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32 CHAPTER2. COMPUTATIONALMETHODS prepared, which includes one less electron in a certain orbital (e.g. in one of the 3d orbitals of Ru if the 3d XPS binding energies of RuO2 is to be calculated). The calculation for the core-ionized system is carried out with this setup, while the ground state calculation is carried out with the standard setup. This method does not include the effects of spin-orbit coupling, the splitting of binding energies into two components that occur in ionization of electrons from orbitals with a net angular momentum l (all orbitals other than s). However, chemical shifts are not expected to be significantly affected by spin-orbit coupling. In the present thesis, X-ray photoelectron shifts have been calculated using pe- riodic descriptions of the considered systems. To avoid unphysical interactions between core-holes, periodic cell sizes of at least 13 to 15 Å were used. Moreover, the spins in the core-ionized system should be unrestricted, as the singly occupied core level can result in polarization of the spins, affecting the total energy. As is the case for other properties, DFT results for binding energies and chemical shifts do not achieve chemical accuracy. Absolute values for binding energies calculated using DFT GGA functionals have been found to differ from experiment by up to 1 eV, depending on the functional used[182], but chemical shifts differ much less[183]. 2.3 Theoretical models for heterogeneous electrochem- ical reactions Apart from using DFT to calculate XPS chemical shifts, I have also performed DFT calculations to model heterogeneous electrochemical reactions. In practice, theoretical studies based on DFT modeling have so far had the most success in de- scribing heterogeneous gas-solid reactions. The reason is the relative simplicity of such systems compared with typical electrochemical systems. In the case of gas- solid reactions, understanding can be obtained even when a reaction is modeled as occurring in vacuum since the interactions between molecules in the gas can be assumed small. Furthermore, the rates are controlled by temperature and pressure, which can be taken into account using well-known expressions from thermody- namics and kinetic rate theory. Another advantage is that several experimental methods exist that give detailed information about reactions at surfaces under vac- uum conditions.[109, 153] Conversely, most heterogeneous electrochemical reactions occur in the interface between a solid catalyst and a liquid electrolyte. The electrolyte is often a concen- trated solution, with high concentrations of one or more ionic compounds. Reac- tants in an electrochemical reaction interact strongly with other molecules close to the surface, leading e.g. to solvation of the reactants by water. A first principles de- scription thus needs to include a description of not only the solid material and thePDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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