Quantum chemical modeling of electron‐deficient hollow Tl_kPb_12–k and Tl_kBi_20–k shells and related endohedral complexes (k = 1; 2)

Abstract

The equilibrium structural parameters, symmetry groups, and dipole moments of the free hollow electron-deficient TlBi 19 , Tl 2 Bi 18 , p-, m-, o-Tl 2 Pb 10 shells and the endohedral (He, Ne)

1H,4H‐1,4‐diborabuckminsterfullerene with pyridine molecules and ytterbium endo‐atom

“…We express the oxidation or reduction number (Ξ or -Ξ, respectively) of the X atom and the atomic group R in the XR molecule having an electric charge ξ through the populations of localized spin-orbitals (n) using formulas ( 1)-( 6) and VALENCY-22 code [22] developed with open source linear algebra libraries OpenBLAS and Armadillo and cross-platform GUI library wxWidgets.…”

“…We express the oxidation or reduction number (Ξ or –Ξ, respectively) of the X atom and the atomic group R in the XR molecule having an electric charge ξ through the populations of localized spin‐orbitals (n) using formulas (1)–(6) and VALENCY‐22 code [22] developed with open source linear algebra libraries OpenBLAS and Armadillo and cross‐platform GUI library wxWidgets. $$$$ {\Xi}_{\mathrm{X}}={\mathrm{Z}}_{\mathrm{X}}-{\sum}_{\mathrm{j}\in \mathrm{X}} Entire\left({n}_{\mathrm{j}}+\upvarepsilon \right). $$$$ $$$$ {\left(\mathbf{SPS}\right)}_{\mathrm{XX}}\ {\mathbf{C}}_{\mathrm{Xj}}={\mathbf{S}}_{\mathrm{XX}}\ {\mathbf{C}}_{\mathrm{Xj}}\ {n}_{\mathrm{j}}.$$…”