An ab-initio evaluation of the local effective interactions in the superconducting compound $\rm Na_{0.35} Co O_2-1.3H_2O$

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 $\rm Na_{0.35} Co O_2-1.3H_2O$ superconducting compound. The effective ligand field splitting within the $t_{2g}$ orbitals was found to be $\delta \sim 300\,\rm meV$, the $a_{1g}$ orbital being destabilized compared to the $e_g^\prime$ ones. The effective Hund's exchange and Coulomb repulsion were evaluated to $J_H\sim 280\, \rm meV$ and $U\sim 4.1$--$4.8\, \rm eV$. 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, supporting the hypothesis of a three band model for this system. Finally we evaluated the NN effective exchange integral to be antiferromagnetic and $J=-66\,\rm meV$