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I have seen this phrase several times across DFT textbooks. However, I am not sure if it still holds. Was there a change or a theorem that proved it otherwise? Several programs display wavefunctions for DFT calculations. For example, Quantum Espresso has the option to collect wave functions. Some of the people that I have to talked to mention the Kohn Sham orbitals as if they were a real physical thing. Shouldn't it not be possible to obtain the wavefunction for a certain state? For example, I thought it was not possible to tell that a Kohn Sham orbital belongs to a wavefunction near the surface of a material.

I know that the Kohn Sham orbitals lack a physical meaning. They are simply wavefunctions that are used to obtain the correct density. They do not have an analogue of Koopmans' Theorem. In addition, "the exact wave function of the target system is not available in density functional theory" (Koch, 2001).

So why do people need/use wavefunctions (after all most DFT programs can group such wavefunctions)? I thought that they were Kohn Sham orbitals. Therefore, there should be seldom any use for them.

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  • $\begingroup$ semantic problem.. $\endgroup$ – Rodriguez May 11 '16 at 7:02
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    $\begingroup$ I recommend this question: KS orbitals have at least interpretational value. Additionally the mapping between electron density and wave function in bijective. That is what the Hohenberg-Kohn theorems show. To say that there are no wave functions in DFT seems to be a bit incomplete. (It would be nice if you could extend your quote with a complete citation.) $\endgroup$ – Martin - マーチン May 11 '16 at 7:02
  • $\begingroup$ @Martin-マーチン The quote is from "A Chemist's Guide to Density Functional Theory." In the section "Do We Know the Ground State Wave Function in DFT?" they mention: "We just have to look at all the wavefunctions associated with the ground state density and select that one for which the energy is is lowest. Of course, like so many results presented in this chapter, this one is also absolutely usless in real applications. We have no access to all these wave funcstions and thus, in real life there is now way whatsoever to identify the correct wave function associated with a particular density." $\endgroup$ – CoffeeIsLife May 11 '16 at 7:22
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There are no wavefunctions in DFT.

I don't like that "wave function" is used here in the plural form and I feel like it reflects OP's misconception. The right way to say this is

There is no wave function in DFT.

See, there exist only one wave function, the function that describes the state of a system in question and can be used to calculate its properties. When it comes to a many-electron system, the wave function is a function that describes the state of all the electrons present in the system interacting with each other. This is the wave function people have in their minds when they say the it is absent in DFT. And that is true: the whole point of DFT is to get rid of this function as a description of state since it is too complex to work with and difficult to visualise.


But that is not the whole story. In practise the Kohn-Sham DFT is used which introduces a fictious system of non-interacting electrons. Each electron in the fictious system is described by a Kohn-Sham orbital, a single-particle wave function, while the whole fictious system is described by the Kohn–Sham wave function, a Slater determinant constructed from a set of Kohn-Sham orbitals. Still there is no wave function in KS-DFT in the above mentioned sense:

  • KS orbitals don't qualify as the wave function just because they do not describe the state of a whole system;
  • the Kohn–Sham wave function doesn't qualify because it describes a different system (fictious non-interacting rather than real interacting).

So, the KS wave function is not the wave function, since it doesn't describe the (real) system. You can't use it to calculate the properties of the (real) system, you have to use the electron density to do so. In this sence, the statement that there is no wave function in DFT holds true for KS-DFT as well.

Can the KS wave functions (both single- and many-particle one) be somehow useful in any other way is a different story. See, for instance, the discussion of the usefulness of KS-orbitals here.

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    $\begingroup$ Section 2.(xii) of Autschbach, J Chem Educ 89: 1032 (2012), doi:10.1021/ed200673w points out some of the meaning that can be found in the KS orbitals. $\endgroup$ – hBy2Py May 12 '16 at 13:47

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