{c}
{title2=$[-\tfrac12\nabla^2+v_{\rm eff}[n]]\phi_i=\epsilon_i\phi_i$}

Effective one-electron equations for orbitals whose density represents that of the interacting electronic system. The effective potential contains nuclear attraction, Hartree repulsion and an exchange-correlation contribution.


Kohn-Sham equations

Exchange-correlation functional

Kohn-Sham energy double-counting correction

Past exam of the advanced Quantum Condensed Matter Physics course of the University of Cambridge / 2013 / Paper 1 / 3 / c / Solution

Kohn-Sham equations ( $[- \frac{1}{2} \nabla^{2} + v_{eff} [n]] ϕ_{i} = ϵ_{i} ϕ_{i}$ )

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Kohn-Sham equations ([−21​∇2+veff​[n]]ϕi​=ϵi​ϕi​)

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Kohn-Sham equations ( $[- \frac{1}{2} \nabla^{2} + v_{eff} [n]] ϕ_{i} = ϵ_{i} ϕ_{i}$ )

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