio of the


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number of adsorbate to the number of surface atoms, so a coverage of 1/4 means the 2 × 2 slab is used, and 1/9 means a 3 × 3 slab is used. Figure 1 shows an example of benzene adsorbed on Pt(111). Each layer of the Pt(111) slab contains 3 × 3 unit cells, and only one benzene molecule is adsorbed on the top layer, so the adsorbate coverage for this system is 1/9.

Figure 1. Benzene adsorbed on Pt(111).

3. Results and Discussion Table 5 shows the reaction energies, mean signed errors (MSEs), and mean unsigned errors (MUEs) for the four functionals we used. In first category, the magnitudes of the MSE for M06-L, GAM and MN15-L are all below 3 kcal/mol, while their MUEs are all above 7 kcal/mol, showing that they don’t have significant systematic errors of overestimation or underestimation. In contrast the magnitude of the MSE of PBE is closer to the MUE. In the second category (molecular nondissociative adsorption), the magnitude of MSE is much less than MUE for three of the functionals, but the MSE is relatively larger for GAM. Table 5. Adsorption Reaction Energies (kcal/mol). No. adsorption reaction open-shell radical adsorption reactions 1 N + Ni(100) → N/Ni(100) 2 H + Pt(111) → H/Pt(111) 3 H + Ni(111)→ H/Ni(111) 4 H + Ni(100) → H/Ni(100) 5 H + Rh(111) → H/Rh(111) 6 H + Pd(111) → H/Pd(111) 7 O + Ni(111) → O/Ni(111) 8 O + Ni(100) → O/Ni(100)

ref. -100.4 -63.4 -66.7 -65.1 -63.4 -65.5 -118.4 -123.7

PBE M06-L -146.7 -62.1 -65.0 -64.1 -64.3 -65.0 -124.8 -132.6


-120.2 -59.8 -58.1 -59.0 -62.9 -61.9 -102.5 -111.4

GAM MN15-L -111.1 -59.5 -74.3 -60.9 -61.2 -59.8 -120.9 -116.2

-131.2 -53.8 -62.1 -50.4 -54.0 -47.8 -124.3 -125.7


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9 10 11 12 13 14 15 16

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O + Pt(111) → O/Pt(111) O + Rh(100) → O/Rh(100) I + Pt(111) → I/Pt(111) CH + Pt(111) → CH/Pt(111) CH3 + Pt(111) → CH3/Pt(111) NO + Pt(111) → NO/Pt(111) NO + Pd(111) → NO/Pd(111) NO + Pd(100) → NO/Pd(100) H2O + 2/3 Pt(111)[1×1] 17 + 1/3 O/Pt(111)[2×2] → 2/9 {3(H2OˑˑˑOH)/Pt(111)[3×3]} MSE (1-17) MUE (1-17) closed-shell molecular adsorption reactions 18 CO + Ni(111) → CO/Ni(111) 19 CO + Pt(111) → CO/Pt(111) 20 CO + Pd(111) → CO/Pd(111) 21 CO + Pd(100) → CO/Pd(100) 22 CO + Rh(111) → CO/Rh(111) 23 CO + Ir(111) → CO/Ir(111) 24 CO + Cu(111) → CO/Cu(111) 25 CO + Ru(0001) → CO/Ru(0001) 26 CO + Co(0001) → CO/Co(0001) 27 NH3 + Cu(100) → NH3/Cu(100) 28 CH3I + Pt(111) → CH3I/Pt(111) 29 CH3OH + Pt(111) → CH3OH/Pt(111) 30 CH4 + Pt(111) → CH4/Pt(111) 31 C2H6 + Pt(111) → C2H6/Pt(111) 32 C3H8 + Pt(111) → C3H8/Pt(111) 33 C4H10 + Pt(111) → C4H10/Pt(111) 34 C6H6 + Pt(111) → C6H6/Pt(111) 35 C6H6 + Cu(111) → C6H6/Cu(111) 36 C6H6 + Ag(111) → C6H6/Ag(111) 37 C6H6 + Au(111) → C6H6/Au(111) 38 C6H10 + Pt(111) → C6H10/Pt(111) 39 H2O + Pt(111) → H2O/Pt(111) MSE (18-39) MUE (18-39)

