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We used fully correlated ab initio calculations to determine the effectiveparameters of Hubbard and t - J models for the thermoelectric misfit compound$\rm Ca_3Co_4O_9$. As for the $\rm Na_xCoO_2$ family the Fermi level orbitalsare the $a_{1g}$ orbitals of the cobalt atoms ; the $e'_g$ being always lowerin energy by more than 240\,meV. The electron correlation is found very large$U/t\sim 26$ as well as the parameters fluctuations as a function of thestructural modulation. The main consequences are a partial $a_{1g}$ electronslocalization and a fluctuation of the in-plane magnetic exchange from AFM toFM. The behavior of the Seebeck coefficient as a function of temperature isdiscussed in view of the ab initio results, as well as the 496\,K phasetransition.

Electronic structure of the $\rm Ca_3Co_4O_9$ compound from ab initio local interactions