This paper analytically solves the "inverse DFT problem" of mapping the ground-state density to the exact XC functional. And the exact density, i.e. the FCC/FCI density, can be expressed as an infinite series of basis sets with transcendentally analytically expressable coefficients(all one-variable polynomial equations are known to be solvable in analytic form using transcendental functions). This means that the exact XC functional can be expressed as an infinite series of analytically expressable terms.

My question now follows- is there any known way to find out any "cancellations" in the expansion before (truncating it to yield approximations)?

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    $\begingroup$ Maybe I misunderstood the work in the paper, but it seems to me like they just inverted the KS equations numerically, like everyone always does in the field. A lot of the paper just reiterates the well-known problems with Gaussian basis sets, and they choose a popular polynomial method (again, like most of the field). I'm mystified how they got a Nature paper out of this, so perhaps I've missed something. $\endgroup$ Nov 22, 2022 at 12:36
  • $\begingroup$ @PhilHasnip I agree $\endgroup$ Nov 30, 2022 at 14:40