-85.3 -102.8 -55.4 -173.7 -59.8 -28.4 -43.5 -39.0

-98.2 -122.4 -55.9 -153.9 -47.1 -40.6 -53.9 -50.9

-81.0 -112.3 -57.4 -147.7 -40.9 -32.7 -48.6 -47.8

-81.0 -105.9 -53.8 -138.1 -39.0 -32.9 -48.8 -45.1

-81.7 -109.5 -57.1 -153.7 -47.8 -42.1 -52.4 -52.5

-15.8 / /

-17.6 -5.6 9.9

-16.3 2.9 8.8

-14.2 2.8 7.5

-17.9 0.4 10.4

-29.6 -29.6 -34.4 -37.5 -33.9 -39.2 -13.6 -38.5 -28.4 -14.3 -20.1 -13.1 -3.3 -6.5 -9.3 -11.5 -38.7 -15.8 -14.6 -16.7 -29.4 -13.1 / /

-44.3 -38.8 -46.8 -43.9 -43.7 -45.5 -17.3 -44.4 -38.3 -10.4 -5.4 -4.6 -0.9 -0.6 -1.2 -1.3 -22.5 -1.2 -0.7 -1.0 -22.5 -4.8 2.3 9.4

-31.4 -33.6 -39.1 -39.5 -38.6 -45.8 -13.8 -40.4 -40.2 -7.6 -9.1 -7.8 -4.3 -4.5 -6.4 -7.7 -20.0 -13.9 -15.4 -12.1 -12.0 -4.8 2.0 5.5

-51.9 -32.2 -41.5 -38.8 -40.4 -43.5 -11.6 -39.0 -30.6 -7.6 -3.2 -2.7 -1.8 -2.6 -3.1 -4.0 -2.9 -3.0 -6.4 -4.0 -11.6 -4.2 4.8 9.0

-17.7 -33.7 -38.7 -37.1 -38.7 -39.9 -4.2 -37.5 -22.5 -12.4 -13.3 -13.7 -6.0 -2.6 -10.0 -15.3 -39.2 -23.4 -20.3 -19.2 -34.7 -7.7 0.2 4.1

To further analyze the data, we compared the errors in our calculations with the errors in the calculations from ref. 1, where the data for reactions 1-13 from ref. 1 have been


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algebraically converted to the new reactions used in this paper. (For PBE we use our own calculations, which give slightly different results than those in ref. 1; the two sets of PBE results are results are compared in detail in the supporting information, and we note that our conclusions would not be changed in any major way if we used the data of ref. 1 for PBE.) The results of this more comprehensive comparison of nine functionals are in Table 6. The nine functionals in Table 6 were developed for different purposes, and they may be classified by their differing ingredients. The GPWL functional depends only on the local spin densities and is classified therefore as an LSDA; since all LSDAs currently in common use give similar results, we just label these results LSDA. LSDAs are of interest for being the simplest possible exchange-correlation functions. The PBE, PBEsol, and RPBE functionals are GGAs, which approximate the exchange and correlation energies separately in term of the local spin densities and local spindensity gradients. The PBE functional was designed to improve on the LSDA but to remain simple by including only the most important dependence on the spin-density gradients. PBEsol is a modification of PBE designed to improve equilibrium properties of densely packed solids and their surfaces, and RPBE is a modifcation7 of revPBE30 (which was proposed to give improved atomization energies of small molecules30 and which was shown7 to also give good chemisorption energetics of atoms and molecules on transitionmetal surfaces) to satisfy the Lieb-Oxford31 bound. The GAM functional is a nonseparable gradient approximation (NGA); an NGA depends on the same variables as a GGA, but it does not separately approximate the exchange and correlation energies. The GAM functional was designed10 to treat molecular problems with a special emphasis on the prediction of quantities important for homogeneous catalysis and other molecular energetics. Adding orbital-dependent local spin-specific kinetic energy density to a GGA or an NGA yields respectively a meta GGA (MGGA) or a meta NGA (MNGA). M06-L is an MGGA designed for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions, and MN15-L is a MNGA designed to have broad accuracy for atoms, molecules, and solids. Whereas all the other functionals studied here depend only on local properties, the BEEF-vdW functional is a GGA augmented by an orbital-independent nonlocal correlation (NLC) functional of the ground-state density; it was designed to treat bond breaking and formation in chemistry, solid-state physics, and surface chemistry while including van der Waals dispersion interactions. Thus, of the functionals studied here, only RPBE and BEEF-vdW were specifically designed to treat adsorption energies (BEEF-vdW was parametrized against multiple data sets including 27 data for chemisorption of simple molecules on the (111), (100), and (0001) facets of late transition-metal surfaces at low coverage), but M06-L and MN15-L were designed to be general-purpose functionals, although no adsorption data was used in their training. ACS Paragon Plus Environment


