The Hume-Rothery matching rule 2k(F)=K-hktl has been theoretically investigated by performing the LMTO-ASA (Linear Muffin-Tin Orbital-Atomic Sphere Approximation) band calculations for the three electron compounds: the gamma-phase Cu5Zn8 compound or gamma-brass, the nearly-free-electron-like Frank-Kasper-type Al30Mg40Zn30 1/1-1/1-1/1 approximant and the Mackay-Icosahedral-type Al68Cu7Ru17Si8 1/1-1/1-1/1 approximant. The zone planes responsible for the formation of the pseudogap across the Fermi level are identified. In the free-electron-like Al-Mg-Zn approximant, the Fermi surface-Brillouin zone interaction participating in the Hume-Rothery matching rule solely gives rise to a sizable pseudogap at the Fermi level. In the case of the gamma-brass and the Al-Cu-Ru-Si approximant, where d-states are involved in the middle of the valence band, we could demonstrate that the particular Fermi surface-Brillouin zone interactions are strongly coupled with the sp-d hybridization to produce a deep pseudogap across the Fermi level. (C) 2003 Elsevier Ltd. All rights reserved.