Ab initio calculation of the superconducting transition temperature

The superconducting transition temperature is calculated for a series of representative metals from a selfconsistent LMTO-bandstructure calculation. We carefully avoid any uncontrolled approximations apart from the use of a local exchange-correlation potential and the rigid-ion approximation for the electron-phonon interaction, Our results for V, Nb, Ta, Mo, W, Pd, Pt, Pb clearly indicate that these popular approximations are incapable of reproducing the observed transition temperatures.