Efficient Method for Modeling Polarons Using Electronic Structure Methods

Abstract

Polarons are localized electronic states that occur in many semiconductors. Modeling polarons at the quantum or atomic scale is often performed using electronic structure methods such as density functional theory (DFT). A problem using DFT to model polarons is that selfinteraction errors (SIEs) often result in delocalized electronic states rather than localized states. Methods such as DFT + U or hybrid functionals can be used to overcome SIE, but these methods may still not form stable polarons. The initial geometries and wavefunctions strongly influence and determine how and if polarons may arise during electronic structure calculations. In this paper, we have assessed different strategies to efficiently obtain low-energy localized polarons in several semiconductors (TiO 2 , m-HfO 2 , and m-BiVO 4 ). These strategies involve distorting the initial geometry to create polaron-like geometries or generating initial wavefunctions that mimic polaronic states. We show that perturbing the crystal's structure to induce polaron formation (which we call the bond distortion method) is a very efficient approach to form stable polarons, requiring less computational time than other methods. In contrast, other methods that we assessed may not lead to stable polaron states or may require much greater time (up to four times more computational time). Having a reliable, efficient method to ensure polaron formation is crucial to modeling polarons. The results described herein will save wasted computational efforts and also enable efforts such as high-throughput simulation of polarons.

Hole Polaron Migration in Bulk Phases of TiO2 Using Hybrid Density Functional Theory

“…As shown recently in a separate study, this approach is highly efficient for obtaining ground state structures of polarons. 58 We then linearly interpolate between the initial and final geometries to define a one-dimensional reaction coordinate for polaron hopping …”

Proton-Coupled Defects Impact O–H Bond Dissociation Free Energies on Metal Oxide Surfaces

“…Proton-coupled electron transfer (PCET) processes comprise the most fundamental elementary steps of important (photo)­electrocatalytic reactions such as oxygen reduction, CO 2 reduction, and water splitting. − On semiconductor surfaces, the pH-dependent redox potentials and band-edge energies of many metal oxides imply that redox processes for these materials are coupled to proton transfer. − Moreover, the thermochemistry of interfacial PCET may be impacted by proton-induced defects at the band edges or trap states within the band gap. − PCET thermochemistry can be described in terms of bond dissociation free energies (BDFEs), which are commonly applied as descriptors for electrocatalytic reactions such as hydrogen evolution. − The X–H BDFE, where X is a surface atom, corresponds to the reaction free energy for homolytic bond dissociation, X–H → X • + H • . BDFEs can be determined experimentally either from electrochemically measured proton-coupled redox potentials or by analyzing reaction equilibria in the presence of PCET oxidants with known BDFEs. ,− On the surface of metal oxides, however, the BDFEs of O–H bonds often depend on the oxidation states of the metal and oxygen surface ions. , Understanding the interplay between proton-coupled defects (i.e., electronic defects due to adsorbed H) − and PCET thermochemistry has broad implications for metal oxide catalysis and electrocatalysis.…”

Polaron in TiO2 from First‐Principles: A Review

“…Generation of a bias initial guess wave function in such a way is a helpful method to study a polaron at a specific site on the lattice. [ 55 ] Deskins and Dupuis showed that both rutile and anatase can form electron polarons and reduce the oxidation state of Ti +4 to Ti +3 at the polaron trapping site. [ 52 ] The formed electron polaron can then migrate to a neighboring Ti +4 ion via a hopping mechanism.…”