Is it wrong to say that Density Functional means that Electron Density is a function of the orbitals (wave function) of all electrons in 3 dimensions, if so, why ?
Answer
In general, a functional F is a mapping from an arbitrary set X of functions to the set of complex numbers C or the set of real numbers R: F:X↦R.
For example, if you consider X as the set of polynomials with real coefficients, you can define a functional F as F[f]=∫10f(x)dx
A density functional is simply a functional F[f] where the argument f is the electron density ρ(→r) (i.e. a density functional is a functional of the electron density). For example Hohenberg and Kohn showed that the energy ϵ of a quantum system is a functional of the density ϵ=E[ρ]
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