Dissociation limit in Kohn–Sham density functional theory. (February 2022) - Behr, Sören; Graswald, Benedikt R.
Abstract: We consider the dissociation limit for molecules of the type X 2 in the Kohn–Sham density functional theory setting, where X can be any element with N electrons. We prove that when the two atoms in the system are torn infinitely far apart, the energy of the system converges to min α ∈ [ 0, N ] ( I α X + I 2 N − α X ), where I α X denotes the energy of the atom with α electrons surrounding it. Depending on the "strength" of the exchange this minimum might not be equal to the symmetric splitting 2 I N X . We show numerically that for the H 2 -molecule with Dirac exchange this gives the expected result of twice the energy of a H-atom 2 I 1 H .