Synergy between Charge Transfer and Spatial Descriptors in Determining the Band Gap of hP4-Na: An Interpretable Machine Learning Approach.

Electrides are a class of materials whose highly localized electrons in the lattice interstices exhibit anion-like behavior, known as interstitial quasi-atoms (ISQs). Nonmetallic electrides are promising for extreme-environment optical and sensing applications due to their pressure-retained band gaps and tunable electronic structures, yet the microscopic mechanisms governing their band gap remain unclear. Using the high-pressure phase hP4-Na, this study reveals these mechanisms through first-principles calculations under pressure and strain, combined with machine learning. Interpretability analysis identifies charge transfer (QNa1) and electron spatial distribution (VISQ/Cell) as dominant factors modulating the band gap. Through symbolic regression, we derive a concise analytical formula based solely on five electronic-structure descriptors, achieving excellent predictive accuracy (R2 > 0.98) against first-principles results. This directly confirms the electronic structure as the physical origin of the band gap in hP4-Na. Unlike previous studies focused on electron localization function, we show that VISQ/Cell is a key descriptor linking seemingly disparate properties like insulating behavior and superconductivity. Our study provides a microscopic understanding and a quantitative predictive framework for hP4-Na's electronic behavior under complex stress, establishing a foundation for rational design of high-pressure electrides.