The effect of chlorine (Cl) chemisorption on the energetics and atomic structure of the Cu(001) surface over a wide range of chlorine pressures and temperatures has been studied using equilibrium ab initio atomistic thermodynamics to elucidate the formation of cuprous chloride (CuCl) as part of the Deacon reaction on copper metal. The calculated surface free energies show that the 1/2 monolayer (ML) c(2 × 2)-Cl phase with chlorine atoms adsorbed at the hollow sites is the most stable structure for a wide range of Cl chemical potential, in agreement with experimental observations. It is also found that at very low pressure and exposure, but elevated temperature, the 1/9 ML and 1/4 ML phases become the most stable. By contrast, a high coverage of Cl does not lead to thermodynamically stable geometries. The subsurface adsorption of Cl atoms, however, dramatically increases the stability of the 1 ML and 2 ML adsorption configurations providing a possible pathway for the formation of the bulk-chloride surface phases in the kinetic regime.

Density functional theory calculations have been performed to study the combined interaction of oxygen and chlorine with the Cu(100) surface. We found the presence of atomic chlorine increases the stability of molecular oxygen adsorption, and that the barrier required to dissociate the oxygen molecule in the presence of chlorine is three times larger than the dissociation barrier of molecular oxygen on the clean Cu(100) surface. In addition, chlorine monoxide was generated on the surface when molecular oxygen was adsorbed horizontally into a hollow site immediately adjacent to atomic chlorine. Our calculations indicate that while chlorine is easily adsorbed dissociatively on the clean Cu(100) surface, it is stable in the molecular form in the presence of atomic oxygen. The presence of chlorine leads to the production of subsurface atomic oxygen and enables an oxygen atom to go into the Cu bulk with a small activation energy barrier.

The interaction of atomic chlorine with the Cu(110) surface is studied using density functional theory and ab initio atomistic thermodynamics. The calculated surface free energies of different Cl/Cu(110) structures as a function of chlorine chemical potential show that under ultrahigh-vacuum conditions, the c(2 Â 2)-Cl structure is the most stable for coverages up to and including 1/2 ML, whereas the (2 Â 3)-Cl and (1 Â 4)-Cl configurations are the most stable at 2/3 and 3/4 ML coverages, respectively. It is also shown that although there are thermodynamically stable geometries for high (1 ML) coverage of Cl, these structures are only kinetically accessible. The morphology of a copper nanostructure terminated by low-index Cu surfaces in a chlorine environment has been predicted using a Wulff construction. It is found that the (111) facets dominate at low chlorine concentration, but as the chlorine concentration is increased, the (100) planes become predominant, resulting in a cubical crystal shape.

We use computational methods to find the irreducible 2-modular characters of Conway's second group. Three of these are produced by probabilistic methods, which means that we have very strong evidence that they are correct, but we do not yet have a complete proof.

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