Excitonic correlations in the intermetallic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">VAl</mml:mi></mml:math>

The intermetallic compound ${\mathrm{Fe}}_{2}\mathrm{VAl}$ looks nonmetallic in transport and strongly metallic in thermodynamic and photoemission data. It has in its band structure a highly differentiated set of valence and conduction bands leading to a semimetallic system with a very low density of carriers. 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 structure are shown to be important, reducing the carrier density by a factor of 3. Spin-orbit coupling results in a redistribution of the holes among pockets at the Brillouin zone center. Doping of this nonmagnetic compound by 0.5 electrons per cell in a virtual crystal fashion results in a moment of $0.5{\ensuremath{\mu}}_{B}$ and destroys the pseudogap. We assess the tendencies toward the formation of an excitonic condensate and toward an excitonic Wigner crystal and find both to be unlikely. We propose a model in which the observed properties result from excitonic correlations arising from two interpenetrating lattices of distinctive electrons ${(e}_{g}$ on V) and holes ${(t}_{2g}$ on Fe) of low density (one carrier of each sign per 350 formula units).