Discrete Topological Routing of Lithium-Ion Pathways in Solid Electrolytes: A Gradient-Free Graph-Based Approach

Identifying lithium-ion migration pathways in solid electrolytes typically relies on the nudged elastic band (NEB) method or molecular dynamics (MD) simulations. These methods require gradient optimization on continuous potential energy surfaces or long-time sampling, causing computational costs to escalate with unit cell complexity. Building upon the Daopological Structural Annealing (DSA) paradigm, this paper proposes a discrete topological routing method that requires neither gradients nor differentiability. We abstract the crystal lattice into a 3D grid graph, mapping framework atoms to obstacle nodes and accessible voids to free nodes, thereby transforming channel search into a graph connectivity optimization problem. The search dynamics are driven by statistical physics annealing over three topological perturbation operators—Local Permutation, Segment Inversion, and Spatial Mutation—using a Hamiltonian composed of path length and steric hindrance. We validated the method on the Li7P3S11 structure from the OBELiX dataset, constructing a 20 × 20 × 20 grid. Comparative experiments demonstrate that, compared to traditional breadth-first search (BFS), our method not only shortens the total path length by 1.06 Å but also increases the minimum distance to framework atoms by 0.09 Å, effectively avoiding high-barrier regions and generating physically wider connected channels.