  Systematic benchmark calculations for elemental bulks are presented to
validate the accuracy of density functional theory for superconductors. We
developed a method to treat the spin-orbit interaction (SOI) together with the
spin fluctuation (SF) and examine their effect on the superconducting
transition temperature. We found the following results from the benchmark
calculations: (1) The calculations, including SOI and SF, reproduce the
experimental 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 reduction
is too weak to reproduce the $T_c$s of Zn and Cd. (4) We reproduced the absence
of superconductivity for alkaline (earth) and noble metals. These calculations
confirm that our method can be applied to a wide range of materials and implies
a direction for the further improvement of the methodology.
