Article pubs.acs.org/JPCC
Screened Hybrid Exact Exchange Correction Scheme for Adsorption Energies on Perovskite Oxides Elton J. G. Santos,†,‡,§,∥ Jens K. Nørskov,†,‡ and A. Vojvodic*,† †
SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States ‡ Department of Chemical Engineering, Stanford University, Stanford, California 94305, United States § School of Mathematics and Physics, Queen’s University Belfast, BT7 1NN, United Kingdom ∥ School of Chemistry and Chemical Engineering, Queen’s University Belfast, BT9 5AL, United Kingdom S Supporting Information *
ABSTRACT: The bond formation between an oxide surface and oxygen, which is of importance for numerous surface reactions including catalytic reactions, is investigated within the framework of hybrid density functional theory that includes nonlocal Fock exchange. We show that there exists a linear correlation between the adsorption energies of oxygen on LaMO3 (M = Sc−Cu) surfaces obtained using a hybrid functional (e.g., Heyd−Scuseria−Ernzerhof) and those obtained using a semilocal density functional (e.g., Perdew−Burke−Ernzerhof) through the magnetic properties of the bulk phase as determined with a hybrid functional. The energetics of the spin-polarized surfaces follows the same trend as corresponding bulk systems, which can be treated at a much lower computational cost. The difference in adsorption energy due to magnetism is linearly correlated to the magnetization energy of bulk, that is, the energy difference between the spinpolarized and the non-spin-polarized solutions. Hence, one can estimate the correction to the adsorption energy as obtained from a semilocal functional directly from the bulk magnetization energy from a hybrid functional.
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on-site repulsion U, which stems from Coulomb interactions between electrons in the same orbitals, is included as an additional assumption in the total Hamiltonian of the system. It has been noted that the electronic structure and reactivity of different perovskite oxide surfaces15 depend quite significantly on the chosen value of U. However, the computational time cost to perform hybrid calculations still being heavy does not allow for a rapid screening of energetic properties which are of key importance for the understanding of surface reactions. Here, we present a correction scheme for determining oxygen adsorption energies on the surface of a group of oxides, the (001) surface of LaMO3 with M = Sc−Cu, at the accuracy of exact exchange calculations based on the Heyd−Scuseria− Ernzerhof (HSE) hybrid functional using the magnetic properties of the bulk structure at HSE level and the O adsorption energies at the generalized gradient approximation (GGA) level using the Perdew−Burke−Ernzerhof (PBE) functional. The existence of this correction is possible because there exist correlations between bulk, surface, and adsorption properties calculated at the HSE level, which are mediated by the intrinsic magnetic interactions present in these oxides. The
erovskite transition metal oxides with the formula AMO3, where A sites are occupied by lanthanide, yttrium, and/or an alkaline earth atom and M by a transition metal atom, have been attracting increasing interest as building blocks of a new class of structures for developing renewable energy production and storage technology.1 With a variety of physical and chemical properties, ranging from Mott−Hubbard insulators and correlated metals2 to catalytic materials for electrocatalysis,1 these materials provide a challenge for theory due to the intrinsic coupling between several physical interactions, for instance, charge, lattice, and spin.2 The localized character of partially filled d orbital states, added to the strong electronic correlations, as well as the self-interaction error present mainly at the M atom, can lead to low accuracy in predicting their physical and chemical properties by a local or semilocal description of the exchange and correlation within density functional theory (DFT).3−8 One alternative solution is to consider a fractional component of the exact exchange from the Hartree−Fock (HF) theory hybridized with the DFT exchangecorrelation functional.9−11 This hybrid approximation has been observed to improve the energetics and overall electronic structure for several AMO3 compounds, resulting in a better agreement with experimental findings.12−14 Moreover, the hybrid approach does not include any external systemdependent parameters which is the case for the HubbardDFT model, the so-called GGA+U approach. In GGA+U, the © 2015 American Chemical Society
Received: April 28, 2015 Revised: July 1, 2015 Published: July 29, 2015 17662
DOI: 10.1021/acs.jpcc.5b04053 J. Phys. Chem. C 2015, 119, 17662−17666
Article
The Journal of Physical Chemistry C
contrast, for LaCrO3, the intermediate filling for which this energy difference is 2.07 eV is the largest in this La-perovskite family. Substantial differences are also observed between different magnetic solutions for both PBE and HSE. For example, at the PBE level the largest energy difference between PBE(FM) and PBE(NM) solutions is found to be 1.13 eV for LaMnO3. Moreover, on LaCrO3 and LaFeO3, which have an AFM ground state, oxygen is found to bind stronger by 0.36 and 0.70 eV, respectively, for the PBE(AFM) solution relative to the PBE(NM) solutions. These energy differences are 0.90 and 1.34 eV if the PBE(AFM) solution is taken relative to the PBE(FM) solution. Similar trends are observed among the HSE(FM, AFM, NM) adsorption energies, however, with overall larger energy differences in comparison to the corresponding PBE values. This suggests that magnetic