Modeling and Detection of Small Electron Polaron: A Comparison between Bond Distortion Method and Occupation Matrix Control Method

When density functional theory (DFT) is used for modeling polaron defects, the delocalized electronic states often appear due to self-interaction errors. Conventionally, the DFT + U method may possibly correct the self-interaction error and thus promote electron localization, but this does not always work. In this paper, based on the GGA + U approach, we have modeled small electron polarons by using bond distortion method (BDM) and occupation matrix control (OMC) method in TiO2. Both of these methods can control the position of the polaron at will. We evaluate the appropriate parameters for constructing stable polarons using the BDM. Meanwhile, the occupation of all orbitals of rutile and only low-energy orbitals of anatase was successfully realized using the OMC method. Calculation results show that the polarons constructed by the BDM are more stable irrespective of the crystal structure for TiO2. Furthermore, whichever method is used, the polarons formed in rutile are more stable. Electronic structure calculations demonstrate that rutile has a larger band gap after successful localization through BDM and OMC methods. On the contrary, the band gap of anatase decreases after localization because of the emergence of a new flat energy level at the Fermi level, generated mainly by localized Ti atoms. In order to better understand the polaron formation, we have studied charge transfer, bonding states, and electrostatic potential distributions around the polaron. In the localized solution, the Ti–O bonds around the polaron are all lengthened, while the stability and covalency of these bonds are reduced. The charge is strongly trapped in a potential well caused by lattice distortion, which leads to a lower electrostatic potential energy at the polaron position. In this work, polaron modeling methods and localized structure in TiO2 contribute to a better understanding of the polaron structure and its related properties.