Short-chain model of chemisorption: Exact and approximate results

The binding energy of an adatom to a chain consisting of three atoms is obtained exactly by computer as a function of adatom Coulomb repulsion, adatom-substrate hopping, and substrate bandwidth. Three simple approximations are also plotted: (i) weak-binding limit, in which the binding energy is given by the expectation value of the adatom-bulk hopping Hamiltonian calculated in second-order perturbation theory; (ii) rebonded surface complex, in which the adatom forms a diatomic molecule with its nearest neighbor in the chain, and the dimer rebonds perturbatively to the indented chain; and (iii) Hartree-Fock, both restricted and unrestricted. The first two schemes can be joined smoothly by hand, and the resulting curve is much better than Hartree-Fock. The physics of all three cases is carefully studied. An appendix treats the surface diatom case of just a single bulk atom. Here the exact solution and unrestricted Hartree-Fock can be performed analytically. Comparison is also given with Brenig and Schönhammer's solution based on Green's-function formalism with matrix self-energy corrections.