here, q is a vector in the first Brillouin zone, G and G ′ are reciprocal-lattice vectors, ω is frequency, f is the state occupation, ψ nk and ε nk are the Kohn-Sham orbitals and energies from the DFT starting point, V is the volume of the simulation cell, and v and c count fully+partially occupied and fully+partially unoccupied bands, respectively.