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.