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Avoiding the Bardeen—Tersoff—Hamann approximation we present calculations of the scanning tunneling microscope (STM) image of benzene or Rh(111). The tunneling current between the tip and the substrate through the benzene is calculated from the generalized Landauer formula. The electronic structure of the complete system made of the tip, of the substrate and of the benzene adsorbate is obtained with its molecular orbitals from an extended Hückel molecular orbital calculation. Experimental and calculated images are in good agreement. This leads to a detailed analysis of the image using the molecular orbital approach in through-space and through-bond tunneling processes.