The possibility to employ higher-order irreducible vertex parts (corresponding to virtual double-excitations) in the calculation of excitonic levels in infinite systems has been discussed. Numerical ab initio Hartree-Fock and correlation calculations in the Møller-Plesset partitioning have been performed on an alternating hydrogen chain. The results show that, while proper renormalization is important in the calculation of absolute excitation energies, the exciton binding energies are stronger influenced by the higher-order terms in the irreducible vertex part.