TDDFT in Chemistry and Biochemistry III - TDDFT.org
TDDFT in Chemistry and Biochemistry III - TDDFT.org
TDDFT in Chemistry and Biochemistry III - TDDFT.org
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Density Matrix FormulationExpansion of l<strong>in</strong>ear response <strong>in</strong> static KS orbitalsγ (1) (ω, r, σ, r ′ , σ) = ∑ ia (X ωia ϕ a (r, σ)ϕ i (r ′ , σ) + Y ωiaσϕ i (r, σ)ϕ a (r ′ , σ)) ,equivalent to expansion of time-dependent KS orbitalsϕ i (t, r, σ) = ϕ i (r, σ) + λ ∑ a (X ωia e iωt + Y ωia e −iωt ) ϕ a (r, σ) .Hilbert space notationX ωia , Y ωia → |X ω , Y ω 〉 ∈ L = L occ ⊗ L virt ⊕ L occ ⊗ L virtL occ , L virt – Hilbert spaces of occupied <strong>and</strong> virtual KS orbitals(L ⊂ L – one-particle Liouville space)Dmitrij Rappoport (Harvard U.) <strong>TDDFT</strong> <strong>in</strong> <strong>Chemistry</strong> <strong>III</strong> <strong>TDDFT</strong> W<strong>in</strong>ter School 2010 10 / 22
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