Jacob’s Ladder for DFT

[meesha]

In DFT, the major unresolved problem is finding the last term of the Kohn-Sham equations — the XC-functional. The LDA approximation provides a good basis for researchers to build on by adding layers of complexity one by one, in a process similar to Jacob’s Ladder in physics.

Each rung of Jacob’s ladder for this problem represents a layer of complexity that brings us closer to the exact XC-functional. As layers are added, the existing ones are kept the same, so the process does not involve any change to the already working portions of the functionals. The first “rung” would be the LDA, which only accounts for electron density. The rungs after that (GGA and onwards) would include surrounding but local density changes, then kinetic energy density, then exact exchange, and finally also exact correlation. If both exact exchange and exact correlation are represented, then the XC-functional will have been defined exactly in its entirety.

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