I was reading this paper which basically outlines the two main types of errors that one encounters in Kohn-Sham DFT : Density-based errors and Functional-based errors. I understand the practical differences between these two: The former refers to the case where the electron density generated through the self-iterative process, is one of poor quality. The latter is just a reflection of the fact that in practice, we sort to approximate functionals and this can lead to errors. My doubt is regarding how one could pin down the nature of error in a DFT calculation. Let us confine ourselves to analyzing the functional error. From what I gather, this seems to be the general procedure:
- Perform an SCF calculation for a system with a given functional (say for example, LDA)
- Fix the charge density from the LDA calculation, but now use a different functional (say, PBE) and do another SCF calculation.
If one observes qualitatively different results between these two steps, then it should imply that the error is inherently functional-based. This is because in one case we perform LDA calculations with the LDA density and in the other, PBE calculations with the LDA density.
My doubt is as follows: How are these two cases different putting into context the H-K theorems? One of the H-K theorems state that the ground state energy is a unique functional of the density. Doesn't this mean that fixing a density is equivalent to fixing the potential?
I'm looking forward to your inputs on this.