These include the Coulomb interaction v(r, r ′ ) and the quasiparticle energies ϵ GW i , obtained from the preceding GW cycle, which also yields the static screened Coulomb interaction W . The indices i, j, k, . . . refer to occupied orbitals, whereas a, b, c, . . . are used for virtual orbitals. Equation ( ) with ( ) is often referred to as a "Casida-like" equation, due to its similarity to the Casida equation known from TD-DFT. The solution of the Casida-like equation yields the transition energies Ω m and the transition density matrix (TDM). The latter can be obtained in the first order in complete analogy to the TD-DFT case as follows 55