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A second neighbor t-J+V model for the chain subsystem of the Sr 14 Cu 24 O41 was extracted from ab-initio calculations. This model does not use periodic approximation but describes the entire chain through the use of the four-dimensional crystallographic description. Second neighbors interactions are found to be of same order than the first neighbors ones. The computed values of the second neighbors magnetic interactions are coherent with experimental estimations of the intra-dimer magnetic interactions, even if slightly smaller. The reasons of this underestimation are detailed. The computed model allowed us to understand the origin of the chain dimerisation and predicts correctly the relative occurrence of dimers and free spins. The orbitals respectively supporting the magnetic electrons and the holes have been found to be essentially supported by the copper 3d orbitals (spins) and the surrounding oxygen 2p orbitals (holes), thus giving a strong footing to the existence of Zhang-Rice singlets. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Sr14Cu24O41: a complete model for the chain sub-system