(370e) Determining the Pd Dopant Effect on the Reducibility of Fe2O3: DFT+U or Hybrid Functionals?

The most common method used for modeling highly correlated systems, like oxides, is DFT+U which applies an energy penalty to the DFT energy proportional to a set U value. Choosing a U value has typically been done in order to accurately reproduce a bulk oxidesâ?? physical parameters, such as band gap or bulk structure. However, there are two problems with this method. First, the application of the U proportional energy penalty can cause the system to converge to a local electronic minimum as opposed to the global electronic minimum unless you perform a computationally expensive scan from a U value of 0 (i.e. no correction) up to the wanted value.[1] Second, accurately reproducing bulk parameters by applying a certain U value does not guarantee that the energetics will also be captured correctly.[2] Kitchin, et al. have proposed a method for determining the correct U value using linear response theory;[2-4] however, this method has thus far been applied to bulk oxide reactions where the U value can be applied consistently throughout the system. The applicability of the linear response method to surface oxide reactions is currently unclear. In this contribution, we study the initial reducibility of the clean and Pd doped Fe₂O₃ (0001) surface using the DFT+U method proposed by Meredig, et al.[1] as well as the hybrid HSE06[5] functional.

The creation of oxygen vacancies in the (0001) surface of clean and Pd doped Fe₂O₃ was studied using both the DFT+U method of Meredig, et al., whereby we scan over numerous U values from low to high, and the HSE06 functional. In order to have a clear picture of the initial reduction of Fe₂O₃, we considered the formation of one, two, and three oxygen vacancies within the surface and first subsurface layer in all possible combinations. For the DFT+U studies, we found that the trend in both the vacancy formation energy and surface energy for the clean Fe₂O₃ (0001) surfaces was highly dependent on the U value, making it difficult to determine the energetic pathway for the reduction of the Fe₂O₃ (0001) surface. Furthermore, when the Fe₂O₃(0001) surface was doped with Pd, the amount of charge transferred between the dopant and oxide surface, as well as the charge distribution itself, significantly changed as U was increased.

These results highlight the difficulty in obtaining accurate models using the DFT+U method for surfaces as there are few if any reliable experimental energies of surface reactions on oxides which can be used to benchmark the U value. Therefore, we have re-examined the reduction of clean and Pd doped Fe₂O₃ (0001) surfaces using the hybrid HSE06 functional in order to obtain accurate trends for oxygen vacancy formation energies in the Fe₂O₃ system. For the clean Fe₂O₃ (0001) surface, our HSE06 results show that vacancies in the subsurface oxygen layer are slightly favored over surface vacancies; however, this process is still highly endothermic. This suggests that after the first surface oxygen vacancy is formed, a subsurface oxygen will diffuse to the surface. The most significant effect of Pd doping on the initial reduction of the Fe₂O₃ (0001) surface is in the creation of the first surface oxygen vacancy which becomes exothermic due to the Pd-O interactions. As creating the first oxygen vacancy in the Fe₂O₃ (0001) surface is the most energy intensive step examined here, the addition of Pd is likely to significantly enhance the reducilibity of the Fe₂O₃ (0001) surface. This work highlights the difficulty in applying the DFT+U method to oxide surface reactions and demonstrates that the HSE06 functional is a useful alternative.

References: 

(1) Meredig, B.; Thompson, A.; Hansen, H.A.; Wolverton, C.; van de Walle, A. Phys. Rev. B 2010, 82, 195128.

(2) Curnan, M.T.; Kitchin, J.R. J. Phys. Chem. C 2014, 118, 28776.

(3) Xu, Z.; Joshi, Y.V.; Raman, S.; Kitchin, J.R. J. Chem. Phys. 2015, 142, 144701.

(4) Xu, Z.; Rossmeisl, J.; Kitchin, J.R. J. Phys. Chem. C 2015, 119, 4827.

(5) Krukau, A.V.; Vydrov, O.A.; Izmaylov, A.F.; Scuseria, G.E. J. Chem. Phys. 2006, 125, 224106.