Quantum-Information Measure of Electron Localization

Understanding electron localization in molecules and materials plays a central role in electronic structure theory, and will increase in importance with the rise of data-driven approaches. The electron localization function (ELF) is widely used to visualize electron organization in molecules and materials, and it remains a central ingredient in modern density-functional approximations. Yet its formulation retains highly empirical elements. Here we introduce a quantum-information measure of electron localization derived from the concurrence of a correlated two-spin mixed state. This construction yields a genuine two-point localization indicator grounded in quantum-information theory, avoiding the heuristic normalization and chosen nonlinear remapping of the ELF. We show that atomic shells, covalent and ionic bonds, lone pairs, molecular dissociation, and charge-transfer processes are captured. The method is straightforward to evaluate numerically.