Perdew-Wang 91 (PW91) generalized gradient approximation $^{25}$. The wave functions were expanded in a plane wave basis with an energy cutoff of 400 eV. The k points were obtained from Monkhorst-Pack scheme $^{26}$, and 3 × 3 × 1 k point mesh was for the geometry opti- mization. The optimization of the atomic geometry was performed via conjugate-gradient minimization of the total energy with respect to the atomic coordinates. The supercell consisted of five layers with each layer having 12 Au atoms. The Au atoms in the top three atomic layers are allowed to relax, while those in the bottom two layers are fixed to simulate bulk-like termination $^{27}$. The vacuum region comprises ten atomic layers, which exceeds substantially the extension of the thioglycolic acid molecule $^{21}$. For charged systems, a uniform compensating background is incorporated to maintain the charge neutrality of the supercell $^{28}$. The harmonic approximation was applied to calculate the Hessian matrix and vibrational frequencies. We calculated the gold lattice constant and found it to agree with the experimental value 29 within 2.1%. In this section, we discuss the adsorption pattern of the HSCH$_{2}$COOH, SCH$_{2}$COOH, HSCH$_{2}$COO − , and SCH$_{2}$COO − on the Au(111) substrate, respectively. The adsorption energy of the system is defined as E$_{ads}$ = E$_{adsorbate}$ + E$_{Au}$$_{(111)}$ - E$_{adsorbate}$$_{+}$$_{Au}$$_{(111)}$ . The symbol top-fcc (or top-hcp) in the following tables represents the S atom being on the atop site of the gold atom, but leaned toward the fcc (or hcp) hollow center, and anologously for the notations bri-fcc, bri-hcp, etc. The units for the bond length and adsorption energy are Angstrom ( ˚ A ) and eV. First, let us begin with our analysis with the geometries and adsorption energies of the optimized structures for the thioglycolic acid on the Au(111) surface at the coverage of 0.25 ML, as displayed in Table I. Here 1.00 ML means one sulfur per three gold atoms, and 0.25ML stands for one thioglycolic acid on a gold surface with twelve gold atoms. In Table I, the entries θ , tilt direct and d$_{S}$$_{−}$$_{Au}$ refer to the polar angle between the normal vector of the surface and the S-C2 direction, the Au(111) surface region towards which the S-C2 is 4 III. RESULTS AND DISCUSSION A. The HSCH$_{2}$COOH molecule on the Au(111) surface