Anthracene and its simplest derivatives with electron-accepting (anthraquinone) and electron-donating (diaminoanthracene) properties in their anionic, neutral and cationic charge states are investigated using the density functional theory. The effect of addition and removal of the electron on the bond lengths, atomic charges, frontier orbitals, ionization potential (IP), electron affinity (EA) and reorganization energy is considered. The computed IP, EA and optical gaps are in rather good agreement with available experimental data.