2 DFT and the Full-Potential Local-Orbital Approach 11 on Fig.2.2.A free minimum of a function of on and a minimum under the constraint 6m>0. 72 ,n=∑nk《o-2l〉+ +"】 rd(rs)o(r's) (2.19) T-T This completes the brief introduction to the state of the art of density func- tional theory of the ground state energy. Just to mention one other realm of possible density functionals,quasipar- ticle excitations are obtained from the coherent part(pole term)of the single particle Green's function (2.3-2.5) Gr,ro)=∑aC+cr,r, (2.20) 1 w-Ek /r[,-(-+uo)+m) +(r,r';ex)x.(r)=x.(r)ek.(2.21) Here,in the inhomogeneous situation of a solid,the self-energy is among other dependencies a functional of the density.This forms the shaky ground (with rather solid boulders placed here and there on it,see for instance also 2.4)for interpreting a KS band structure as a quasi-particle spectrum. In principle from the full ss(r,r;w)the total energy might also be ob- tained. 2.2 Full-Potential Local-Orbital Band Structure Scheme (FPLO) This chapter deals with task (iii)mentioned in the introduction to Chap.1. A highly accurate and very effective tool to solve the KS equations self consistently is sketched.The basic ideas are described in 2.6,see http://www.ifw-dresden.de/agtheo/FPLO/for actual details of the imple- mentation.2 DFT and the Full-Potential Local-Orbital Approach 11 ✏✏ δn ✏ Fig. 2.2. A free minimum of a function of δn and a minimum under the constraint δn > 0. k[φk, nk] = k nkφk| − ∇2 2 |φk
+ + kk
nknk
2  ss
 d3rd3r |φk(rs)| 2|φk
(r s )| 2 |r − r | . (2.19) This completes the brief introduction to the state of the art of density func￾tional theory of the ground state energy. Just to mention one other realm of possible density functionals, quasipar￾ticle excitations are obtained from the coherent part (pole term) of the single particle Green’s function ([2.3–2.5]) Gss
(r, r ; ω) =  k χs(r)η∗ s
(r ) ω − εk + Gincoh ss
(r, r ; ω) , (2.20)  s
 d3r  δ(r − r )  −∇2 2 + u(r) + uH(r)  + Σss
(r, r ; k)  χs
(r ) = χs(r)εk . (2.21) Here, in the inhomogeneous situation of a solid, the self-energy Σ is among other dependencies a functional of the density. This forms the shaky ground (with rather solid boulders placed here and there on it, see for instance also [2.4]) for interpreting a KS band structure as a quasi-particle spectrum. In principle from the full Σss
(r, r ; ω) the total energy might also be ob￾tained. 2.2 Full-Potential Local-Orbital Band Structure Scheme (FPLO) This chapter deals with task (iii) mentioned in the introduction to Chap. 1. A highly accurate and very effective tool to solve the KS equations self￾consistently is sketched. The basic ideas are described in [2.6, see http://www.ifw-dresden.de/agtheo/FPLO/ for actual details of the imple￾mentation].