PNNL

Abstract

Migration and formation of hole polarons in bulk rutile and anatase TiO2 were modeled using density functional theory. We previously applied a similar method to model electron polarons and extended the approach to hole polarons. Holes were formed by removal of an O(2p) valence electron, and their quantum mechanical characterization (reorganization energy and electronic coupling) was performed with the DFT+U method, a method that corrects for the self-interaction errors and facilitates charge localization, combined with cluster calculations. We found that activation energies for hole hopping are about twice as large as those for electron hopping, in agreement with experiment. Activation energies typically vary in the range of 0.5 and 0.6 eV. We found that most of the hole hopping processes are adiabatic in rutile but non-adiabatic in anatase. Lattice distortions around hole polarons are also about twice as large as distortions around electron polarons. Our results show that holes are thermodynamically more stable in the rutile phase, while electrons are more stable in the anatase phase. A hole trapping site with hemi-bond structure (hole charge shared between two non-bonded oxygen sites) was identified in anatase as the result of the electronic coupling between the initial and final states being so large that the trapping structure corresponds to a hole delocalized between two oxygen atoms. We also modeled the formation of hole and electron polarons at the (110) surface. The activation energy for hole transfer on the surface is about 0.07 eV larger than in the bulk, while the activation energy for electron transfer on the surface is about 0.11 eV larger than in the bulk. These results form the basis for further development of models to describe polaron transport in TiO2 structures such as surfaces, interfaces, or non-perfect crystals. Funding was provided by the Department of Energy, Office of Basic Energy Sciences. Computational resources were provided by the Molecular Science Computing Facility located at the Environmental Molecular Science Laboratory in Richland, WA. All work was performed at Pacific Northwest National Laboratory (PNNL). Battelle operates PNNL for the U.S. Department of Energy.