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For some reason I thought that the term DFT and Kohn Sham DFT were interchangeable. Kohn Sham DFT is certainly one of the most popular. But are there other types of DFT that are in use today? I have been able to find orbital free DFT is gaining momentum (http://www.sciencedirect.com/science/article/pii/S0022509607000221) But are there more DFT types?

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    $\begingroup$ For example en.wikipedia.org/wiki/… $\endgroup$ – Mithoron Nov 24 '16 at 17:39
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    $\begingroup$ @Fl.pf. MP2 is in no way a formulation of HF. KS-DFT is a theoretical "implementation" of DFT, and MPn is n-th order perturbation theory. It would be more correct to say something like Rayleigh-Schrodinger PT and Brillouin-Wigner PT are forms of PT. $\endgroup$ – pentavalentcarbon Nov 29 '16 at 15:56
  • $\begingroup$ @pentavalentcarbon I didn't mean it was. That comment was a little hasty and doesn't show very good what I meant to say. I'll delete it. $\endgroup$ – Fl.pf. Nov 29 '16 at 16:03
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    $\begingroup$ @Fl.pf. That's fine; I'll leave mine up because others might not know that. By the way, thank you for participating, we need more people interested in theory and computation. $\endgroup$ – pentavalentcarbon Nov 29 '16 at 16:06
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KS-DFT is the basis for all orbital-based DFT Formulations. In it you have different specialities (constricted DFT, TD-DFT, rs-DFT to name a few).

KS-DFT is used for molecular problems, because of atom bonds etc.

TD-DFT is used for time-dependend problems like excitation energies, polarizabilities etc.

RS-DFT is using range-separated functionals (long-range, short-range) to handle effects better in the long-range domain.

Addition by @pentavalentcarbon: Current cDFT implementations are based on KS-DFT and perform a real-space partitioning of the electron density.

Plane Wave DFT (no orbitals, electron density calculated with plane waves, was the first DFT) is used for periodic problems like metals etc.

DFTB (Density Functional Tight Binding) is good for Molecular Dynamics since its an approximate DFT and allows handling of larger systems and greater timescales. Addition by @pentavalentcarbon: A good analogy for DFTB would be that it is similar to semiempirical methods (PM7, other NDDO parametrizations) where certain integral matrix elements are replaced with precomputed, fitted parameters, but there is a minimal basis set present.

KS-DFT is dominant because as computational chemists we are mostly working with molecules. As that we need a simulation of atom bonds. There is a good Book about DFT which I can only recommend (A chemists guide to Density Functional Theory): http://www.goodreads.com/book/show/70706.A_Chemist_s_Guide_to_Density_Functional_Theory

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  • $\begingroup$ Current cDFT implementations are based on KS-DFT and perform a real-space partitioning of the electron density. A good analogy for DFTB would be that it is similar to semiempirical methods (PM7, other NDDO parametrizations) where certain integral matrix elements are replaced with precomputed, fitted parameters, but there is a minimal basis set present. $\endgroup$ – pentavalentcarbon Nov 29 '16 at 15:52
  • $\begingroup$ @pentavalentcarbon Thank you, I have included your information in the answer. All DFT methods are semi-empiric (because of the XC-Functional) $\endgroup$ – Fl.pf. Nov 29 '16 at 15:55
  • $\begingroup$ While it is certainly a spectrum, I would argue that not all XC functionals are semiempirical (Slater exchange, VWN correlation, and their descendants) in the same way that PM7 is semiempirical. These may only be fitted to the homogeneous electron gas, with less than a handful of parameters, as opposed to M06, which is definitely semiempirical. $\endgroup$ – pentavalentcarbon Nov 29 '16 at 16:01
  • $\begingroup$ Some other good reads: quantum-chemistry-history.com/Hist_Dat/DFT_Dat/DFT_Ob1.htm and simplecompchem.blogspot.com/2016/06/dft-advices.html $\endgroup$ – LordStryker Nov 29 '16 at 16:06
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    $\begingroup$ @pentavalentcarbon I think the definition of semiempirical is used a little loose here. There are people who say that DFT is "not really ab-initio anymore" so maybe a little semiempiric... In german we would say its "Haarspalterei" :) $\endgroup$ – Fl.pf. Nov 29 '16 at 16:08

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