We present a combined theoretical and experimental study of chemisorption parameters and STM images for C2H2, C2H, and C-2 on Cu(001). The geometric and electronic structure, and vibrational energies were obtained from density functional calculations. The calculated STM images were obtained from Kohn-Sham wave functions using the Tersoff and Hamann approximation. A dramatically enhanced resolution in the experimental STM images were obtained using a tip that was obtained by irreversible dissociation of H2S. We find a near-quantitative agreement between experimental and calculated image for this tip and for a normal tip at appropriate tip-surface distances. An analysis shows that protrusions that appear in all images derive from adsorbate-induced resonances at the Fermi energy. All images also exhibit a wide depression that we attribute to the screening of the electronegative adsorbates by the metal conduction electrons.