Periodic Electron Density Overlap Descriptors for Crystal Band Gap Prediction

A valence electron density encodes spatial electronic structure that complements an atomic position representation. We examine whether a periodic adaptation of the smooth overlap of electron densities (SOED) improves the modeling of density functional theory band gaps in inorganic crystals. Atom-centered neighborhoods are sampled directly from periodic valence density grids, expanded in radial functions and spherical harmonics, and summarized by rotationally invariant power spectra. A scaffold density constructed from atomic positions supplies a SOAP-inspired control with the same overlap machinery. We evaluate 40490 structures from MP-20-Charge after filtering undefined Pauling electronegativities and repartitioning by reduced formula. A validation-selected electronic SOED ensemble attains a held-out RMSE of 0.6179 eV, compared with 0.6595 eV for a local chemistry-matched SOAP control. The reduction of 0.0415 eV has a 95% formula-cluster bootstrap interval of 0.0255 to 0.0578 eV. Five formula-group splits, including the primary split, give mean errors of 0.6315 and 0.6581 eV, respectively. These results support periodic density overlap descriptors for modeling computed band gaps when valence charge densities are available.