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Systematic benchmark calculations for elemental bulks are presented tovalidate the accuracy of density functional theory for superconductors. Wedeveloped a method to treat the spin-orbit interaction (SOI) together with thespin fluctuation (SF) and examine their effect on the superconductingtransition temperature. We found the following results from the benchmarkcalculations: (1) The calculations, including SOI and SF, reproduce theexperimental superconducting transition temperature ($T_c$) quantitatively. (2)The effect by SOI is small excepting a few elements such as Pb, Tl, and Re. (3)SF reduces $T_c$s, especially for the transition metals, while this reductionis too weak to reproduce the $T_c$s of Zn and Cd. (4) We reproduced the absenceof superconductivity for alkaline (earth) and noble metals. These calculationsconfirm that our method can be applied to a wide range of materials and impliesa direction for the further improvement of the methodology.

Benchmark of density functional theory for superconductors in elemental materials