# IMP LE M EN TA Ç Ã O N O C O N TE X T O D A

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(1) (1) (1) (1) E = hΨ | ˆ H |Ψ i < hΨ | ˆ H |Ψ i,112 2 .@AL/ E = hΨ 1 | ˆ T + ˆ V ee + ˆ V ext,1 |Ψ 1 i < hΨ 2 | ˆ T + ˆ V ee + ˆ V ext,1 |Ψ 2 i,.@AM/ #8 C%# Ψ 1 # Ψ 2 7<) *7 H%'DN#7 (# )'(* () #7,*() H%'(*8#',*- *77)5&6 V V 6= Ψ E < E d r n + 2 (r) V ext,1 (r) − ˆ V ext,2 (r) . kσ kσ s KS,σ kσ '()*-+./012X N σ 12 v xc,σ [n](r) = |ψ kσ (r)| [u xc,kσ [n](r) + f kσ v ¯ xc,kσ [n] − ¯ u xc,kσ [n]]2n (r) σ k ∗ ∗ ∗ −ψ (r)ˆ t Ψ (r) + Ψ (r)ˆ t ψ (r) + ψ (r)v (r)Ψ (r) kσ s s kσ kσ KS,σ kσ kσ kσ + c.c.

### IMPLEMENTAđấO NO CONTEXTO DA FORMULAđấO KOHN-SHAM DA TEORIA DO FUNCIONAL DA DENSIDADE

(1) (1) (1) (1) E = hΨ | ˆ H |Ψ i < hΨ | ˆ H |Ψ i,112 2 .@AL/ E = hΨ 1 | ˆ T + ˆ V ee + ˆ V ext,1 |Ψ 1 i < hΨ 2 | ˆ T + ˆ V ee + ˆ V ext,1 |Ψ 2 i,.@AM/ #8 C%# Ψ 1 # Ψ 2 7<) *7 H%'DN#7 (# )'(* () #7,*() H%'(*8#',*- *77)5&6 V V 6= Ψ E < E d r n + 2 (r) V ext,1 (r) − ˆ V ext,2 (r) . kσ kσ s KS,σ kσ '()*-+./012X N σ 12 v xc,σ [n](r) = |ψ kσ (r)| [u xc,kσ [n](r) + f kσ v ¯ xc,kσ [n] − ¯ u xc,kσ [n]]2n (r) σ k ∗ ∗ ∗ −ψ (r)ˆ t Ψ (r) + Ψ (r)ˆ t ψ (r) + ψ (r)v (r)Ψ (r) kσ s s kσ kσ KS,σ kσ kσ kσ + c.c.