Valence-skipping and negative-U in the d-band from repulsive local Coulomb interaction

We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate d-band, resulting in effective negative-U. This effect is shown to originate from anisotropic orbital-multipole scattering, and occurs only for $d^1$, $d^4$, $d^6$ and $d^9$ fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived and the paramagnetic phase diagram for $d^4$ and $d^6$ is calculated. We also establish that the valence-skipping metal is very different, in terms of its local valence distribution, compared to the atomic-like Hund's metal. These findings explains why transition metal compounds with the aforementioned d-band fillings are more prone to valence-skipping charge order and anomalous superconductivity.