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Abstract
Exchange interaction in ring chains of N transition ions with n unpaired electrons per ion is investigated. The study is focused on the case where N becomes very great, i.e. on the case of one-dimensional magnetic compounds. The main results are the following: (i) An orbital justification to the use of the phenomenological spin hamiltonian of the Heisenberg-Dirac-Van Vleck model 
is given. (ii) The exchange interaction parameter J is expressed as a function of orbital integrals related to the real mechanism of the phenomenon. The key expression is 
in which Sμμ is the overlap integral between two magnetic orbitals of the same symmetry centred on nearest-neighbour transition ions, Δμ is the width of the molecular orbital band built from the magnetic orbitals of symmetry μ for the spectroscopic term of highest spin multiplicity. Finally J μν is the two-electron exchange integral between magnetic orbitals of symmetry μ and ν respectively, centred on nearest-neighbour ions.