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56 CHAPTER4. RESULTSANDDISCUSSION et al. [165]. The effect for a number of other dopants, such as In, Ge, Sn, Pb, As, Sb, Bi and Se, are quite small. However, our results indicate that the application of a U =2 eV might result in a less accurate description than that obtained at the RPBE level. First off, the application of a U value changes the magnetic properties of the materials in a way that is not expected. It is known that Co, Cr, Fe, and Mn-doped TiO2 are magnetic[215, 216]. For the bare surfaces (without O adsorbate), both RPBE+U and RPBE calculations predict these materials to be magnetic, while for the sur- faces with an Oc adsorbate only the RPBE-level calculations predict that the ma- terials are magnetic. At the same time, the RPBE+U calculations predict that O-covered In- or Cd-doped surfaces should become magnetic, even though both RPBE and RPBE+U calculations predict that bare Mn- or Fe-doped TiO2 sur- faces have the highest magnetic moments. RPBE gives a consistent description of the magnetic properties, for both bare and O-covered slabs. Apart from mag- netic properties, the application of a Hubbard U results in much larger changes in adsorption energy of O for pure TiO2 than what is found by carrying out an ac- tual self-interaction correction using the method of Perdew and Zunger[204, 217] (PZ-SIC). Applying a PZ-SIC when calculating the adsorption energy of O on the (110) surface of rutile TiO2, Valdés et al. [217] found that the adsorption en- ergy was changed by only 0.03 eV. In contrast, the application of a Hubbard U on Ti d-states results in a weakening of the adsorption energy of ca 0.3eV, a ten times larger change. It is expected that the SIE should be small for systems with low d-orbital occupancy[218, 219], and this is reflected in the PZ-SIC re- sult, but not in the Hubbard-U result. The U that is found through linear response calculations[209] is about 5 eV, an even higher value than what we considered here. Such a high value allows the value of the band gap for TiO2 to be calculated correctly, but it actually results in a much worse value for the enthalpy of formation of Ti2O3 from TiO2 (it changes the enthalpy of formation by more than 1.5 eV and changes the sign of the formation energy)[165], and, as we indicate, it is much too high to be consistent with a correction for the SIE. These results, combined with the good performance of RBPE for chemical energetics[147], lead me to conclude that the usage of RPBE without a Hubbard U correction results in more consistent (and possibly more accurate) results for adsorption energies, even for doped TiO2. I suggest that higher-level calculations, e.g. using RPA+EXX or QMC, are needed to benchmark GGA, GGA+U and hybrid DFAs before a final conclusion about the applicability of Hubbard U methods for chemisorption energies can be made. Fi- nally, the important observation that linear scaling relations obtained at the GGA level are usually maintained at the GGA+U level indicates that our results should be qualitatively correct regardless of the results of such a comparison[165, 209]. The results presented hereafter are from calculations on the RPBE level.PDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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