Other stability criteria, namely dynamic stability, were obtained by studying phonons, defined as quanta of vibrations. The phonon energy is quantized by the Planck constant h multiplied by the frequency ω, giving the phonon energy E = (h/2π)ω. The calculations of the phonons for C 18 , ene-C 21 and yne-C 24 are illustrated with the corresponding band structures shown in Fig. . Along the horizontal direction, the bands run along the main lines of the hexagonal Brillouin zone (reciprocal k-space). The frequencies ω along the vertical direction are given in units of terahertz (THz). There are 3N-3 optical modes found at higher energy than three acoustic modes that start from zero energy (ω = 0) at the  point, center of the Brillouin zone, up to a few terahertz. The acoustic modes correspond to the lattice rigid translations with two transverse and one longitudinal. In all three panels all frequencies are positive signaling stable systems. Marked differences between the three carbon allotropes are observed for the highest frequencies of the optical modes. In C 18 they culminate at ω ~ 40 THz, a magnitude observed for diamond by Raman spectroscopy . In ene-C 21 they culminate at ω max ~ 42 THz, a magnitude also observed for ene-like C 10 , C 14 , as well as in tetragonal C 6 with 3 tetrahedral and 3 trigonal carbons, where the flat band was attributed to antisymmetric C-C-C stretching in the allene (propadiene) molecule . The phonon band structure of yne-C 24 , exhibits flat bands at 70 THz, which can be assigned to CC characterized by much shorter distance than in ene-C 21 .