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There are many different DFT method available, is this simply because individuals find a better DFT method to suit specific types of molecules?

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The issue is that unlike for the methods based on Hartree-Fock, there isn't a systematic path to improving DFT. Unlike for HF, where we can treat the correlation as a pertubation (MP-n) or include excited Slater determinants (CI and CC) to generally improve our description of a molecule, we still don't have a way of determining the true form of the density functional (specifically the part governing exchange correlation) in DFT, so for now we use educated guesses for the general form (Local Density Approximation, Generalized Gradient Approximation, etc) and optimize them for specific systems.

In principle, if the exact form of the functional were known, DFT would be exact. This is why some authors like to use a separate term DFA (Density Functional Approximation) to describe the instances of DFT in use today.

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    $\begingroup$ I think there's an image that's useful to conceptually understand this crucial point - when we apply DFT, we are not actually solving electron systems - we are solving "particles quite-similar-to-but-not-exactly-like-electrons" as defined by interactions (exchange and correlation) that are similar to electrons, but not the same. So if we found the actual functional for electrons, the very same methods we use now would be exact for all cases, but for now we're stuck with solving "almost-electron" systems and using them as approximations for the actual electron systems. $\endgroup$ – user41033 Mar 18 '18 at 17:32
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    $\begingroup$ Might be of further interest: Is density functional theory an ab initio method? (DFA always :D) $\endgroup$ – Martin - マーチン Apr 12 '18 at 11:38
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There are not that many DFT methods, at least not much more than WFT methods. DFT itself is a method, though. And if you really mean DFT as a method, than there are these methods, because people are working on this field and try to solve there scientific problems using DFT methods.

I guess, you probably mean, why there are so many (exchange correlation) functionals around. That is, because we don't know the exact functional and it is neither trivial to find nor is it easy to improve, if you have found a nice approximation.

And yes, you are right, many functionals exist for special purposes. But the goal is to find a functional that is able to treat as many cases as possible as best as possible.

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