Studies of clusters using self-consistent field molecular orbital theory and a combination of all-electron real atoms and valence-electron model atoms

Abstract

A valence-electron theory based on model potentials for atomic cores has been developed to allow one readily to calculate for clusters such quantities as relative geometries and energies, valence orbital energies and ionization energies, charge distributions, and so on. To examine core-electron binding energies, we have extended the theory by making a composite system consisting of an all-electron real atom for the atom whose core is to be examined, while describing the remainder of the system by the valence-electron model potential theory. Some illustrations of 2p core ionization in Al 2 and Al 4 show the accuracy of the techniques for both frozen-orbital ionization (“Koopmans' theorem”) and relaxed ionic state ionization (Δ E SCF). Then we discuss the structures and both O and N 1s ionizations in AlNO and AlON, along with some chemically interesting results for NO + Al 2. Finally, some investigations of O atoms and the clusters Al, Al 2, Al 3, and Al 4 are analyzed. In OAl 2, OAl 3, and OAl 4, the most stable geometry occurs when the O “penetrates” the cluster to lie in the plane, symmetrically centered amongst the Al atoms, causing substantial lengthening of the Al-Al distance from bulk value in Al 2 and Al 3, but not in Al 4. Population analyses of the optimum planar OAl 3 and OAl 4 geometries show a transfer of about 1.4 electrons to the O 2p Orbitals from Al 3s and 3p, and indicate clearly the strong participation of the doubly degenerate O 2pσ in-surface orbitals in the clusters. Though O ls binding energies have been previously measured for Al metal exposed to oxygen, our calculations of them here are the first direct theoretical treatment they have received. For OAl 3 and OAl 4, which are minimal models for the (111) and (100) surfaces, respectively, of bulk Al, we predict fully relaxed, Hartree-Fock O ls binding energies for such clusters in the bulk metal of 531.8 and 531.7 eV, respectively. These are remarkably close to recently reported experimental values in the region 531.5–531.9 eV for modest exposure of polycrystalline Al to oxygen, and somewhat below the measured value of 532.4 eV for heavily oxidized Al, dramatically illustrating the utility of our method and indicating many similar future studies of clusters.