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The results in Table 6 show that some of the adsorbates show systematic errors across most of the functionals. In particular, reactions 1, 12, 18, and 34 have errors greater than 10 kcal/mol for all but one or two of the nine functionals. Table 6. Reference Values and Errors in Adsorption Energies (kcal/mol).

No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ref. -100.4 -63.4 -66.7 -65.1 -63.4 -65.5 -118.4 -123.7 -85.3 -102.8 -55.4 -173.7 -59.8 -28.4 -43.5 -39.0 -15.8

LSDA 1992 GPWL -72.9 -12.2 -11.7 -13.0 -14.6 -12.9 -34.3 -37.9 -37.2 -48.2 -18.1 -20.8 -3.3 -37.5 -31.8 -35.4 -13.4

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

-29.6 -29.6 -34.4 -37.5 -33.9 -39.2 -13.6 -38.5 -28.4 -14.3 -20.1 -13.1 -3.3 -6.5 -9.3 -11.5 -38.7

-34.4 -21.3 -29.6 -23.4 -24.4 -19.1 -17.9 -18.9 -27.5 -6.5 1.9 -3.6 -1.7 -3.8 -5.7 -7.9 -24.6

GGA 1991 PW91 -40.9 -0.4 1.4 0.5 -2.5 -0.8 -7.6 -8.7 -12.3 -19.0 -2.5 17.7 12.3 -13.9 -8.4 -9.8 1.0

GGA 1996 PBE -46.3 1.2 1.7 1.1 -0.9 0.5 -6.4 -8.9 -13.0 -19.5 -0.6 19.8 12.7 -12.2 -10.4 -12.0 -1.8

GGA 1999 RPBE -31.1 2.8 4.6 4.3 0.6 2.3 4.8 4.1 -0.3 -6.2 5.5 32.8 21.3 -6.9 -1.4 -2.2 8.6

GGA 2008 PBEsol -53.0 -5.2 -3.7 -5.3 -7.5 -5.7 -17.8 -20.4 -21.4 -31.2 -12.4 4.4 5.7 -23.9 -18.2 -20.8 -4.5

NGA 2015 GAM -10.7 3.8 -7.6 4.2 2.2 5.8 -2.6 7.6 4.2 -3.1 1.6 35.5 20.9 -4.5 -5.3 -6.1 1.6

MGGA 2006 M06-L -19.8 3.6 8.6 6.1 0.5 3.6 15.8 12.4 4.2 -9.5 -2.0 26.0 18.9 -4.3 -5.1 -8.9 -0.5

MNGA 2016 MN15-L -30.8 9.6 4.6 14.7 9.3 17.7 -5.9 -2.0 3.5 -6.6 -1.8 20.0 12.0 -13.6 -8.9 -13.5 -2.2

GGA+NLC 2012 BEEF-vdW -23.4 1.8 3.2 2.6 -0.5 1.7 5.2 4.3 -0.6 -6.6 0.3 30.8 15.2 -7.2 -1.0 -2.6 3.3

-12.7 -7.6 -10.5 -5.7 -10.3 -6.2 -4.3 -5.5 -10.3 4.3 13.9 8.4 2.6 5.3 7.9 9.3 17.2

-14.7 -9.1 -12.4 -6.4 -9.8 -6.3 -3.7 -5.9 -9.9 3.9 14.7 8.6 2.5 5.8 8.1 10.2 16.2

-3.8 -2.9 -2.2 0.7 -5.0 -1.2 0.2 -0.2 -4.3 5.7 16.3 9.3 3.1 5.7 8.4 10.0 36.3

-23.2 -14.3 -20.3 -14.3 -17.2 -12.4 -11.0 -12.2 -17.7 0.0 8.4 4.3 2.2 2.9 3.8 3.6 -7.4

