(474f) Improved Saddle Point Convergence with Dynamic and Selective Optimizations of Nudged Elastic Bands

The nudged elastic band (NEB)^1,2 method is one of the most widely used algorithms for first-order saddle point calculations. This method samples the high-energy region between two local minima on the potential energy surface (PES) with interior states connected by Hookean springs. In the nudging force projection, only parallel spring forces and PES-derived forces perpendicular to the reaction pathway are included.

Part of the allure of the NEB method is that it parallelizes well; computational resources can be easily distributed between states. The efficiency of the parallelization scheme is dependent upon the uniformity of the convergence of states. However, most bands are highly non-uniform; states in close vicinity to local minima tend to converge faster than those in high-energy regions of the PES. This non-uniformity is particularly severe for electronically grand canonical schemes, where the number of electrons change in the course of the reaction to keep the work function (applied potential) constant. Such semi-grand canonical methods are necessary when calculating electrochemical reaction barriers, since surface charge depletion can significantly alter the work function of the electrode in finite-sized unit cells^3,4. Here, the iterative work function scheme requires more calculations in regions close to the saddle point, since most of the charge transfer occurs at or around the saddle point⁵. This could make parallel NEB schemes unsuitable, since a large fraction of computational resources will idle while a small fraction of resources is used to calculate states at the saddle point.

We introduce a serial NEB method that dynamically and selectively optimizes states along the reaction pathway. States are dynamically optimized with scaled convergence criteria to focus on the region of interest, i.e., the saddle point. We show that this method can significantly reduce the number of force calls—up to 50-75%—for both non-electrochemical and electrochemical reaction barriers without loss of resolution at the saddle point.

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