TDDFT in Chemistry and Biochemistry III - TDDFT.org

Higher-Order ResponseExpansion of nth-order response in static KS orbitalsγ (n) (ω, ω, . . . ,r, σ, r ′ , σ) = ∑ ia(X (n)iaϕ a(r, σ)ϕ i (r ′ , σ) + Y (n)iaσ ϕ i(r, σ)ϕ a (r ′ , σ)+ K (n)ijϕ i (r, σ)ϕ j (r ′ , σ) + K (n)ab ϕ a(r, σ)ϕ b (r ′ , σ))Occ-occ and virt-virt blocks K (n)ij, K (n)abare products of lower-orderresponse by virtue of idempotency constraint;Occ-virt and virt-occ blocks are determined from nth-order equationof motion,(Λ − nω∆)|X (n) , Y (n) 〉 = −|P (n) , Q (n) 〉 ;Right-hand sides |P (n) , Q (n) 〉 contain only lower-order response.Dmitrij Rappoport (Harvard U.) TDDFT in Chemistry III TDDFT Winter School 2010 14 / 22