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Table 3 Isotopic equilibrium fractionation between molecular clusters and their corresponding aqueous solutions

From: Improved volume variable cluster model method for crystal-lattice optimization: effect on isotope fractionation factor

Cluster Calculated bond length (Å) Experimental bond length (Å) 1000lnβ (cluster, 298 K, ‰) 1000lnβ (aquocomplex, 298 K, ‰) Δ cluster-aquocomplex
(298 K, ‰)
Si–Qtz 1.63, 1.62a, 1.61b 1.61c, 1.62d 73.65 71.63 2.02 (Si isotopes)
O–Qtz 1.63 1.61c 110.31 74.26 36.05 (O isotopes)
Zn–Al LDH 2.10 2.08e 4.87 3.75 1.12 (Zn isotopes)
Cd–Cal 2.28 2.30f 2.62 \(2.88^{{\text{g}}}\)  − 0.26 (Cd isotopes)
  1. aSi–O bond length (α–quartz, Ab initio LDF theory, Purton et al. [64])
  2. bSi–O bond length (quartz, DFT calculations, He and Liu [22])
  3. cSi–O bond length (quartz, X-ray diffraction, Hazen et al. [39])
  4. dSi–O bond length (quartz, X-ray diffraction at 848 K, Kihara [48])
  5. eZn–O bond length (X-ray diffraction and EXAFS, Gou et al. [3])
  6. fCd–O bond length (EXAFS, Bailey et al. [65])
  7. gDFT calculations (He et al. [25])