Recent work by Hilton, March & Curtis (1967) has shown how the Bloch density matrix may be calculated for an attractive scattering centre in a Fermi gas which is strong enough to lead to bound states. Using this pseudoatom description, and expressing the zero order approximation of independent pseudoatoms by writing the total partition function as a product of the single-centre functions, we develop a systematic procedure for calculating energy band structures. The convergence of the method depends on the magnitude of the overlaps of the effective potential matrix U introduced by Hilton, March & Curtis, for pseudoatoms on adjacent sites. To illustrate the method, calculation of the partition function of metallic Be is carried out from the earlier one-centre results for a charge Z = 4 in a Fermi gas. A preliminary estimate of the density of states in Be is reported, from this partition function.