A general SCF-SCAO theory for computations of the electronic structure in polymeric species is presented. The theory is essentially a tight-binding model expressed in a manner close to the self-consistent field-LCAO matrix formalism and restricted to closed-shell cases. Particular care has been taken to ensure a theory which can be easily applied in practical applications. A computer program, POLYMOL, has been programmed and a short description is included at the end of this paper. Throughout the paper reference is given to the (H 2) infinite chain, as an example.