This work introduces an analysis of the relationship of first-principles calculations based on DFT method with the results of free particle model for ring-shaped aromatic molecules. However, the main aim of the study is to reveal the angular electronic band structure of the ring-shaped molecules. As in the case of spherical molecules such as fullerene, it is possible to observe a parabolic dispersion of electronic states with the variation of angular quantum number in the planar ring-shaped molecules. This work also discusses the transition probabilities between the occupied and virtual states by analyzing the angular electronic band structure and the possibility of ring currents in the case of spin angular momentum (SAM) or orbital angular momentum (OAM) carrying light. Current study focuses on the benzene molecule to obtain its angular electronic band structure. The obtained electronic band structure can be considered as a useful tool to see the transition probabilities between the electronic states and possible contribution of the states to the ring currents. The photoinduced current due to the transfer of SAM into the benzene molecule has been investigated by using analytical calculations within the frame of time-dependent perturbation theory.