In order to combine the advantages of tight-binding integral equation methods with basis sets not restricted to the lowest two orbital quantum numbers we extend the molecular fluid approach for the sp³ model of Lomba et al to arbitrarily high orbital quantum numbers. As an example, we present a single-superchain/effective-medium calculation of the electronic density of states for liquid silicon within a tight-binding approximation that includes, besides the 3s and 3p orbitals, also the 3d orbitals. Comparison with results from the sp³ model and different molecular dynamics results shows that within this sp³ d⁵ model very good agreement with plane-wave calculations is found whereas the sp³ model leads to unsatisfactory results.