Lucia Reining - TDDFT.org

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BSE and TDDFT :”Mapping theory”TDDFT:χ = χ 0 + χ 0 (v+f xc ) χχ =X (X - χ 0 (v+f xc )X) -1 χ 0χ =X (X - χ 0 v X + Τ) -1 χ 0χ 0 with GW energiesT= Σ vc,v’c’ 1/(E c -E v -ω) |vc> > >
Advantages over BSE: Diago,inversion SumAdvantages of this approach:- interpolation,……- change order of operations no 4point- modelisation (long range etc)Reining et al, PRL 88, 066404 (2002); Sottile et al, PRL 91, 056402 (2003)Perturbation theory:- work with χ 0 f xc , not f xc- flexible: χ 0 XAdragna PhD thesis and PRB 68, 165108 (2003),Marini et al PRL 91, 256402 (2003) :X χ 0 )
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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 (
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1b) TDDFT in practicei) Finite syst
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EELS : v is dominantOlevano and Rei
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Absorption: no long range in RPA.An
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So which potential in the “real w
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So which potential ?cv
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Koopman’s theorem(e.g. Hartee Foc
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Hartree :Hartree - Fock :Beyond :ρ
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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 and 72: Comparison in“Transition” space
Page 73 and 74: Reining, Olevano, Rubio, Onida (PRL
Page 76 and 77: Botti, Vast, Reining, Olevano, Andr
Page 78 and 79: •The lack of a long range term in
Page 80 and 81: BSE and TDDFT: merge!TDDFT:χ = χ
Page 82 and 83: BSE and TDDFT: merge!TDDFT:χ = χ
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Lucia Reining - TDDFT.org

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