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 Na0.35​CoO2​−1.3H2​O superconducting compound. The effective ligand field splitting within the t2g​ orbitals was found to be δ∼300meV, the a1g​ orbital being destabilized compared to the eg′​ ones. The effective Hund's exchange and Coulomb repulsion were evaluated to JH​∼280meV and U∼4.1--4.8eV. The NN hopping parameters were determined within the three t2g​ orbitals and found to be of the same order of magnitude as the t2g​ 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=−66meV