A Kohn-Sham (KS) inversion determines a KS potential and orbitals corresponding to given electron density, procedure that has applications in developing evaluating functionals used density functional theory. Despite the utility of inversions, application these methods among research community is disproportionately small. We implement Zhao-Morrison-Parr Wu-Yang framework simplifies analysis conv...

Proof I : Assume that there exist two potentials V (1) ext (~r) and V (2) ext (~r) differing by more than a constant and giving rise to the same ground state density, n(~r). Obviously, V (1) ext (~r) and V (2) ext (~r) belong to distinct Hamiltonians Ĥ (1) ext(~r) and Ĥ (2) ext(~r), which give rise to distinct wavefunctions Ψ (1) ext(~r) and Ψ (2) ext(~r). Because of the variational principle, ...

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another...

We establish a full range of Caffarelli-Kohn-Nirenberg inequalities and their variants for fractional Sobolev spaces.