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54 CHAPTER4. RESULTSANDDISCUSSION ab 1cus 3a 3b 4a 4b 1br 2a 2b Oc Oc Figure 4.6: a) The model systems studied, as well as the different positions where the dopant could be placed in the studies of Karlsson et al.[16, 17]. b) A three- dimensional image of the (110) surface of an Ru-doped TiO2-slab. all physical properties, and it has been found that the U -value needed to e.g. cor- rect the band gap of a material might be too high to recover the correct enthalpy of formation of the material[165]. Furthermore, it is not straightforward to de- termine which orbitals should be altered with a U -value[209]. It is possible that a method where the U -value is determined self-consistently using the linear response method[207], at every step in e.g. a relaxation calculation, and for all orbitals out- side of the frozen core, might correct for these deficiencies, but this is not practiced at present. There are other methods that might approach chemically accurate en- ergies (energies with an error of less than 1–2 kcal/mol≈0.04–0.08 eV), including calculations where the exchange energy is evaluated exactly using the Kohn-Sham orbitals (EXX) and the correlation energy is evaluated using the random-phase approximation (RPA)[211] and quantum Monte Carlo (QMC)[212], but both of these methods are presently too computationally demanding to be used in screen- ing studies. In the present studies[16, 17], we have used the Hubbard+U method, applied on 3d or 4d states of either dopants, Ti cations, or both, to ascertain the importance of a partial SIE correction. For the RuO2-TiO2-system, we first found that as long as spin polarization is neglected, which is acceptable for nonmagnetic materials such as DSA, the addition of a U value, in the range of 1 eV to 6 eV, on the Ti d states resulted in only minor effects on adsorption energies[16]. However, in the later O Ti RuPDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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