Modification of individual chemisorbed benzene molecules on Cu(100) has recently been performed in atomic manipulation experiments [J. Phys. Chem. A. 104, 2463 (2000); Surf. Sci 451, 219 (2000)]. Benzene dissociates under controlled voltage pulses in a scanning tunneling microscope (STM) junction. The reaction is characterized as a dehydrogenation process and the fragments are identified as benzyne, C6H4. Here we present a density functional theory investigation of the chemisorption of benzene on the Cu(100) surface, the nature of the bonding and its effect on the STM images. The fragments phenyl and benzyne formed after one-fold and two-fold dehydrogenation of chemisorbed benzene are studied in the same manner. The stability of the fragments is explored via their chemisorption energy, their electronic structure on the surface and their affinity for hydrogen. Benzyne fragments seem to be the most stable, in agreement with the conclusion of the aforementioned STM experiments.