  Two-dimensional (2D) hybrid sp-sp2 carbon systems are an appealing subject
for science and technology. For these materials, topology and structure
significantly affect electronic and vibrational properties. We investigate here
by periodic density-functional theory (DFT) calculations we here investigate
the Raman and IR spectra of 2D carbon crystals belonging to the family of
graphdiynes (GDYs) and having different structures and topologies. By joining
DFT calculations with symmetry analysis, we assign the IR and Raman modes in
the spectra of all the investigated systems. On this basis, we discuss how the
modulation of the Raman and IR active bands depends on the different
interactions between sp and sp2 domains. The symmetry-based classification
allows identifying the marker bands sensitive to the different peculiar
topologies. These results show the effectiveness of vibrational spectroscopy
for the characterization of new nanostructures, deepening the knowledge of the
subtle interactions that take place in these 2D materials.
