The resulting MAOs, χ are thus expressed in terms of the AO's, ω, as χ = ωC MAO . The MAOs are orthogonal, and typically localize onto atoms. The MAOs exactly span the space of the occupied orbitals, and can be used for population analysis among other things. Let us denote p as an MAO label for χ p , which is centered at r p = χ p |r|χ p . Using A, B as atom labels, and given that the density matrix in the MAO basis is