There are many flavors of DFT that are alternative to, or go beyond the Kohn-Sham formulation (KS-DFT). Some of these are based on approximations that sacrifice accuracy when compared to KS-DFT, but in exchange are computationally cheaper and allow the modeling of larger systems.

Two popular methods of this kind, are Orbital-Free DFT (link to an answer on OFDFT here) and Density Functional Tight-Binding.

I have not yet seen a comparative study on the performance of these methods, but I wonder if anyone here is able to offer any insights about how they may compare?

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    $\begingroup$ +1. Someone asked me this question by email a few days ago. I'll try to write an answer when I have more time later. (I wrote the OFDFT answer you linked to.) $\endgroup$
    – wcw
    Jul 26, 2020 at 9:30
  • $\begingroup$ No way! Before I saw your answer, I was going to ask for a justification of OFDFT, (in similar spirit to this question, but you covered that. Seeing that however really reminded me of DFTB. Looking forward to that answer! :) $\endgroup$ Jul 26, 2020 at 9:32
  • $\begingroup$ It's a good question. I should say that I'm not an expert on DFTB, so it will be good to hear from others too. $\endgroup$
    – wcw
    Jul 26, 2020 at 9:42
  • $\begingroup$ @wcw I thought of you the moment I saw this question's title! If you answer quickly it will become a hot network question 🔥 $\endgroup$ Jul 26, 2020 at 12:49
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    $\begingroup$ Are you sure you want to compare these two directly? One is a tight-binding method… $\endgroup$
    – Greg
    Nov 25, 2021 at 19:04