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 FormulationDensity matrix of Kohn–Sham systemγ(t, r, σ, r ′ , σ ′ ) = ∑ i ϕ i(t, r, σ) ϕ ∗ i (t, r ′ , σ ′ )γ(t) rema<strong>in</strong>s idempotent for all t,γ 2 (t) = γ(t) ;Diagonal of γ(t) is time-dependent density,ρ(t, r, σ) = γ(t, r, σ, r, σ) ;Time evolution is given by one-particle Liouville equation,i ∂ ∂t γ(t) = [HKS , γ(t)] .F. Furche, J. Chem. Phys., 2001, 114, 5982.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 7 / 22