After the Hamiltonian matrix H G ′ , G k together with the overlap matrix S G ′ , G k = ⟨ ϕ ϕ k , G ′ | ϕ ϕ k , G ⟩ is set up, the Kohn-Sham orbitals are obtained as eigenfunctions from the algebraic generalized dense Hermitian eigenvalue problem