The integration of DNA and RNA nucleobases to improve the performance of organic light-emitting diodes, as a low-cost and environmentally friendly optoelectronic device, has attracted a lot of interest in recent years. As a contribution to an improved understanding of the DNA/RNA-based devices in the solid state, we presented here a dispersion corrected density functional theory (DFT) and time-dependent DFT calculations to obtain the optimized geometries, Kohn-Sham band structures, charge distribution, optical absorption, Frenkel exciton binding energies, and complex dielectric functions of the five DNA/RNA nucleobases anhydrous crystals. Optical absorption measurements on the DNA/RNA nucleobase powders were also performed for comparison with the simulations. Effective masses for the carriers were calculated, indicating that the guanine and the cytosine crystals have potential applications in optoelectronics as a direct gap semiconductor, with the other nucleobases (adenine, thymine, and uracil) presenting either a semiconductor or an insulator character, depending on the carrier type.