Researchers introduce a practical screening method to find hydrogen-rich materials that might superconduct under very high pressure. Calculating superconducting temperatures from first principles is slow because it requires detailed electron–phonon coupling (EPC) calculations. The team sidesteps most of that cost by defining an intermediate quantity, called the spectral moment A1, and by using a three-stage search that narrows candidates before doing expensive EPC work.

The paper studies many binary hydrides at 50 and 200 gigapascals (GPa). EPC means how electrons interact with atomic vibrations (phonons) and is central to “conventional” superconductivity. The usual EPC measure, called lambda, blows up or becomes ill-defined when some vibrational modes are very soft or imaginary. A1 is built from the same spectral data but in a form that stays finite even when harmonic phonons soften. That makes A1 a usable screening number for structures that would otherwise be discarded early in searches.

For dynamically stable cubic hydrides at 200 GPa, A1 correlates strongly with three simple properties: the fraction of electronic states at the Fermi level coming from hydrogen 1s orbitals (α), a projected Fermi-surface descriptor (β) that captures how electronic states line up for scattering, and the atomic number density (ρ). The authors summarize the trend roughly as A1 ≈ h·α·β·ρ, where h depends on the structural framework and pressure. They stress that this relation is a ranking tool for related cubic hydrides, not a universal formula for the superconducting transition temperature (Tc).

These ideas are folded into a three-stage evolutionary workflow. First, multiobjective structure searches use the αβρ descriptor and enthalpy (energetic competitiveness) to find promising compositions and shapes. Second, harmonic-phonon calculations filter out clearly unstable structures. Third, a smaller set of candidates gets coarse density-functional perturbation theory (DFPT) EPC calculations for direct Tc estimates. Applied to over 100,000 binary hydride structures, the workflow flagged several families worth detailed study and highlighted sodium-rich NaH6 structures.