The second generalization is to perform TDDFT/TDA calculations in the basis of embedding orbitals. The required occupied/virtual orbitals and their energies can be readily obtained by diagonalizing the Fock matrix in Eq. (11). The corresponding TDDFT/TDA excited states can then be solved for iteratively, where the main computationally intensive tasks are the evaluation of 2-electron repulsion integrals and exchange-correlation response kernel, 56 ∂ 2 f xc ∂ ξ ∂ ξ ′ , (where ξ and ξ ′ refer to alpha/beta electron densities and their gradients, ρ α , ρ β , ρ x α , ρ y α , ρ z α , ρ x β , ρ y β , ρ z β ) based on the ground-state electron density of the entire chromophore-solvent complex, as well as their contractions with the trial vectors. In general, the bath orbitals are expected to be localized on solvent molecules close to the impurity. In our pilot implementation of the eo-TDA method, however, such locality has not been utilized to enable an efficient numerical integration on the atomic grid.