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4.2. SELECTIVITY BETWEEN CL2 AND O2 53 4.2.2 Theoretical studies of the connection between oxide com- position and ClER and OER activity and selectivity 4.2.2.1 Computational details We have performed a fundamental study of the effect on electrocatalytic properties of doping TiO2 with both conventional dopants such as Ru or Ir, and also 36 other dopants, including all fourth, fifth and sixth-row transition metals[17]. A deeper study was performed of the TiO2-RuO2 mixed oxide[16]. In both cases, DFT on the RPBE-level[150] was used to calculate the adsorption energy of O on the CUS: ∆E(Oc)=E(Oc)−E(c)−E(H2O)+E(H2), (4.7) This adsorption energy has been found to serve as a descriptor for both OER and ClER[108], meaning that this adsorption energy can be used, together with the vol- cano plot of Hansen et al. [108] (Figure 2.5), to predict the activity and selectivity of different rutile oxide materials for ClER and OER. The selectivity was evalu- ated based on the difference between the electrode potential U required for OER and the one required for ClER, for a certain material. We considered both binary and ternary combinations of TiO2 and other oxide materials, as well as the distance dependence of the effects. This was done by calculating ∆E(Oc) with one or two dopants placed into a unit cell with 8 cations (in the binary systems) or either 8 or 16 cations (in the ternary systems). The positions in the 8 cation-cell where dopants could be placed are indicated in Figure 4.6, where the three-dimensional structure of the surface is also indicated. 4.2.2.2 The self-interaction error A key challenge in modeling mixed oxide materials is the self-interaction error (SIE), which is related to the failure of presently available density functionals to completely correct for the classical self-interaction (see Section 2.1.3.2). This error causes the electronic density to delocalize in an unphysical way, and this is a partic- ular problem for the description of dopants and defects[159, 164, 204]. The most popular way of correcting for this error in theoretical studies of (electro)catalysis is the Hubbard-U method, where the energy of the d orbitals of different atoms in the solid are altered to describe the electronic density correctly. However, this method is usually applied in a non-self-consistent manner, where the U value is determined in some way and then kept constant during calculation of e.g. adsorp- tion energies. Two main methods of determining the U involve either fitting the value to recover some experimental thermochemical data[165, 205, 206], or fitting the value to recover the correct curvature of the total energy with changes in the number of electrons in a system (the so-called linear response U [207–210]). Still, in neither of these methods does the resulting U value correct the description ofPDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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