Vibrational Spectra and Quantum Chemical Calculations of the Pure and Mixed Cluster Anions [SixGe4–x]4– and [GexSn4–x]4– (x = 0–4) in Compounds with Potassium and Cesium


  • In Memory of Professor Hans Georg von Schnering


The Raman spectroscopic studies on samples with the starting compositions Cs4[Si2Ge2] and M4[Ge2Sn2] (M = K, Cs) verify unambiguously the presence of phases composed of the mixed cluster moieties [SixGe4–x]4– and [GexSn4–x]4– (x = 1–3) including the pure anions [E4]4– (E = Si, Ge, Sn). The assignment of the vibrational frequencies is supported by normal coordinate analysis (NCA). The results for the mixed cluster anions are discussed in context with their isoelectronic analogs PxAs4–x (x = 1–3) and SbP3. Using the characteristic breathing frequencies, one obtains for the ratio factor of the mixed moieties κ = ν([SixGe4–x]4–) / ν(PxAs4–x) = 0.79, which is in good agreement with the reported value of 0.77 for the pure cluster series [E4]4– (E = Si, Ge, Sn) and X4 (X = P, As, Sb). The experimental average force constants f(Si-Ge) = 1.01 Ncm–1 and f(Ge-Sn) = 0.77 Ncm–1 correspond to arithmetic mean of those obtained for the pure anions in the binaries M4E4 (M = K, Rb, Cs; E = Si, Ge, Sn). The phonon frequencies of binary M4E4 (M = K, Cs; E = Si, Ge, Sn) and ternary K4ExE4–x (E, E′ = Si, Ge or Ge, Sn, EE′, x = 1, 2, 3) were calculated by using pseudopotential electronic structure method SIESTA. Excellent agreement between the calculated and experimental frequencies was obtained for the pure binaries. The theoretical results compare also well with experimental values for the mixed series [SixGe4–x]4–, whereas for the corresponding mixed Ge-Sn species the differences between measured and calculated frequencies are greater than 10 %.