The application of hopping theory to predict charge (hole) mobility in amorphous organic molecular materials is studied in detail. Application is made to amorphous cells of N,N'-diphenyl-N,N'-bis-(3-methylphenylene)-1,1'-diphenyl-4,4'-diamine (TPD), 1,1-bis-(4,4'-diethylaminophenyl)-4,4-diphenyl-1,3,butadinene (DEPB), N4,N4'-di(biphenyl-3-yl)-N4,N4'-diphenylbiphenyl-4,4'-diamine (mBPD), N1,N4-di(naphthalen-1-yl)-N1,N4-diphenylbenzene-1,4-diamine (NNP), and N,N'-bis[9,9-dimethyl-2-fluorenyl]-N,N'-diphenyl-9,9-dimethylfluorene-2,7-diamine (pFFA). Detailed analysis of the computation of each of the parameters in the equations for hopping rate is presented, including studies of their convergence with respect to various numerical approximations. Based on these convergence studies, the most robust methodology is then applied to investigate the dependence of mobility on such parameters as the monomer reorganization energy, the monomer-monomer coupling, and the material density. The results give insight into what will be required to improve the accuracy of predictions of mobility in amorphous organic materials, and what factors should be controlled to develop materials with higher (or lower) charge (hole) mobility.

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Understanding the water oxidation process on small metal oxide complexes is fundamental for developing photocatalysts for solar fuel production. Titanium oxide and manganese oxide complexes have high potential as components of a cheap, nontoxic, and stable photocatalyst. In this theoretical work, the water oxidation process on Mn(x)Ti(2-x)O4 (x = 0-2) clusters is investigated at the BP86 level of theory using two water molecules and fully saturated systems. In the oxidation cycle using two water molecules, Mn reduces the reaction energy; however, Mn does not reduce the reaction energy on the fully saturated system. When two water molecules are used, the highest reaction energy in the water oxidation cycle is lower than 3 eV, but the highest reaction energy is higher than 3 eV on fully saturated systems except for the pure titanium oxide complex which has a highest reaction energy of 2.56 eV. Dehydrogenation processes in the water oxidation cycle require higher energy than the O-O formation or water adsorption processes. The overall dehydrogenation energy is usually smaller on complexes including at least one Mn atom and it is smallest on the Mn2O4 complex that has two water molecules. Considering the highest reaction energy in the overall water oxidation cycle, water oxidation at the manganese atom of MnTiO4 hydrated with two water molecules is the most favorable in energy.

Metal oxide complexes have high catalytic potential in many fields, such as oxidation, dehydrogenation, dehydration, reductive coupling, etc. The adsorption of molecules is a fundamental process in catalytic reactions on the metal oxide complex. In this study, water adsorption and dissociation processes on small Mn-doped TiO2 complexes are investigated at the density functional theory (DFT) level of theory. Water adsorption at terminal Mn atoms is typically found to have an energy around -0.7 eV, which is smaller than the -1.2 eV observed at terminal Ti atoms. Dissociation energies at Mn atoms are determined to be about -0.6 eV, which are also smaller than the approximately -1.2 eV dissociation energies at Ti atoms. Molecular adsorption without dissociation is favorable in energy after water adsorbs at each metal atom. Mn doping reduces the reaction energy; the reaction energy of the doped system is not similar to that of the pure manganese oxide complex.

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