A Linear Response DFT+U Study of Trends in the Oxygen Evolution Activity of Transition Metal Rutile Dioxides
Zhongnan Xu, Jan Rossmeisl and John R. Kitchin, “A Linear Response DFT+U Study of Trends in the Oxygen Evolution Activity of Transition Metal Rutile Dioxides”, The Journal of Physical Chemistry C 119(9), 4827-4833 (2015). https://doi.org/10.1021/jp511426q
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Question
Plain GGA functionals mistreat the d electrons of oxidized transition metals, and the Hubbard U is the cheapest correction, but the right U is usually fitted to experimental data that rarely exist for surface adsorption. The established computational picture of the oxygen evolution reaction (OER) on oxides, in which a few adsorption energies scale with each other and produce an activity volcano, was built without any U. The paper asks whether adding U, and in particular a U computed from first principles by linear response, changes adsorption energies, breaks the scaling relations, or improves predicted activity trends relative to experiment (Xu et al. 2015).
Approach
Calculations used Quantum ESPRESSO with PBE, GBRV ultrasoft pseudopotentials and spin polarization. Ten rutile dioxides were studied: TiO2, CrO2, MnO2, NbO2, MoO2, RuO2, RhO2, ReO2, IrO2 and PtO2. Bulk lattice parameters and ground-state magnetic order were found first (CrO2 and MnO2 ferromagnetic, the rest nonmagnetic), and a bulk linear response U was computed for each in 48-atom supercells. These U values ranged from 3.32 eV (NbO2) to 7.15 eV (CrO2), with 5.91 eV for IrO2 and 6.73 eV for RuO2.
OH, O and OOH adsorption at the five-fold coordinated cation site of the (110) surface was computed for U from 0 to 8 eV in 0.5 eV steps, more than 400 calculations in all. To keep this affordable, a two-layer slab with hydrogen-terminated bottom was used and validated against a four-layer slab at U = 0: agreement was excellent for OOH, good for OH and reasonable for O, and both slab models fell on the same scaling lines. Activity was assessed with the standard four-step proton-electron transfer model, where the theoretical overpotential is the largest step free energy minus 1.23 V.
Key findings
For the 4d and 5d oxides, any U > 0 made all adsorption energies more endothermic. For late oxides (RuO2, RhO2, IrO2, PtO2) the change was smooth up to U = 8 eV. For early oxides (NbO2, MoO2, ReO2) the change was smooth at low U but became irregular at high U, and the computed linear response U sat right where this breakdown begins, which the authors read as a sign that large U values are inappropriate for these oxides with few d electrons. In every 4d and 5d case, the U-induced shifts kept the adsorption energies on the scaling relations established at U = 0.
The 3d oxides were mixed. CrO2 and MnO2 behaved similarly: adsorption weakened smoothly with U until OOH was no longer stably bound (above about 4 eV for MnO2), which is what broke the OH/OOH scaling there. TiO2 was the exception: OOH binding became more exothermic with U, the changes were small (OH moved by less than 0.1 eV up to 8 eV), and scaling was not preserved. The authors attribute this to the d0 Ti site, where adsorbates bond mainly with oxygen p states, and suggest that bulk U may not describe this situation, proposing DFT + U(R) or U on O 2p states as possible remedies.
Activity trends were compared for RuO2, RhO2, IrO2 and PtO2, chosen because they are stable under acidic OER conditions (MnO2 and TiO2 were excluded for the reasons above). Because scaling holds, applying linear response U slides each oxide along a leg of the unchanged volcano rather than reshaping it, always toward weaker binding. IrO2 and RuO2 moved toward the peak from the strong-binding side, while RhO2 and PtO2 moved away from it on the weak-binding side. The predicted ordering changed from RhO2 > IrO2 > PtO2 > RuO2 at U = 0 to IrO2 > RhO2 > RuO2 > PtO2 with U, closer to the experimental RuO2 ≈ IrO2 > RhO2 > PtO2, although RuO2 versus RhO2 remains wrong. The reaction-energy shifts were only about 0.2 to 0.4 eV, never enough to move an oxide across the volcano peak. Input and output files were deposited on Zenodo.
Significance
The study supports the robustness of oxide scaling relations to the Hubbard U and suggests that screening studies done at U = 0 should reach similar conclusions with U, except perhaps near the volcano top where small shifts reorder candidates. It also shows that a non-empirical linear response U can improve OER trend predictions, while flagging d0 TiO2 and high U on early oxides as cases where the bulk U is questionable (Xu et al. 2015).