By using a realistic tight-binding or LCAO (linear combination of atomic orbitals) model, detailed calculations of surface states, local densities of states, and theoretically simulated photoemission spectra have been carried out for two qualitatively distinct structural models for chemisorption of atomic hydrogen on Si(111)1×1 surfaces. In the low-coverage model, called the monohydride phase or Si(111):H, it is assumed that a single hydrogen atom sits on top of each surface Si atom, thus saturating all dangling bonds. In the high-coverage model, designated as the trihydride phase or Si(111):SiH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> , SiH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> radicals are bonded to the surface Si atoms. Due to the radically different atomic structures, the theoretical spectra of the two phases show striking differences. A comparison of the theoretical spectra with the ultraviolet photoemission spectra taken during hydrogen chemisorption on the quenched Si(111)1×1 surface clearly shows that at low coverages the monohydride is formed, while at high coverages the trihydride phase is formed. Formation of the monohydride phase is expected on simple chemical and structural considerations, and it has been observed on other Si surfaces. However, formation of the trihydride phase is unique to Si(111)1×1 and as such, it has important implications regarding the structure and stability of clean Si(111)1×1.