Kohn-Sham DFT: Self-Consistent Field

Kohn-Sham DFT maps the interacting many-electron problem onto a set of non-interacting particles in an effective potential. The SCF loop: (1) guess n(r) → (2) build V_eff = V_ext + V_H[n] + V_xc[n] → (3) solve KS equations −½∇²ψ + V_eff ψ = ε ψ → (4) compute new n(r) = Σ|ψᵢ|² → (5) check convergence. The Hartree potential V_H accounts for classical Coulomb repulsion; V_xc captures all quantum exchange and correlation (LDA: V_xc ∝ −n^{1/3}). Convergence requires careful density mixing (damping).