The overlap of two Slater determinants can be evaluated by computing the determinant of the orbital overlap matrix. Let {|p⟩ , p = 1, . . . , N } and {|q ′ ⟩ , q = 1, . . . , N } be two arbitrary sets of orbitals (not necessarily orthonormal). Following Refs. 29,30, the overlap of the two determinants is