First-principles studies of superconductivity often neglect anharmonic effects (AHE), despite their crucial role in achieving quantitative accuracy in many materials. To bridge this gap, we introduce a general computational approach, termed anharmonic superconducting density functional theory (ah-SCDFT) which systematically incorporates anharmonic corrections into standard SCDFT. This approach allows for high-fidelity predictions of superconducting properties with only a modest increase in computational cost for a limited number of superconducting calculation convergence steps. We demonstrate the effectiveness and reliability of ah-SCDFT by applying it to the prototypical superconductor ${\mathrm{MgB}}_2$, accurately reproducing its superconducting behavior under both ambient conditions and applied pressure in excellent agreement with experiment. Our results establish ah-SCDFT as a powerful, efficient, and broadly applicable approach for quantitatively reliable studies of superconductivity and a promising tool for the prediction of new superconducting materials.

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• Superconductivity
• First-principles calculations
• Methods in superconductivity