-22.3 -2.5 -7.1 -1.3 -6.5 -4.3 2.0 -0.5 -2.2 6.8 16.8 10.5 1.6 3.9 6.2 7.5 35.8

-1.8 -4.0 -4.7 -1.9 -4.7 -6.6 -0.2 -1.9 -11.8 6.7 11.0 5.4 -0.9 2.0 2.9 3.8 18.7

12.0 -4.1 -4.3 0.5 -4.8 -0.7 9.4 1.0 5.9 2.0 6.8 -0.6 -2.6 3.8 -0.7 -3.8 -0.5

-5.3 -2.2 -2.9 1.7 -4.8 -1.4 0.5 -0.2 -4.5 4.5 11.5 5.7 -0.2 1.4 2.4 2.4 20.6


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35 36 37 38 39

-15.8 -14.6 -16.7 -29.4 -13.1

11 -2.6 0.0 7.4 -12.9 -1.9

9.3 13.1 20.8 11.7 8.1

14.6 13.9 15.8 6.9 8.4

11.0 17.0 22.0 23.9 12.0

7.4 11.2 17.7 -0.5 4.3

12.8 8.2 12.7 17.8 9.0

1.8 -0.8 4.7 17.4 8.3

-7.6 -5.7 -2.5 -5.3 5.4

Reactions 1, 14, 15, and 16 all involve open-shell N species. All nine functionals overestimate the magnitude of the energies for all four reactions (overbinding). However, reaction 27 involves a closed-shell molecule (NH3) containing N, and all the functionals except LSDA underestimate the magnitude of the energies. Reactions 2-10 are for H and O adsorption. The LSDA and PBEsol functionals have negative errors (overbinding); PBE and PW91 have small errors for H adsorption but large negative errors for O adsorption; MN15-L has a striking error distribution for these cases, all positive errors for H binding and three out of four negative errors for O binding. RPBE, GAM, M06-L, and BEEF-vdW have errors of both signs for both H and O. For CH and CH3 adsorption (reactions 12 and 13), all except LSDA have positive errors. Reactions 18-26 are CO adsorption reactions, and six functionals overestimate the magnitude of the adsorption energies (negative values for the errors of these exoergic processes) in all nine cases. BEEF-vdW, RPBE, and MN15-L overestimate the binding in only seven, seven, and four cases, respectively. Reactions 28-38 are organic molecule adsorption reactions, and all the functionals except LSDA and MN15-L tend to underestimate the magnitude of the organic molecule adsorption energies (positive values), showing that the weak interaction between the organic molecules and metal surfaces is not be fully captured by seven of these functionals. For reaction 30 (benzene adsorption on Pt(111) surface), the errors in all functionals are, somewhat surprisingly, all rather small. In Table 7, we order the nine studied functionals based on their MUEs for the two kinds of adsorptions. This table shows that BEEF-vdW, GAM, and RPBE are the best performing functionals for open-shell radical adsorption reactions, and MN15-L, BEEFvdW, and M06-L are the best for closed-shell molecular adsorption reactions. The orderings of these functionals for the two categories of reactions are very similar: BEEFvdW, GAM, RPBE and M06-L are among the top five functionals; PW91, PBE, PBEsol, LSDA are at the bottom in both charts. The only exception is MN15-L, which performs much better for closed-shell molecular adsorption reactions than for open-shell radical adsorption reactions. It is interesting that GAM performs as well as (even slightly better than) RPBE for closed-shell adsorption and significantly better than RPBE for open-shell adsorption since both functionals have the same ingredients, but GAM was developed for molecules, whereas RPBE was developed for studying adsorption.


-3.8 9.6 12.4 9.1 8.1


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BEEF-vdW is the only functional studied with an error below 7 kcal/mol for both categories of adsorption, and M06-L and BEEF-vdW are the only functionals studied for which the magnitude of the MUE is less than 9 kcal/mol for both kinds of adsorbate. The molecular adsorbates bind entirely due to noncovalent, nonionic interactions. We know from previous work on molecular and rare-gas interactions that local meta functionals can perform well for noncovalent interactions at van der Waals distances. We note that the motivation for including nonlocal correlation in BEEF-vdW is to improve adsorption energies for complexes bound by dispersion-like interactions, but Table 7 shows that M06-L and MN15-L, which have only local terms, are competitive. The relatively good results for the newest functional, MN15-L, are especially encouraging. Table 7. MUEs and MSEs for Each Functional (kcal/mol). open-shell reactions 1-17 functional MUE MSE 1 BEEF-vdW 6.5 1.6 GAM 7.5 2.8 RPBE 8.2 2.6 M06-L 8.8 2.9 PW91 9.4 -5.5 PBE 9.9 -5.6 MN15-L 10.4 0.4 PBEsol 15.3 -14.2 1 LSDA 26.8 -26.8

