In continuing our investigations on the stability of nitrogen doped heterofullerenes with many NN connections, other isomers of two molecules C40N20 and C42N18 have been found out which possess a nitrogen chain. In these isomers the nitrogen chain is not in the middle of spherical fullerene, despite the previously introduced NB-isomers containing a nitrogen belt that NN continuum was in the middle of fullerene molecule. All quantum chemical calculations have been carried out using Gaussian 09W and NBO 5.0 programs, via HF and DFT method at the B3LYP level. Geometrical analysis, energy and frequency calculations express acceptable stability of these isomers with a nitrogen chain. The stability in these structures is a result of breaking some NN bonds and creation bigger rings for getting rid from the unfavorable strain besides formation of all-carbon hexagonal rings. Ionization potential, electron affinity, electronegativity, HOMO/LUMO surface energies and their gap, dipole moment, polarizability, hyperpolarizability and NBO charges have been calculated for the isomers with a nitrogen chain and compared with those for the NB-isomers, SN-isomers with separated nitrogen atoms, and also with C60 fullerene as a reference. From the results, it is predicted that the objective isomers exhibit more electron acceptor characters than C60 and also other isomers containing separated nitrogens. The electron acceptor property of these isomers, accompanied by an opening cavity in these structures, with no functional group on the edge of the cavity, might be useful for inserting inside the fullerene cage. In addition to the small HOMO-LUMO gaps and great polarizability of these structures, superior third order optical applications could be predicted for these isomers with a nitrogen chain, even more than those for the NB-isomers.