Dissociation of diatomic molecules and the exact-exchange Kohn-Sham potential: The case of LiF

Abstract

We examine the role of the exact-exchange (EXX) Kohn-Sham potential in curing the problem of fractional molecular dissociation. This is achieved by performing EXX calculations for the illustrative case of the LiF molecule. We show that by choosing the lowest-energy electronic configuration for each interatomic distance, a qualitatively correct binding energy curve, reflecting integer dissociation, is obtained. Surprisingly, for LiF this comes at the cost of violating the Aufbau principle, a phenomenon we discuss at length. Furthermore, we numerically confirm that in the EXX potential of the diatomic molecule, one of the atomic potentials is shifted by a constant while the other one is not, depending on where the highest occupied molecular orbital is localized. This changes the relative positions of the energies of each atom and enforces the integer configuration by preventing spurious charge transfer. The size of the constant shift becomes increasingly unstable numerically the larger the interatomic separation is, reflecting the increasing absence of coupling between the atoms.

Origin of static and dynamic steps in exact Kohn-Sham potentials

“…This means that for any subsystem's density which does not decay with the ionization energy of the whole system, there must be a second change in the local effective ionization energy far from the system, and therefore another step must form. This second step was first observed by Perdew 19 and also by Makmal et al 27 in the exact exchange potential for LiF, where they attribute the steps to shifts in the KS eigenvalues. They discuss the 'domain' of each atom being dominated by the HOMO of that atom, resulting in a plateau to correct for the nonzero asymptotic limit caused by the HOMO eigenvalue being non-zero.…”

Full self-consistency in the Fermi-orbital self-interaction correction

“…[51]. The LiF molecular potential energy curve provides a good example of this problem [51][52][53]. In this case, LSDA total energies as functions of charge on the separated systems predict that the ground state of a separate Li and separated F has approximately 2.3 units of charge on the Li and 9.7 units of charge on the F (this result depends slightly on choice of functional).…”

Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density-functional theory using the ensemble-generalization approach

“…Then, in terms of the total energy, the molecular energy curve E A...B (q) would have possessed a non-analytical minimum at q = 0, obeying the principle of integer preference. In terms of the KS potential, a 'plateau' in the vicinity of one of the atoms would have emerged, shifting the KS potential and the energy levels associated with that atom [16,33,[47][48][49][50][51][52]. Because all these desired features are absent in the standard local density approximation, spurious transfer of fractional charge is not precluded.…”