  The effect on the electronic structure of an indirect Mn-Mn interaction
mediated by the valence states and the sp-d hybridisation is presented. In
Al(rich)-Mn phases related to quasicrystals (Al12Mn, o-Al6Mn, alpha-Al9Mn2Si),
this indirect interaction creates a Hume-Rothery pseudogap in the density of
states together with a minimisation of the band energy. It is shown that Mn-Mn
interaction up to distances around 1.0-2.0 nm plays an essential role in
stabilizing related quasicrystal structures.