closed-shell reactions 18-39 functional MUE MSE MN15-L 4.1 0.2 BEEF-vdW1 5.2 2.9 M06-L 5.5 2.0 GAM 9.0 4.8 1 RPBE 9.1 7.4 1 PW91 9.3 2.7 PBE 9.4 2.3 1 PBEsol 9.8 -3.9 1 LSDA 13.5 -12.7

4. Conclusions A recent paper by Wellendorff et al. collected a database of 39 experimental transition-metal–surface adsorbate energies. The atomic-scale geometries of these systems were believed to be well-characterized, and the experimental techniques were considered to be reliable so the adsorption energies can be used as benchmarks for calibrating computational methods. The paper also compared the experimental data to DFT calculations with six functionals. In the present work, we divided the reference energies into two categories: open-shell radical adsorption reactions and closed-shell molecular adsorption reactions, and then we recalculated the energies with PBE and calculated the energies with the previously unexamined M06-L, GAM and MN15-L functionals. We find that BEEF-vdW, GAM, RPBE, and M06-L are best performing functionals for the first category, and MN15-L is the best for the second category, followed by BEEF-vdW, M06-L, and GAM. The occurrence of GAM in both lists is ACS Paragon Plus Environment

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13

especially interesting because of its limited list of independent variables (only spin densities and their gradients). Although MN15-L performs better than the other functionals for closed-shall interactions, BEEF-vdW, M06-L, and GAM all perform better than MN15-L for openshell interactions and have relatively good performance in general. The four lowest overall mean unsigned errors (averaged over all 39 data, in kcal/mol) are 5.8 (BEEFvdW), 6.8 (MN15-L), 6.9 (M06-L), and 8.3 (GAM), with the five other functionals having values from 8.7 (RPBE) to 19.3 (LSDA) kcal/mol. This is especially encouraging for the universality of MN15-L, M06-L, and GAM since no adsorption data were used in their parametrization. The good performance of the four best performing functionals, combined with their previously demonstrated good performance for molecular bond energies and chemical reaction barrier heights,8,9,10,11 makes them good candidates for applications to heterogeneous catalysis. ASSOCIATED CONTENT The Supporting Information contains optimized lattice constants of the metals and coordinates of all species optimized with PBE, molecular dissociation energies, the energies calculated for the original reactions 1-13, and comparison of the PBE calculations of this work to those of Ref. 1. The Supporting Information is available free of charge on the ACS Publications website. AUTHOR INFORMATION Corresponding Author

*Email: [email protected] Present Address

†Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095-1592 ACKNOWLEDGMENT The authors are grateful to Pragya Verma for valuable discussions. This work is supported as part of the Inorganometallic Catalysis Design Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0012702.



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E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision C.01; Gaussian, Inc., Wallingford CT, 2010. 28 Zhao, Y.; Peverati, R.; Yang, K. R.; Luo, S.; Yu, H.; He, X.; Truhlar, D. G. Minnesota Density Functionals Module 6.7; 2016. See http://comp.chem.umn.edu/mn-gfm/ for details (accessed Feb. 27, 2016). 29 Lew, W.; Crowe, M. C.; Campbell, C. T.; Carrasco, J.; Michaelides, A. The Energy of Hydroxyl Coadsorbed with Water on Pt(111). J. Phys. Chem. C 2011, 115, 23008‒ 23012. 30 Zhang, Y.; Yang, W. A Comment on the Letter by John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Phys. Rev. Lett. 1998, 80, 890. 31 Lieb, E. H.; Oxford, S. Improved lower bound on the indirect Coulomb energy. Int. J. Quantum Chem. 1981, 19, 427-439.


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TOC Graphic

cyclohexene/Pt(111 ) Energy of adsorption



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Validation of Density Functionals for Adsorption Energies on

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