Application of the DV-Xα cluster method to calculations of the electronic structure of silicate and phosphate glasses

The electronic structure of simple silicate and phosphate clusters, which are assumed to exist in rapidly quenched Li₂O---SiO₂ and Li₂O---P₂O₅ glasses, has been calculated by the discrete variational (DV)-Xα molecular orbital method. The calculations have been carried out for several sizes of clusters, namely, tetrahedral units (SiO₄⁴⁻ and PO₄³⁻), dimers (Si₂O₇⁶⁻ and P₂O₇⁴⁻), and trimers (Si₃O₉⁶⁻ and P₃O₉³⁻). For both systems the valence electronic state is characterized by an occupied valence band, with O 2p components, and an unoccupied band of Si or P orbitals, separated by an energy gap. The energy gap between the highest occupied molecular orbital (HOMO) and the loest unoccupied molecular orbital (LUMO) decreases with increasing cluster size. A mulliken population analysis show that the negative effective charge on the non-bridging oxygens is decreased with decreasing energy gap. The bond order of the Si---O and P---O bonds, and thus the strength of these bonds, is increased with increasing cluster size.