TDDFT in Chemistry and Biochemistry III - TDDFT.org

Kohn–Sham Orbital ResponseGround state Kohn–Sham determinant∣ ∣∣∣∣∣∣∣ ϕ 1 (r 1 , σ 1 ) ϕ 2 (r 1 , σ 1 ) . . . ϕ n (r 1 , σ 1 )Φ KS (r 1 , σ 1 , . . . , r n , σ n ) = √ 1ϕ 1 (r 2 , σ 2 ) ϕ 2 (r 2 , σ 2 ) . . . ϕ n (r 2 , σ 2 )n! . . . . . . . . . . . .ϕ 1 (r n , σ n ) ϕ 2 (r n , σ n ) . . . ϕ n (r n , σ n ) ∣Static (ground-state) Kohn–Sham orbitalsH (0),KS ϕ i (r, σ) = ε i ϕ i (r, σ)ϕ i (r, σ) i = 1, . . . , N occ Occupied orbitalsϕ a (r, σ) a = 1, . . . , N virt Virtual orbitalsϕ p (r, σ) a = 1, . . . , N General orbitalsDmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 5 / 22