Scalable cell filter nudged elastic band (CFNEB) for large-scale transition-path calculations

TL;DR

This work presents CFNEB, a scalable cell-filter nudged elastic band framework that enables transition-path calculations in systems up to $10^5$ atoms by coupling a deformation-based generalized coordinate transformation with adaptive image insertion. Implemented in both CPU (ASE) and GPU (GPUMD) pipelines, CFNEB achieves throughput on the order of $10^6$ atom$\cdot$steps s$^{-1}$, allowing NEB calculations with ~100 images. Applications to the $\beta$-$\lambda$ transition in Ti$_3$O$_5$ and the graphite-to-diamond transformation reveal that large cells can exhibit nucleation-like pathways and symmetry-breaking mechanisms that are not accessible in small systems, highlighting significant finite-size effects and the method’s potential for realistic solid-state transition-path exploration.

Abstract

The nudged elastic band (NEB) method is one of the most widely used techniques for determining minimum-energy reaction pathways and activation barriers between known initial and final states. However, conventional implementations face steep computational scaling with system size, which makes nucleation-type transitions in realistically large supercells practically inaccessible. In this work, we develop a scalable cell-filter nudged elastic band (CFNEB) framework that enables efficient transition-path calculations in systems containing up to $10^5$ atoms. The method combines a deformation-based cell filtering scheme, which treats lattice vectors as generalized coordinates while removing spurious rotational degrees of freedom, with an adaptive image insertion and deletion strategy that dynamically refines the reaction path. We implement CFNEB both within the ASE environment and in a fully GPU-accelerated version using the Graphics Processing Units Molecular Dynamics (GPUMD) engine, achieving throughput on the order of $10^6$ atom$\cdot$steps per second on consumer GPUs. We demonstrate the method on two representative systems: the layer-by-layer $β$-$λ$ transition in $Ti_3O_5$ and the nucleation-driven graphite-to-diamond transformation. These examples illustrate that CFNEB not only reproduces known concerted pathways but also captures spontaneous symmetry breaking toward nucleated mechanisms when the simulation cell is sufficiently large. Our results establish CFNEB as a practical route to exploring realistic transition mechanisms in large-scale solid-state systems.

Figures (3)

• Figure 1: The workflow diagram of CFNEB.
• Figure 2: The variable cell NEB pathway of Ti3O5 $\beta$-$\lambda$ phase transition. (a) the initial state of Ti3O5 $\beta$ phase. (b) The relative energy per formula with respect to the normalized coordinate. (c) the final state $\lambda$ phase. The atoms in blue color refer to the $\beta$ state and the ones in red refer to the $\lambda$ state. (d) is the front view of five intermediate states. (e) is the side view of five states and only the atoms sliced by the dash line rectangle in (c) are shown. II and IV are local minima. The large and small balls represent the Ti and O atoms and the colors are set by the normalized displacement magnitude of each atoms which represents the degree of location phase transition. The color legend is shown at the bottom.
• Figure 3: The transition path of graphite-to-CD transition under 40GPa. (a) the intermediate states of the transition process. II is the saddle point. (b) the energy path from graphite to CD. (c) the shape of nucleus extracted from state II. The atoms is colored by identify diamond structure modifier in OVITO.maras_global_2016