The amino acid L-cysteine (Cys) adsorbs in highly ordered (3 root 3 x 6) R30 degrees lattices on Au(111) electrodes from 50 mM ammonium acetate, pH 4.6. We provide new high-resolution in situ scanning tunneling microscopy (STM) data for the L-Cys adlayer. The data substantiate previous data with higher resolution, now at the submolecular level, where each L-Cys molecule shows a bilobed feature. The high image resolution has warranted a quantum chemical computational effort. The present work offers a density functional study of the geometry optimized adsorption of four L-Cys forms - the molecule, the anion, the neutral radical, and its zwitterion adsorbed a-top - at the bridge and at the threefold hollow site of a planar Au(111) Au-12 cluster. This model is crude but enables the inclusion of other effects, particularly the tungsten tip represented as a single or small cluster of W-atoms, and the solvation of the L-Cys surface cluster. The computational data are recast as constant current-height profiles as the most common in situ STM mode. The computations show that the approximately neutral radical, with the carboxyl group pointing toward and the amino group pointing away from the surface, gives the most stable adsorption, with little difference between the a-top and threefold sites. Attractive dipolar interactions screened by a dielectric medium stabilize around a cluster size of six L-Cys entities, as observed experimentally. The computed STM images are different for the different L-Cys forms. Both lateral and vertical dimensions of the radical accord with the observed dimensions, while those of the molecule and anion are significantly more extended. A-top L-Cys radical adsorption further gives a bilobed height profile resembling the observed images, with comparable contributions from sulfur and the amino group. L-Cys radical a-top adsorption therefore emerges as the best representation of L-Cys adsorption on Au(111).