The intermetallic compound Fe2VAl looks nonmetallic in transport and s
trongly metallic in thermodynamic and photoemission data. It has in it
s band structure a highly differentiated set of valence and conduction
bands leading to a semimetallic system with a very low density of car
riers. The pseudogap itself is sensitive to the presence of Al states,
but the resulting carriers have only minor Al character. The effects
of generalized gradient corrections to the local density band structur
e are shown to be important, reducing the carrier density by a factor
of 3. Spin-orbit coupling results in a redistribution of the holes amo
ng pockets at the Brillouin zone center. Doping of this nonmagnetic co
mpound by 0.5 electrons per cell in a virtual crystal fashion results
in a moment of 0.5 mu(B) and destroys the pseudogap. We assess the ten
dencies toward the formation of an excitonic condensate and toward an
excitonic Wigner crystal and find both to be unlikely. We propose a mo
del in which the observed properties result from excitonic correlation
s arising from two interpenetrating lattices of distinctive electrons
(e(g) on V) and holes (t(2g) on Fe) of low density (one carrier of eac
h sign per 350 formula units).