A Geometric–Delocalization Model for Material Classification in the M–D Parameter Space

Abstract

This study introduces a two-parameter geometric–electronic framework for classifying materials based on structural regularity and electronic delocalization. The model uses two normalized indices: (1) M_geom, capturing coordination environment, crystallographic symmetry, and density; and (2) D_delok, measuring electronic delocalization through hybridization character, π-orbital participation, dimensionality, and band-gap behavior. Using Materials Project structures for seven representative materials —including metallic alloys, carbon allotropes, silicates, and actinide compounds—we demonstrate that the proposed model consistently separates metals, semimetals, and insulators in the M–D phase space. The approach provides a compact, data-consistent alternative to traditional organic–inorganic classification schemes and suggests a more universal structure–property mapping framework. Language editing assistance was provided using an AI-based tool