Using ab initio density functional theory for superconductors (SCDFT), we systematically study the quaternary borocarbides $R{M}_2{\mathrm{B}}_2\mathrm{C}$. Treating the retarded (frequency-dependent) interaction $W\left(\omega \right)$ within the random-phase approximation, we find good agreement with experiments for the calculated superconducting critical temperature $T_c$ in the nonmagnetic Ni- and Pd-based compounds. Replacing the density functional theory (DFT) bands with a one-shot $GW$-derived quasiparticle band structure in the SCDFT calculations further improves the agreement with experiment for several of the tested systems. We argue that the problem of accurately placing the $f$ bands within DFT, and possibly the lack of an explicit magnetic pair-breaking mechanism, explains the difficulties of SCDFT in reproducing $T_c$ in members of the magnetic $R{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$ series ($R$ rare-earth elements with partially filled $4f$ states). While the calculated $T_c$ is overestimated, SCDFT qualitatively captures the experimentally observed trend along the rare-earth series, which indicates that the electron-phonon couplings and dynamically screened interactions have a significant effect on $T_c$.

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• Superconductivity
• Density functional theory
• Electron-correlation calculations
• First-principles calculations
• Methods in superconductivity
• Random phase approximation