Propagation delay of signals by interlayer dielectrics in LSI interconnects is becoming a dominant issue. Materials of low dielectric constant have been widely studied in order to reduce the delay of signals. In this study we try to design theoretically novel low-k materials based on ab initio quantum chemical methods and the density functional perturbation theory (DFPT). The Clausius-Mossotti equation shows that dielectric constants are related to polarizabilities of materials and a low dielectric constant corresponds to a small polarizability and a small number density of a material. We calculated molecular volumes and polarizabilities of oligomers: hydrocarbon C_nH_2n+2 and fluorocarbon C_nF_2n+2, based on the HF, MP2 and B3LYP methods using the 6-31G** basis set. Dielectric constants of their polymers were then obtained by extrapolation. Quantum chemical calculations have been carried out using the program GAUSSIAN98. Next, we applied the DFPT to the calculation of dielectric constants of periodic organic polymers using pseudopotential. Calculations have been carried out using the program ABINIT. The results nicely agree with that of quantum chemical calculations. We are currently studying amorphous carbon nitrides, a-CN_x, which are noticed as potential low-k materials. The x-dependence in dielectric constants of CN_x will also be discussed.