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What ab-initio Quantum Chemistry (AIQC) and Density Functional Theory (DFT) can learn from each other

Starting from the common origin of AIQC and DFT, differences between AIQC and DFT are analyzed. The respective advantages and drawbacks of the two classes of methods are pointed out. A chain of approximations is presented that starts from genuine DFT, where the entire internal energy is treated as an unknown functional of the density, via Kohn-Sham type theories, orbital functional theories, and density matrix functional theory to a rigorous n-electron theory. On this way the dependence on an unknown functional is gradually reduced, while the information content of the parametrization of the state is increased. Particular attention is payed to formulations of the n-electron problem in terms of the 2-particle density matrix or rather the one-particle density matrix and the two-particle cumulant ​
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