effects play an important role in the chemisorption of O on the LaMO3(001) surfaces mainly for the systems with partially filled d-bands. When it comes to experimentally measured data of oxygen adsorption energies on La-based oxide surfaces, it is lacking despite the urgent need to benchmark our theoretical predictions of the reactivity of oxide surfaces in general due to their existing and potential applications. However, Bockris et al.16 have studied a group of La-based perovskite oxides for their oxygen electrochemistry. They show that as the magnetic moment of the LaMO3 compound increases the current density for the oxygen evolution reaction decreases according to the magnetic character (paramagnetic, ferro, or antiferromagnetic); that is, the higher the magnetic polarization the lower the production of oxygen. Conversely, the highest electrocatalytic activity was observed for weaker magnetic compounds. Even though the catalytic activity is intricately coupled to among other things the reactivity of the surfaces toward multiple intermediates, it has previously been shown that the O adsorption energy can be used as a first-order descriptor for the overpotential.17 A quantification of such magnetic effects can be obtained by analyzing the magnetic stabilization energy EM, defined as the energy difference between the FM and NM solutions, EM = EFM − ENM. Large negative EM values correspond to high magnetic stability, which corresponds to a strong ferromagnetic oxide. Figure 1b shows EM for bulk and surface LaMO3 as a function of the atomic number of the metal constituent of the oxide. Oxides with partially filled d-bands (see Figure S1 in Supporting Information) exhibit the highest magnetic stability, independently of the structural phase analyzed (bulk or surface). For LaMO3 with M = V, Cr, Mn, and Fe, we find a progressive increment of the magnetic stability from bulk to surface independently of the level of theory. It is worth mentioning that these systems also show the largest differences in adsorption energies between the spinpolarized and non-spin-polarized solutions as discussed above (Figure 1a). Hence, this implies that there exists a correlation between the O adsorption energies and EM, which is shown in Figure 2. This correlation can be expressed by means of a simple linear equation as ΔEOads = ξ + γΔExM, where x stands for bulk or surface magnetic stabilization energy, and ξ and γ can be determined from the energy difference between PBE and HSE calculations as discussed above. Figure 2a shows the adsorption energy difference between HSE(FM) and PBE(FM) as a function of EBulk M . For compounds with high magnetic stability, i.e., LaMO3 with M = V, Cr, Mn, Fe, and Ni, the calculations reveal a correlation between the O adsorption energy and the magnetic properties of the bulk. We
difference between PBE and HSE calculated adsorption energies follows the energetic cost to stabilize the magnetic moments of the 3d metal ions, which are found to show a similar behavior for the two different exchange-correlation functionals. The presented scheme has predictive power and provides insight into the design of new catalysts at a higher level of accuracy but at a low computational cost. Figure 1a shows the calculated adsorption energies of O on top of the M atom of the LaMO3(001) surface as a function of
Figure 1. (a) Hybrid HSE and semilocal PBE calculated adsorption energies of atomic O on top of the M site of the LaMO3(001) surfaces (M = Sc−Cu) as a function of the atomic number of the metal constituent for different magnetic spin orderings. The ferromagnetic (FM) and nonmagnetic (NM) spin solutions are modeled using a 1 × 1 × 3 surface unit cell, while the antiferromagnetic (AFM) solutions are modeled with a 2 × 2 × 3 surface unit cell. Symbols indicate calculated values for individual perovskites, while the lines show a guide to the eye interpolation between the points. (b) Magnetic stabilization energies EM for bulk and surface LaMO3 structures obtained using HSE and PBE functionals.
the 3d atomic number of the metal constituent of the oxide as obtained at two levels of theory, GGA (PBE) and exact exchange (HSE). Different magnetic solutions are considered: nonmagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM). The O adsorption energies are calculated relative to H2O and H2 according to the following equation O ΔEads = E[O*] − E[*] − (E[H 2O] − E[H 2])
(1)
where E[O*], E[*], E[H2O], and E[H2] are the ground-state energies of the perovskite surface with adsorbed O, the clean surface, and the H2O and H2 molecules in the gas phase, respectively. We found that PBE and HSE reproduce qualitatively similar trends in the adsorption energies across the LaMO3 series despite the magnetic ordering assumed. Both sets of calculations show weaker binding strengths at low and high 3d band fillings than for intermediate band filling values. In particular, the energy difference for the FM solutions between PBE and HSE, ΔEOads(eV)PBE(FM)−HSE(FM), is small approaching 0.20 and 0.60 eV for Sc and Cu, respectively. In 17663
DOI: 10.1021/acs.jpcc.5b04053 J. Phys. Chem. C 2015, 119, 17662−17666
Article
The Journal of Physical Chemistry C
Figure 2. (a) Difference in HSE(FM) and PBE(FM) calculated O adsorption energies on LaMO3(001) surfaces as a function of the bulk magnetization energy EBulk M . Symbols indicate calculated values for individual perovskite oxides, and the line shows the best linear fit to versus the bulk these data. (b) Surface magnetization energies ESurface M magnetization energies for different perovskites as displayed in (a). The lines show the best linear fit for each set of simulations.
