We present a comprehensive ab initio study of superconductivity in NbTi, the workhorse for many applications. Despite being a “textbook” material, NbTi turns out to be a major challenge for computational superconductivity. In fact, anharmonic effects are crucial to obtain dynamically stable phonons for the ordered bcc phase, unstable at the harmonic level, and beyond-Morel-Anderson effects in the Coulomb interaction reduce the $T_c$ by more than 20%. Lattice disorder causes an additional large discrepancy in $T_c$ compared to experiment. Our results imply that a quantitative description of technologically relevant superconductors requires methodological developments beyond the current standards.

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• Electronic structure
• First-principles calculations
• Phonons
• Superconductivity
• Low-temperature superconductors
• Density functional theory
• Eliashberg theory