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 () and electron spatial distribution () 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 ( > 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 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.