TDDFT in Chemistry and Biochemistry III - TDDFT.org

Kohn–Sham Orbital ResponseTime-dependent Kohn–Sham equationsi ∂ ∂t ϕ i(t, r, σ) = H KS ϕ i (t, r, σ)External potential includes periodic perturbationH KS = − 1 2 ∆ + v (0)ext (r) + ∑ σ ′∫dr ′ ρ(t, r ′ , σ ′ )|r − r ′ |+ v xc [ρ](t, r, σ)− c x v HF [γ](r, r ′ , t) + λ(v (1) (ω)e iωt + v (1) (−ω)e −iωt )Coupling parameter λ defines the strength of external perturbationv (1) (e. g., electric field strength E );c x is hybrid mixing parameter, interpolates between pure densityfunctionals (c x = 0) and Hartree–Fock (c x = 1, v xc [ρ] = 0).Dmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 6 / 22