Permutation-invariant collective variable to track and drive vacancy dynamics in simulations of solids

Abstract

Vacancy dynamics in oxides are vital for understanding redox reactions and resulting memristive effects or catalytic activity. We present a method to track and drive vacancies which we apply to metadynamics simulation of oxygen vacancies (V 2+ O ) in rutile, demonstrating its effectiveness. Using the density functional based tight binding method, it is possible to explore the free energy hyperplane of oxygen vacancies in TiO2. We show that the migration of V 2+O in TiO2 is governed by the jump with the highest degree of topological interconnection. Free energy profiles are consistent with minimum energy paths. PACS numbers: 61.72.jd, 66.30.Lw, 02.70.Ns Transition metal oxides exhibit a highly complex behavior, with strong coupling between electronic and ionic transport processes, making them highly interesting as electronic materials beyond their traditional use as dielectrics. The most prominent example of such effects is the memristive behavior 1 of TiO 2−x and many other substoichiometric oxides 2 . In titania, the memristive behavior is linked to the formation and dissolution of conducing filaments 1 or layers 3 of room-temperature metallic Ti n O 2n−1 Magnéli phases 4 in the insulating TiO 2 . These phases of titania are modifications of the rutile crystal structure in which oxygen vacancies (V O ) are ordered in slip-planes. In order to understand their formation and dissolution it is essential to understand the dynamics of oxygen vacancies aggregating and dispersing.Yet, the memristive effect is far from being the only interesting physics of metal oxides in which vacancy dynamics play a crucial role. Catalytic effects at oxide surfaces can rely on the presence and ability to replenish surface vacancies 5,6 or O ion transport through the catalyst 5,7 . To be efficient, the latter relies on vacancies and can in fact be mapped to a vacancy transport process in the reverse direction. Oxide based (photo)catalysis is regarded as one of the most promising fields of renewable energy conversion.These examples show that complex physical processes at the surface and in the bulk of reducible metal oxides require intimate understanding of the dynamical behavior of V O defects and the relevant driving forces. Many of these processes are rare events, i.e. their activation energy is larger than the average thermal energy at relevant conditions, which makes them inaccessible to unbiased molecular dynamics simulation. Techniques for rare event simulation8-11 rely on reaction coordinates describing the transition of interest. In most cases, the reaction coordinate is required to be continuous and at least piecewise differentiable with respect to the atomic positions r lat i . Achieving this for a vacancy coordinate r v is difficult, as vacancies are not directly simulated objects but an emergent property. In the strictest sense, the position of a vacancy cannot be continuous, as it is defined as an unoccupied lattice position. Yet, since a vacancy can change its position, albeit indirectly, a generalization of the vacanc...

How the aggregation of oxygen vacancies in rutile-basedTiO2−δphases causes memristive behavior

“…Even though our present study is static in nature, the very high migration barriers found in bulk rutile 42 , combined with the fact that TiO 2−δ films used in existing devices are grown in the amorphous state, suggest that the transition is not amorphous→rutile→Magnéli. We rather expect the vacancy agglomeration to occur in a lower density phase, either amorphous or anatase (the latter having been observed in situ 11 ).…”

Dcdftbmd: Divide‐and‐Conquer Density Functional Tight‐Binding Program for Huge‐System Quantum Mechanical Molecular Dynamics Simulations

“…The applications of DFTB‐based metadynamics are recently growing, yet their investigated system size has been less than a few hundreds of atoms. The combination with the DC method may be feasible to analyze large complex systems as demonstrated in simulation example section.…”

Rigorous pKa Estimation of Amine Species Using Density-Functional Tight-Binding-Based Metadynamics Simulations

“…In the present study, we have estimated the p K a values of amine species in solution using metadynamics simulations at the DFTB level. Although the combination of the DFTB method and the metadynamics technique has attracted recent interest for application in complex environments and yielded encouraging results, − evaluation of DFTB accuracy for various types of amine species needs to be addressed for prediction purpose. To this end, the calculated p K a values are compared with available experimental data for 34 amine species.…”