Structural and electronic properties of Genm− and KGen− Zintl anions (n=3–10;m=2–4) from density functional theory

Structural optimizations and frequency analyses have been performed on free Genm− and KGen− (n=3–10, m=2–4) Zintl anions and ionization potentials and electron affinities calculated for KGen using the density functional theory (DFT) of Becke’s three-parameter hybrid functional with the Perdew/Wang 91 expression. The DFT results obtained for small clusters (n=3–5) are further checked with both the second-order Møller–Plesset perturbation theory (MP2) and the configuration interaction calculations with all single and double substitutions from the Hartree–Fock reference determinant (CISD). Free Gen2− anions are found to share the same geometries as naked Zintl anions observed in solids with a systematical expansion in bond lengths within about 5%. Intensive searches indicate that two isomers, a tricapped trigonal prism (D3h) and a slightly distorted tricapped trigonal prism (C2v), exist for Ge92− and Ge93−, while nido-Ge94− clearly favors the monocapped antisquare prism (C4v) structure. HOMO-LUMO energy gaps >2.23 eV are obtained for Genm− series at the DFT level, except Ge93− which has a much narrower energy gap of 1.16 eV. The calculated Gibbs free energy change of Ge92−+Ge94−=2 Ge93− conversion reaction involving nonagermanides has the value of ΔG°=−2.91×105 J mol−1, providing the first quantum chemistry evidence that the geometrically deduced mixed valent couple of Ge92− and Ge94− in a previous study is thermodynamically unstable compared to two Ge93− anions. The calculated stabilization energies of Gen2−, Gen−, and Gen exhibit similar variation trends, clearly indicating a maximum at n=7, a minimum at n=8, and an obvious recovery at n=9 and 10. The calculated normal vibrational frequencies reproduce the six observed Raman peaks of naked Ge52− with an averaged discrepancy of 11 cm−1. Face-capped or edge-capped deltahedral structures are predicted for binary KGen− anions and KGen and K2Gen neutrals. The magic numbers at n=5, 9, and 10 obtained in both stabilization energies and ionization potentials well reproduce the abundance distributions of KGen− observed in time-of-flight mass spectra. The validity of the Zintl–Klemm–Busmann principle in KGen and K2Gen neutrals is supported by the finding that sizable electron transfers from K atoms to Gen nuclei occur in these clusters and the Gen nuclei approach corresponding structures of free closo-Gen2− anions.