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 FormulationCoupl<strong>in</strong>g due to Hartree <strong>and</strong> xc <strong>in</strong>teractionsH (1),KS = ∑ σ ′Hartree kernel∫( )dr ′ f H (r, r ′ ) + f xc (ω, r, σ, r ′ , σ ′ ) ρ (1) (r ′ , σ ′ )− c x v HF [γ (1) ] + v (1)f H (r, r ′ ) =xc Kernel <strong>in</strong> adiabatic approximation1|r − r ′ | ;f xc (ω, r, σ, r ′ , σ ′ ) = f xc (0, r, σ, r ′ , σ ′ ) =Non-local (Hartree–Fock) exchangev HF [γ](r, r ′ ) = γ(r, r ′ )|r − r ′ | .δ 2 E xcδρ(r) δρ(r ′ ) ;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 9 / 22
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