  Graphdiynes (GDYs) as two-dimensional carbon structures based on sp2
hybridized aromatic rings connected by sp-hybridized acetylenic linear links
are gathering an increasing popularity, both for their peculiar properties and
for the promising applications. In these materials, structural features affect
the degree of pi-electron conjugation resulting in different electronic,
optical and vibrational properties. In particular, how topology, connectivity
between sp and sp2 domains and system size are related with the final
properties is fundamental to understand structure-property relationships and to
tailor the properties by proper structure design. By using a computational
approach based on density functional theory calculations, we here investigate
structure-property relations in a class of 1D and 2D GDY molecular fragments as
building block models of extended structures. By analysing how the structure
can modulate the pi-electron conjugation in these systems, HOMO-LUMO gap is
found to depend on the peculiar topology and connections between linear sp
domains and aromatic units. A topological indicator is computed, showing a
trend with the gap and with the frequency of the main vibrational mode
occurring in Raman spectra. Our findings can contribute to guide the molecular
design of new GDY-based sp-sp2 carbon materials, aiming at tuning their
properties by precise control of the structure.
