We report density functional calculations of the electronic structure, Fermi surface, phonon spectrum and electron--phonon coupling for newly discovered superconductor LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$. Significant similarity between LaO$_{0.5}$F$_{0.5}
$BiS$_{2}$ and LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is found, i.e. there is a strong Fermi surface nesting at ($pi $,$pi $,0), which results in unstable phonon branches. Combining the frozen phonon total energy calculations and an anharmonic oscillator model, we find that the quantum fluctuation prevents the appearance of static long--range order. The calculation shows that LaO$_{0.5}$F$_{0.5}$BiSe$_{2}$ is highly anisotropic, and same as LaO$_{0.5}$F$_{0.5}$BiS$_{2}$, this compound is also a conventional electron-phonon coupling induced superconductor.
The nature of the stereochemically active lone pair has long been in debate. Here, by application of our recently developed orbital selective external potential (OSEP) method, we have studied the microscopic mechanism of stereochemically active lone
pairs in various compounds. The OSEP method allows us to shift the energy level of specific atomic orbital, therefore is helpful to identify unambiguously the role of this orbital to the chemical and physical properties of the system we are interested in. Our numerical results, with compelling proofs, demonstrate that the on-site mixing of cation valence s orbital with the nominally empty p orbitals of the same subshell is crucial to the formation of lone pair, whereas the anion p orbital has only small effect. Our detailed investigation of Sn and Pb monochalcogenides show that structures of these systems have significant effects on lone pairs. In return, the formation of lone pair, which can be controlled by our OSEP method, could result in structural instabilities of Sn and Pb monochalcogenides.
