Effect of covalency and interactions on the trigonal splitting in NaxCoO2

We calculate the effective trigonal crystal field Delta which splits the t2g levels of effective models for NaxCoO2 as the local symmetry around a Co ion is reduced from Oh to D3d. To this end we solve numerically a CoO6 cluster containing a Co ion with all 3d states and their interactions included, and its six nearest-neighbor O atoms, with the geometry of the system, in which the CoO6 octahedron is compressed along a C3 axis. We obtain Delta near 130 meV, with the sign that agrees with previous quantum chemistry calculations, but disagrees with first-principles results in the local density approximation (LDA). We find that Delta is very sensitive to a Coulomb parameter which controls the Hund coupling and charge distribution among the d orbitals. The origin of the discrepancy with LDA results is discussed.