We used ab initio quantum chemical methods, treating explicitly the strong correlation effects within the cobalt $3d$ shell, as well as the screening effects on the effective integrals, for accurately determining on-site and nearest-neighbor (NN) interactions in the ${\mathrm{Na}}_{0.35}\mathrm{Co}{\mathrm{O}}_2\bullet 1.3{\mathrm{H}}_2\mathrm{O}$ superconducting compound. The effective ligand field splitting within the $t_{2g}$ orbitals was found to be $\delta \sim 300\mathrm{meV}$, the $a_{1g}$ orbital being destabilized compared to the $e_g^{\prime }$ ones. The effective Hund’s exchange and Coulomb repulsion were evaluated to $J_H\sim 280\mathrm{meV}$ and $U\sim 4.1–4.8\mathrm{eV}$ for the $a_{1g}$ orbitals. The NN hopping parameters were determined within the three $t_{2g}$ orbitals and found to be of the same order of magnitude as the $t_{2g}$ ligand field splitting. This result supports the hypothesis that a three band model would be better suited than a one-band model for this system. Finally we evaluated the NN effective exchange integral to be antiferromagnetic and $J=-66\mathrm{meV}$.

• Received 18 May 2006

DOI:https://doi.org/10.1103/PhysRevB.74.184507