Lucia Reining - TDDFT.org

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Asymptotic long-range behaviorof the xc KernelΦ (v,k (v,k,c,k ,c,k +q +q ;G ;G =0) =0) q → q 0 0O (q (q))→constq→0F (n1n2)(n3n4) q→0(n1n2)(n3n4)( )ffxc ( ,G G' 0) q 02xc ( q ,G = G' = 0) → q 0 O 1 q 2
<strong>Reining</strong>, Olevano, Rubio, Onida (PRL 2002)
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How to describe………………
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What is a spectrum?
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hνWhat is a spectrum?
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hνWhat is a spectrum?
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…but also:Perturbation -- Respons
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Perturbation -- ResponseResponse =>
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Perturbation -- ResponseResponse =>
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V ind = (δV H /δρ + δV xc /δρ
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ρ ind = χ V extχ = χ 0 + χ 0 (
Page 22 and 23: 1b) TDDFT in practicei) Finite syst
Page 24 and 25: EELS : v is dominantOlevano and Rei
Page 26 and 27: Absorption: no long range in RPA.An
Page 28 and 29: So which potential in the “real w
Page 30 and 31: So which potential ?cv
Page 32 and 33: Koopman’s theorem(e.g. Hartee Foc
Page 34 and 35: Hartree :Hartree - Fock :Beyond :ρ
Page 36 and 37: From ∂ρ/∂tto:∂/∂t G =…
Page 38 and 39: Σ = i ∫GWΓW = v + ∫v P WP = -
Page 40 and 41: Σ = i ∫GWΓW = v + ∫v P WP = -
Page 42 and 43: E c -E v (minimum, eV)DFT-KSΣ=iGWE
Page 44 and 45: Γ = δΣ = i ∫GWΓW = v + ∫v P
Page 46 and 47: χ = P 0 + P 0 (v-W) χδV H /δρ
Page 48 and 49: χ = P 0 + P 0 (v-W) χδV H /δρ
Page 50 and 51: Absorption ?cv
Page 52 and 53: Absorption ?cVariation of potential
Page 54: (H el + H hole + H el-hole ) A λ =
Page 59 and 60: BSE and TDDFT: different worlds, sa
Page 67 and 68: TDLDA
Page 71: Comparison in“Transition” space
Page 76 and 77: Botti, Vast, Reining, Olevano, Andr
Page 78 and 79: •The lack of a long range term in
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Page 92 and 93: All of us:•Potentially efficient
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Lucia Reining - TDDFT.org

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