Lucia Reining - TDDFT.org

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1b) <strong>TDDFT</strong> in practicei) Finite system: 1 electron V xc = -V H(T+ V ext + V H –V H ) ϕ = ε ϕf xc = -vχ = χ 0χ = χ 0 + χ 0 (v+f xc ) χ“χ 0 is fine….” (for χand χ)more electrons: screening of f xcv becomes dominant“RPA is fine….” (for χand χ)“TDLDA is fine….” (for χand χ)
) Infinite system: long range important!RPA: α=1RPAABS: χ = χ 0 + χ 0 (v- v 0 ) χEELS: χ = χ 0 + χ 0 (v) χGeneral: v-αv 0Sottile et al (2002)EELS: α=0
Page 2: How to describe………………
Page 5 and 6: What is a spectrum?
Page 7 and 8: hνWhat is a spectrum?
Page 9: hνWhat is a spectrum?
Page 12 and 13: …but also:Perturbation -- Respons
Page 14 and 15: Perturbation -- ResponseResponse =>
Page 16 and 17: Perturbation -- ResponseResponse =>
Page 18 and 19: V ind = (δV H /δρ + δV xc /δρ
Page 20 and 21: ρ ind = χ V extχ = χ 0 + χ 0 (
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 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
Page 90 and 91:
BSE and TDDFT :”Mapping theory”
Page 92 and 93:
All of us:•Potentially efficient
Page 94:
How to describe exchange and correl
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Lucia Reining - TDDFT.org

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