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 response expansionγ(t) =γ (0) + λ(γ (1) (ω)e iωt + γ (1) (−ω)e −iωt ) + λ 2 (γ (2) (ω, ω)e 2iωt+ γ (2) (ω, −ω) + γ (2) (−ω, ω) + γ (2) (−ω, −ω)e −2iωt ) + . . .Response equations[H (0),KS , γ (0) ] = 0 Static KS equations[H (1),KS , γ (0) ] + [H (0),KS , γ (1) ] = ωγ (1) L<strong>in</strong>ear response[H (2),KS , γ (0) ] + 2 [H (1),KS , γ (1) ]+[H (0),KS , γ (2) ] = 2ωγ (1)Quadratic responseDmitrij 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 8 / 22
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