Charge Disproportionation without Charge Transfer in the Rare-Earth-Element Nickelates as a Possible Mechanism for the Metal-Insulator Transition

We study a model for the metal-insulator (M-I) transition in the rare-earth-element nickelates RNiO₃, based upon a negative charge transfer energy and coupling to a rocksaltlike lattice distortion of the NiO₆ octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with a ground state of predominantly d⁸L character, where _L denotes a ligand hole. For sufficiently large distortions (δd_Ni-O~0.05--0.10), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with (d⁸_L²)S=0(d⁸)S=1 character, where S is the total spin. Thus the M-I transition may be viewed as being driven by an internal volume ``collapse'' where the NiO₆ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2$, $1/2$, $1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of charge ordering achieved without any actual movement of the charge.