TDDFT in Chemistry and Biochemistry III - TDDFT.org

Linear ResponseEquation of motion for linear response∑jb (A + B) iajb(X + Y ) ω jb − ω(X − Y )ω ia = −(P + Q) ia∑jb (A − B) iajb(X − Y ) ω jb − ω(X + Y )ω ia = −(P − Q) iaOrbital rotation Hessians(A + B) iajb = (ε a − ε i )δ ij δ ab + 2fiajb H xc+ 2fiajb − c x[fjaib H + f abij H ](A − B) iajb = (ε a − ε i )δ ij δ ab + c x [fjaib H − f abij H ]∫f iajb = d 3 r d 3 r ′ ϕ i (r, σ)ϕ a (r, σ)f (r, σ, r ′ , σ ′ )ϕ j (r, ′ σ ′ )ϕ b (r ′ , σ ′ )Right-hand side contains the external perturbation(P + Q) ia = 2 v (1)ia; (P − Q) ia = 0Dmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 11 / 22