Coinage Metal–Sulfur Complexes: Stability on Metal(111) Surfaces and in the Gas Phase

Abstract

We provide a comprehensive theoretical assessment at the level of density functional theory (DFT) of the stability of various coinage metal-sulfur complexes, both in the gas phase and also for the complexes adsorbed on the (111) surface of the same coinage metal. Our primary interest lies in the latter where earlier scanning tunneling microscopy (STM) experiments were interpreted to suggest the existence of adsorbed S-decorated metal trimers, sometimes as a component of more complex adlayer structures. Recent STM studies at 5 K directly observed other isolated adsorbed metal-sulfur complexes. For these adsorbed species, we calculate various aspects of their energetics including a natural measure of stability corresponding to their formation energy from sulfur adsorbed on terraces and from metal atoms that are in thermal equilibrium with the substrate. From this perspective, our DFT analysis shows that all of Ag2S3, Ag3S3, and many larger complexes on Ag(111) are strongly stable, Cu2S3 is stable, and some larger complexes are marginally stable on Cu(111), but only Au4S4 on Au(111) is stable. Results are consistent with STM observations for Cu(111) and Ag(111) surfaces but appear to deviate slightly for Au(111). A systematic analysis relating stability in the gas phase with that of adsorbed species is achieved within the framework of Hess's law. This analysis also unambiguously elucidates various energetic contributions to stability.

Sulfur adsorption on coinage metal(100) surfaces: propensity for metal–sulfur complex formation relative to (111) surfaces

“…6 A recent more comprehensive DFT study considered nine distinct M-S complexes on M(111) for coinage metals M = Cu, Ag, and Au, as is appropriate for development of a comprehensive and reliable kinetic model for enhanced mass transport. 18 The above observations motivate the comprehensive DFT study presented in this paper of M-S complexes on M(100) surfaces for M = Cu, Ag, and Au at very low coverages of S. In this regime, behavior is not impacted by ordered adsorbate structures or reconstructions which can occur for higher S coverages. Of particular interest is comparison of behavior to that on M(111) surfaces.…”

“…See ref. 18 for more details. We found excellent consistency for the PBE functional between the PW and GTO basis set analyses when using large quadruple zeta basis sets for the latter.…”

“…Indeed, our recent analysis of M-S complexes on M(111) indicates a trend of decreasing chemical potential at 0 K for increasing Ag-S complex size consistent with the observation of large complexes. 18 To assess behavior for T 4 0, Russell et al 15 used a kinetic 'polymerization' model to argue that the equilibrium population, P n , of linear aggregates of n ''monomer units'' with neighboring attractive bond strength f 4 0 satisfies P n E r exp[+f/(k B T)]P nÀ1 where the monomer density r { 1 increases with y S . This result supports the picture that upon increasing T, there is a switch from dominance of large complexes to small complexes.…”

“…Rather than the surface atomization energy described above, generally the most appropriate measure of the stability of adsorbed complexes is their formation energy from S adatoms on terraces, and from M atoms extracted from the substrate (e.g., via detachment of M atoms at kink sites along step edges). 6,8,13,18,25 Schematically, this reaction is represented as…”

“…With the use of free energies and chemical potentials in eqn (3) rather than just energies at T = 0 K), there is no ambiguity regarding the choice of reference states. 18 M is regarded as being equilibrated with the substrate, so that m M is the same for isolated adatoms, kink and step edge atoms, and bulk atoms. Thus, m M can be determined from bulk metal calculations.…”