A novel carbon/germanium conic structure: theoretical study using density functional theory

Abstract

Complete optimization without geometry constraints and calculation of electronic properties of novel conic molecules such as $\hbox {C}_{n}\hbox {H}_{n}\hbox {Ge}_{n}\hbox {H}_{n}$ and $\hbox {C}_{n}\hbox {Ge}_{n}\hbox {H}_{n}$, with $n = 3{-}8$, was carried out with density functional theory using B3LYP and PBE1PBE functionals with 6-31$+$G(d, p) and cc-pVTZ basis sets. Calculations of formation energy showed stable and peculiar geometric and electronic properties. All carbon and germanium atoms for $\hbox {C}_{n}\hbox {H}_{n}\hbox {Ge}_{n}\hbox {H}_{n}$ compounds, which are $\hbox {sp}^{\mathrm {3}}$-hybridized, were located in the same plane. This finding contradicts the notions of hybridization known to date. For these new molecular compounds, quantum descriptors such as electrochemical potential ($\mu$), chemical hardness ($\eta$), electrophilicity index ($\omega$), dipole moment, energy gap and the shape of the molecular orbital have been calculated in addition to nucleus independent chemical shifts, polarizability and harmonic oscillator model of aromaticity which are important tools for determining the aromaticity of the studied compounds. Thus, the aim of the work is, on the one hand, to propose new stable molecular structures formed of carbon and germanium atoms, and on the other hand, to challenge our understanding of hybridization and aromaticity notion.