We present a systematic study of the electronic structure of Al-based
Hume-Rothery alloys containing transition elements performed with the
use of the linear muffin-tin orbital in atomic-sphere approximation me
thod. Our analysis focuses on the formation of the pseudogap at the Fe
rmi level leading to the stability of materials containing transition-
metal elements in small concentration. From the self-consistent calcul
ated density of states, we observe a strong deviation from the two cla
ssical limits: (a) the Friedel-Anderson virtual bond state's model and
(b) the nearly-free-electron diffraction by some Bragg planes in the
usual Hume-Rothery picture of simple metal alloys. Transition-metal at
oms have a crucial role on electronic structure via the combined effec
t of the sp-d hybridization and of a strong interaction between the Fe
rmi surface and a predominant Brillouin zone.