Density functional studies of vibronic coupling in a hole-transporting material in organic light-emitting diodes (OLED), carbazole, biphenyl and fluorene are reported as well as Hartree–Fock calculations. Vibronic coupling density (VCD) analysis reveals that strong localization of electron-density differences on the carbazole N atom is responsible for the small vibronic coupling constants (VCC) of carbazole. A heteroatom bridge such as an imino group is expected to enhance hole-transporting properties, and localized electron-density difference on the atom is expected to decrease vibronic coupling. The difference between the density functional and Hartree–Fock calculations are discussed.