Chemisorption theory for metallic surfaces: Convergence of surface localized orbitals for Ti(0001) clusters

A theory for treating chemisorption on metallic surfaces has been proposed based on a large cluster model for the lattice, treated approximately from which an $N$-electron subspace for a local region is defined by a unitary, localization transformation. The local $N$-electron subspace is then treated accurately by configuration interaction as embedded in the fixed field of the interior of the lattice. Exchange energy maximization with sites on the Ti(0001) surface is examined for clusters of titanium atoms ${\mathrm{Ti}}_M$ ($M=1,10,28,30,54,84\mathrm{}$) to study the convergence of the localized-orbital description as a function of cluster size. Localized orbitals are obtained by transformation of the self-consistent-field solution and the energetics of these orbitals are examined by diagonalization of the Fock operator subject to the localization constraint. Results for one-, two-, and three-layer models show rapid convergence of the localized description with increasing cluster size in contrast to much slower convergence of the bulk description, which for clusters is strongly influenced by the ratio of boundary to interior atoms.