In the present work, the novel superhard tetragonal carbon allotropes C 5 , C 6 , and C 7 characterized with mixed sp 2 and sp 3 carbon hybridizations, were found to be cohesive and stable both mechanically (elastic constants and their combinations) and dynamically (phonon band structures). While C 5 and C 6 contain ethene-like >C=C< subunits, C 7 shows both ethene-like and propadiene-like >C=C=C< subunits, with signatures observed from the highest phonon frequencies correlating with Raman vibrations of ethene and propadiene molecules. The density decreases along the C 5 -C 6 -C 7 series due to the increasing openness of the structures and consequently leads to a decrease in mechanical properties. The energy-volume equations of state show metastability of all three allotropes over the whole range of experimentally accessible pressures, but this does not exclude their possible formation under high pressure -high temperature conditions. Thermodynamically, the temperature dependencies of the heat capacity and entropy of all three allotropes were found to be higher than those of diamond due to the insulating electronic properties of the latter compared to the conducting C 5 , C 6 , and C 7 as identified from their electronic band structures. Delocalized π electrons of C(sp 2 ) atoms are considered to be responsible for the conductivity of the new carbon allotropes.