Electron-vibration interactions giving rise to infrared (IR) intensities characteristic of the radical cations of polycyclic aromatic hydrocarbons (PAHs) are examined theoretically. Density functional calculations are performed for the radical cations of naphthalene, anthracene, tetracene, pentacene, pyrene, perylene, and phenanthrene at the B3LYP/6-311G* level. A theoretical formulation for analyzing the vibrational motions giving rise to strong IR intensities is presented. It is shown from the algebraic properties of the expression for IR intensities that three vibrational degrees of freedom responsible for all the IR intensities of a given molecule, called the intensity-carrying modes, can be derived from dipole derivatives in the Cartesian coordinate system. By using this theory, the origin of the IR intensities may be examined even when it is difficult to define an appropriate nonredundant set of internal coordinates. For molecules with C-2 upsilon or higher symmetry (including D-2h), each intensity-carrying mode belongs to each of the three IR-active symmetry species. It is shown that the vibrational patterns of the intensity-carrying modes and the directions of their dipole derivatives in the PAH radical cations are explained by the following two mechanisms. One is the mechanism involving long-range charge flux between distant benzene rings. By this mechanism, the vibrational motion of each ring occurs in the direction of the structural change between the neutral and charged benzene, and the vibrational motions of distant rings are combined out of phase to give rise to long-range charge flux. The other involves short-range charge flux within each benzene ring. The relation between vibrational motion and charge flux induced by this mechanism is explained by regarding the benzene radical cation as building "blocks" constituting the molecule and considering the intensity-carrying modes of each block. In both cases, the phase relationship of the singly occupied molecular orbital (SOMO) determines which of the two Jahn-Teller distorted structures of the benzene radical cation should be considered. It may be said, therefore, that the vibrational patterns of the intensity-carrying modes and the directions of their dipole derivatives are closely related to the electronic structures.