Generalizations of OPDOS, GPDOS, PDOS

As observed above, the basis functions in the above expressions may be primitive basis functions ('Slater type orbitals'), but of course the formulas are equally applicable for other types of MO expansions. In dos the user may select either the expansion in primitive basis functions ('BAS') or the expansion in SFOs (Symmetrized Fragment Orbitals) for the DOS analyses.

It is also possible in DOS to treat a set of basis functions simultaneously. For instance, the GPDOS for a set of basis functions μ₁, μ₂, ... is simply defined as the summation of the corresponding single-function GPDOS(E) values

N_μ-set(E) = ∑_μ∈μ-set ∑_i GP_i,μ L(E-ε_i)   (3.3.13)

In a similar fashion the OPDOS can be defined for two sets of basis functions μ₁, μ₂, ... and ν₁, ν₂, ... as

N_{μ-set,ν-set}(E) = ∑_μ∈μ-set ∑_ν∈ν-set ∑_i OP_i,μν L(E-ε_i)   (3.3.14)

and finally for the PDOS we get in similar fashion

N_μ-set(E) = ∑_μ∈μ-set ∑_i |⟨ χ_μ| φ_i ⟩|² L(E-ε_i)   (3.3.15)