We present first-principles calculations of carbon and silicon chiral framework structures (CFSs). In this system, proposed recently by Pickard and Needs [Phys. Rev. B 81, 014106 (2010)], atoms form only pentagonal cycles. This configuration enables unambiguous analysis of the effects of pentagons on electronic, vibrational, and thermodynamic properties. The local density approximation electronic band gaps in CFSs were found to be equal to or greater than those of clathrates using the same formalism, as confirmed by GW calculations: 1.8 and 5.5 eV for Si and C-CFS, respectively. We show that, as in clathrates, an increasing electronic band gap is correlated with the contraction of the valence bands, resulting from the frustration of the p shells. The electron localized function and Wannier analysis confirm the sp(3) nature of the bonds. Finally, we discuss vibrational and related properties. We show that CFSs present singularities, in particular, that the higher frequencies are not located at the Gamma point.