Figure 3. (a) Calculated adsorption energies at the HSE(FM) level versus the model predictions. The model data have been generated and EPBE using only EBulk−HSE M ads energies. (b) Schematic diagram showing how the different calculations for bulk and surface structures at two different levels of theory (HSE and PBE) are correlated to each other . The correlation via the magnetic energy differences ΔEBulk,Surface M between bulk and surface calculations for a given exchange-correlation themselves. functional is mediated by the magnetic energies ESurface,Bulk M The arrows indicate the components needed to calculate the adsorption energies at the HSE level using the functional relation HSE Bulk−HSE PBE [EM , Eads ]. The computational time to calculate the Eads energies increases either vertically or horizontally as given by the Cartesian axis. The dashed lines between surface energies and adsorption energies show the nontrivial correlation between both HSE and PBE sets of calculations.
find that the larger the bulk or surface magnetization of LaMO3 oxides is, the more significant the role of magnetization on the O adsorption energy. The largest deviations from the linear relation are found for perovskites of lower or no magnetic character, for instance, LaScO3 and LaTiO3. In addition, we find that ESurface and EBulk M M follow a similar relationship at the PBE and HSE levels of theory but with different linear coefficients as shown in Figure 2b. Therefore, the differences in O adsorption energies between PBE and HSE can be obtained solely based on the bulk HSE magnetic energies, which are computationally less demanding than those at surfaces due to the reduced number of atoms in the unit cell. In order to obtain a correction scheme for the adsorption energies on LaMO3 at the HSE level, we can utilize the magnetic energies EBulk M at the HSE(FM) level and the adsorption energies EOads at the PBE(FM) level to determine the slopes in ΔEOads = ξ + γΔExM. Figure 3a shows a schematic where the functional form Bulk−HSE EHSE , EPBE ads [EM ads ] summarizes the main procedure. Figure 3b shows a comparison between the adsorption energies as determined by the correction scheme. Using the coefficients (ξ,γ) as reported in Figure 2a results in ΔEOads = 0.53−0.46EBulk and the fully HSE(FM) calculated adsorption M energies. If only perovskites with high magnetic stability are used in the regression, the correlation coefficient is 0.988, which is slightly higher than that using all the data, 0.978. This means that the linear relation based on the functional form Bulk−HSE PBE EHSE , Eads ] performs better for perovskites with larger ads [EM magnetic stability than the nonmagnetic ones. These findings show that the developed correction scheme has the power to
describe the O adsorption energies on perovskite surfaces at a low computational cost. In conclusion, we have demonstrated that a correction scheme for adsorption energies between semilocal and hybrid density functional obtained values exists for La-based oxide surfaces. It is based on energetic correlations originating from the magnetic properties of the oxides which are systematically inherited from the bulk to the surface, not only for a given exchange-correlation functional but also between the semilocal and the hybrid functional. The adsorption energy of oxygen on the (001) surfaces of LaMO3 (M = Sc−Cu) at the HSE level of accuracy can be obtained by utilizing the bulk magnetic stabilization energy at the HSE level and the O adsorption energy at the PBE level. The developed correction scheme reproduces with high accuracy the HSE calculated adsorption energies. It is likely that the oxygen chemistry reported here for LaMO3 with 3d metal constituents will be found in other compounds of similar structure, e.g., BaMO3, CaMO3, SrMO3, and YMO3. This opens up possibilities of studying and 17664
DOI: 10.1021/acs.jpcc.5b04053 J. Phys. Chem. C 2015, 119, 17662−17666
The Journal of Physical Chemistry C
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ACKNOWLEDGMENTS The authors acknowledge support from the U.S. Department of Energy Office of Basic Science to the SUNCAT Center for Interface Science and Catalysis for the Predictive Theory of Transition Metal Oxide Catalysis: DOE Materials Genome Project (DE-AC02-76SF00515) grant. The authors thank Andrew Doyle and Joseph Montoya for valuable discussions and input.
screening the chemistry of a larger group of perovskite oxides, that is, 4d and 5d families, in a computationally feasible way.
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METHODS All the simulations reported here were performed using the density-functional-theory (DFT) formalism as implemented in the VASP code.18,19 The generalized gradient approximation (GGA) using the Perdew−Burke−Ernzerhof (PBE) functional20 was used for the semilocal treatment of the exchange and correlation. For the screened hybrid-DFT simulations, we used the Heyd−Scuseria−Ernzerhof (HSE) hybrid functional,21 where part of the short-range PBE exchange energy is replaced by a portion of exact Hartree−Fock exchange energy. Here we used HSE as an example of a hybrid functional because of its successful applications in solids in comparison, for instance, to the B3LYP functional,22−24 and because of its less expensive computational cost to treat the slow-decaying long-range part of the exchange interaction in comparison to the PBE0 functional.25 A well-converged plane-wave cutoff energy of 400 eV combined with the projector-augmented-wave (PAW)26,27 method was used in both PBE and HSE simulations. Atoms were allowed to relax using a quasi-Newton algorithm until all forces were smaller than 0.03 eV/Å and the error in total energy was smaller than 0.1 × 10−2 eV. Tests performed at a higher accuracy (
