Jacob’s ladder

[Iulia ZAI]

In the context of DFT, the Jacob’s Ladder analogy refers to the iterative approach of adding extra layers of complexity starting from the simplest density functional in the search for the “divine functional”, where both exchange and correlation are known exactly. Starting from the ground level where E_{xc}=0, the first rung in the ladder is represented by LDA, which only takes into consideration the electron density of a material system. The second rung is formed by GGA, which adds a gradient to this density, followed by the third of meta-GGAs, which introduce kinetic energy density to satisfy more exact constraints. On the fourth rung, hybrid functionals such as SIC use the Kohn-Sham one-particle density matrix to construct the exact exchange energy and, finally the fifth rung – RPA – like approximation – takes this exact exchange energy into consideration along with the unoccupied orbitals and all orbital energies in order to also evaluate correlation exactly.

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