Hash-matching-based local density matrix reuse method for efficient <i>ab initio</i> electronic structure construction in large-scale complex systems

Abstract

First-principles electronic structure calculations for large-scale material systems with defects or dopants remain a major computational bottleneck in atomistic simulations. Here, we propose a target-driven, non-learning-based method termed HaMLR (Hash-Matching-based Local density-matrix Reuse) to efficiently construct the density matrix of periodic atomic structures containing local defects or dopants. Leveraging the nearsightedness principle of electronic matter, the method systematically scans all atoms in the target system to extract local substructures within a defined nearsightedness radius, thereby covering the full sample space of local environments. Each substructure is encoded based on its geometric and chemical features, hashed, and deduplicated. Distinct substructures are then evaluated using self-consistent density functional theory (DFT) calculations to obtain the density-matrix blocks between the central atom and its neighbors within the cutoff radius. During reconstruction, the full-system density matrix is assembled by matching local environments via hash values and reusing the precomputed local density blocks—thereby avoiding full-scale DFT calculations. Unlike machine learning-based approaches, HaMLR does not require model training, offering improved physical consistency and computational efficiency. Validation on defective graphene, MoS2, and doped silicon demonstrates that HaMLR achieves high accuracy while significantly accelerating density-matrix construction, providing an efficient and robust alternative for large-scale electronic structure modeling.