Periodic Trends and a Physics-Based Multistage Search for High-T_c Hydride Superconductors

Hydrogen-rich materials under pressure are candidates for conventional phonon-mediated superconductivity, but first-principles electron--phonon-coupling (EPC) calculations are computationally demanding. We develop an interpretable multistage workflow for prioritizing binary hydride superconductors before full EPC calculations. Using controlled cubic X_mH_n prototypes at 200~GPa, we introduce the spectral moment A_1 as an intermediate measure of electron--phonon perturbation strength. In its linewidth-based construction, A_1 remains finite as harmonic phonons soften, allowing related structures with imaginary harmonic modes to be screened; it does not establish superconductivity or physical realizability for unstable structures. For dynamically stable cubic systems, A_1 correlates strongly with the H-1s density-of-states fraction at the Fermi level, α, a projected Fermi-surface descriptor, β, and atomic number density, ρ. These trends are summarized heuristically by A_1approx hαβρ, where h is framework- and pressure-dependent; the descriptor is used for ranking, not as a universal T_c predictor. We incorporate αβρ and enthalpic competitiveness into a three-stage evolutionary search comprising multiobjective structural screening, harmonic-phonon stability filtering, and coarse density-functional perturbation-theory (DFPT) EPC calculations. Application to more than 100,000 binary hydride structures at 50 and 200~GPa identifies candidates and prioritizes NaH_6 structural families. Higher-accuracy calculations show that Pm3m NaH_6 is dynamically stable down to 50~GPa and has a harmonic Allen--Dynes estimate of T_capprox230~K. The framework combines electronic descriptors with progressively more expensive stability and EPC calculations for scalable hydride exploration.