An efficient algorithm for finding the minimum energy path for cation migration in ionic materials.

Ziqin Rong,Daniil Kitchaev,Wenxuan Huang,Gerbrand Ceder,Pieremanuele Canepa

doi:10.1063/1.4960790

Ziqin Rong, Daniil Kitchaev + Show 3 more

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https://doi.org/10.1063/1.4960790

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Abstract

The Nudged Elastic Band (NEB) is an established method for finding minimum-energy paths and energy barriers of ion migration in materials, but has been hampered in its general application by its significant computational expense when coupled with density functional theory (DFT) calculations. Typically, an NEB calculation is initialized from a linear interpolation of successive intermediate structures (also known as images) between known initial and final states. However, the linear interpolation introduces two problems: (1) slow convergence of the calculation, particularly in cases where the final path exhibits notable curvature; (2) divergence of the NEB calculations if any intermediate image comes too close to a non-diffusing species, causing instabilities in the ensuing calculation. In this work, we propose a new scheme to accelerate NEB calculations through an improved path initialization and associated energy estimation workflow. We demonstrate that for cation migration in an ionic framework, initializing the diffusion path as the minimum energy path through a static potential built upon the DFT charge density reproduces the true NEB path within a 0.2 Å deviation and yields up to a 25% improvement in typical NEB runtimes. Furthermore, we find that the locally relaxed energy barrier derived from this initialization yields a good approximation of the NEB barrier, with errors within 20 meV of the true NEB value, while reducing computational expense by up to a factor of 5. Finally, and of critical importance for the automation of migration path calculations in high-throughput studies, we find that the new approach significantly enhances the stability of the calculation by avoiding unphysical image initialization. Our algorithm promises to enable efficient calculations of diffusion pathways, resolving a long-standing obstacle to the computational screening of intercalation compounds for Li-ion and multivalent batteries.

Highlights

The nudged elastic band (NEB) method is an established technique for finding the minimum energy path (MEP) between the given initial and final states of a transition.1,2 This method has been used in conjunction with Density Functional Theory (DFT)3–6 and empirical potentials7–9 for studying ion and molecule diffusion in a variety of systems such as semiconductors, metals, and organic molecules
ApproxNEB is discussed in detail in the section titled “Methods.” We show that ApproxNEB is able to predict migration barriers within an error of ∼20 meV from those obtained with traditional Nudged Elastic Band (NEB) calculations, while reducing the central processing unit (CPU) time by up to a factor of 5
As we expect the PathFinder and ApproxNEB methods to yield improved performance relative to standard NEB in cases where the migration paths deviate substantially from the straight-line paths, we report the curvature of the mean energy path (MEP) as obtained by the NEB calculations

Summary

Introduction

The nudged elastic band (NEB) method is an established technique for finding the minimum energy path (MEP) between the given initial and final states of a transition. This method has been used in conjunction with Density Functional Theory (DFT) and empirical potentials for studying ion and molecule diffusion in a variety of systems such as semiconductors, metals, and organic molecules. The nudged elastic band (NEB) method is an established technique for finding the minimum energy path (MEP) between the given initial and final states of a transition.. The nudged elastic band (NEB) method is an established technique for finding the minimum energy path (MEP) between the given initial and final states of a transition.1,2 This method has been used in conjunction with Density Functional Theory (DFT) and empirical potentials for studying ion and molecule diffusion in a variety of systems such as semiconductors, metals, and organic molecules. Henkelman et al proposed the climbing image method and the improved tangent estimate, which are available as part of the open-source VTST [Vienna Ab Initio Simulation Package (VASP) Transition State Tools] code. Maragakis et al. presented the adaptive nudged elastic band method, where NEBs are iteratively calculated to move the initial and final states closer to the saddle point.

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Conclusion