We are presenting results based on the density-functional theory, DFT, in order to obtain stable structures of the doxorubicin molecule that may lead for healthier ways to inhibit cancer cells for humans. We obtained several electrochemical properties; such as electronic affinity, chemical potential, chemical hardness, electrophilicity index, and ionization potential. The maximum reactivity zone of a molecule is obtained founding its HOMO-LUMO boundary molecular orbitals and reactive sites were determined by Fukui indices. The distribution of electric charges and Mulliken population were obtained to determine areas and sites with excess or deficit of electrons. The Raman spectrum was theoretically obtained. The information presented would be very useful for possible new anticancer drugs.