An ab-initio evaluation of the local effective interactions in the superconducting compound $Na\_0.35CoO\_2-1.3H\_2O$

Abstract

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 $Na\_0.35CoO\_2-1.3H\_2O$ 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 $U\sim 4.1$--$4.8\mathrm{eV}$. 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 $J=-66\mathrm{meV}$.

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