A theoretical study of rotational profiles of molecular absorption bands is essential for direct comparison with observations of diffuse interstellar bands. Applications using a Gaussian quantum-chemical approach within density functional theory are presented. Structural and vibrational properties of the polycyclic aromatic hydrocarbon ovalene cation (C32H14+) are obtained. We discuss the expected profile of the first electronic transition of such molecule, obtained with a Monte Carlo model of its rotation in the physical conditions of low temperatures and absence of collisions which are characteristic of the interstellar medium.