Lucia Reining - TDDFT.org

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All of us:•Potentially efficient 2-point simulation of BSE results•Inspired by TDDFT•Is it TDDFT? (We have still QP energies)χ= χ 0QP+ χ 0QP(v+f xcmb) χχ= χ 0KS+ χ 0KS(v+f xc ) χ f xc = f xcmb+ (χ 0QP) -1 -(χ 0KS) -1
ConclusionWe can get DF quantities from MBPT (well known)The aim is to simplify our life:MBPT is more “understandable”DFT is more “efficient”.The difficulty: get the DF answer without solving the wholemany-body problem first!In the case of the BSE – TDDFT this has worked out fine.
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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 =…
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Σ = i ∫GWΓW = v + ∫v P WP = -
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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
Page 84 and 85: BSE and TDDFT:”Mapping theory”T
Page 86 and 87: Silicon: Optical AbsorptionF. Sotti
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Lucia Reining - TDDFT.org

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