Electronic band structure and chemical bonding in trigonal Se and Te

Herein, the electronic band structure and charge density distribution are theoretically studied in trigonal Se and Te to clarify the uncertainty stemming from the different views on the types of chemical bonding in their crystals and to reconsider the role of valence s- and p-electrons in bonding. The lack of overlapping of the lower and upper bands of valence p-electrons in trigonal Se and the large band separation of valence s- and p-electrons present an opportunity to estimate the contributions of valence s- and p-electrons to the charge densities of two types of bond critical points (BCPs) in trigonal Se. Valence s-electrons and lower p-electrons significantly contribute to the charge density of BCPs of the first type, covalently connecting the nearest neighboring atoms within helical chains. In contrast, the lower and upper valence p-electrons are mainly responsible for the BCPs of the second type linking the neighboring chains in the Se and Te trigonal crystal structures. The nonlocal long-range van der Waals (vdW) correlation functional vdW-DF2, which is important for determining lattice constants, has a minimal effect on BCP parameters, which define the chemical bonding types. The exchange potential of Becke and Johnson modified by Tran and Blaha and the short-range electron–electron correlations considered in the local density approximation correctly reproduce not only the energy bandgap values but also various peculiarities in the electronic band structure of trigonal Se and Te, such as band crossings (Weyl nodes) of the valence p-electrons recently found in trigonal Te via angle-resolved photoemission spectroscopy experiments.