Modified Single Iteration Synchronous-Transit Approach to Bound Diffusion Barriers for Solid-State Reactions.

Herein, we detail an approach to accelerate the computational screening of materials for properties dictated by the kinetics of solid-state diffusion through reliably and rapidly identifying upper and lower bounds to the transition state (TS) energy through our proposed modified single iteration synchronous-transit (MSIST) approach. While this sacrifices providing detailed information of the explicit TS structure, it requires only 30% of the force evaluations of a full nudged elastic band (NEB) TS search and reduces the computational demand to compute estimated diffusion barriers by ∼70% on average. In all 53 cases in which we explicitly compared our results to those of an NEB calculation, the upper and lower bounds identified using this approach bracketed the TS energy calculated with explicit NEB calculations. We use the applications of diffusion of Na+ in potential sodium-ion battery electrodes and oxygen vacancy diffusion in solid-oxide fuel cell electrodes and redox mediators for solar thermochemical hydrogen production to demonstrate the power of MSIST for analyzing the kinetics of bulk diffusion. For Na+ diffusion through 13 proposed electrode materials in which the average diffusion barrier was 0.28 eV, the average difference between the upper and lower bounds was 0.08 eV. An iterative application of this approach to the three materials with the largest difference between their upper and lower bounds further narrowed the average range of the bounded TS energies to 0.04 eV while still requiring fewer force evaluations than an NEB TS calculation. When applied in a high-throughput manner to study 514 diffusion pathways in 97 different materials, the average difference between the upper and lower bounds was 0.33 eV and the average barrier, as calculated by the average of all upper and lower bounds, was ∼1.7 eV. Because the MSIST approach produces explicit errors, i.e., the difference between the upper and lower bounds energies, even predicted barrier ranges with large errors can be reliably modeled with weighted regression techniques. MSIST enables the analysis of the kinetics of solid-state diffusion across larger sets of materials and can thus efficiently provide data to train statistically learned models of diffusion and to develop physical insights into the diffusion process.