  Bottom-up synthesis from molecular precursors is a powerful route for the
creation of novel synthetic carbon-based low-dimensional materials, such as
planar carbon lattices. The wealth of conceivable precursor molecules
introduces a significant number of degrees-of-freedom for the design of
materials with defined physical properties. In this context, a priori knowledge
of the electronic, vibrational and optical properties provided by modern ab
initio simulation methods can act as a valuable guide for the design of novel
synthetic carbon-based building blocks. Using density functional theory, we
performed simulations of the electronic properties of armchair-edged graphene
nanoribbons (AGNR) with a bisecting 4-8 ring defect line. We show that the
electronic structures of the defective nanoribbons of increasing width can be
classified into three distinct families of semiconductors, similar to the case
of pristine AGNR. In contrast to the latter, we find that every third
nanoribbon is a zero-gap semiconductor with Dirac-type crossing of linear bands
at the Fermi energy. By employing tight-binding models including interactions
up to third-nearest neighbors, we show that the family behavior, the formation
of direct and indirect band gaps and of linear band crossings in the defective
nanoribbons is rooted in the electronic properties of the individual nanoribbon
halves on either side of the defect lines, and can be effectively through
introduction of additional 'interhalf' coupling terms.
