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Solid Sulfur Allotropes 39 Table 16 Molecular structure parameters of orthorhombic S20 [104] Point group Av. bond lengths (pm) Range Av. bond angles () Range Av. torsion angles ()a Range a Absolute values 2–C2 204.7(5) 202.3–210.4 106.5(2) 104.6–107.7 83.0(4) 66.3–89.9 two twofold in-plane axes of rotation perpendicular to another C2 axis indi- cating a molecular symmetry of D2 (see Fig. 14). The atoms are arranged in five nearly parallel planes, each plane containing four atoms. The distances between the planes are small; thus, the S20 molecule is a very flat ring. Sur- prising for an even-membered ring, there is one large bond distance (210 pm) neighbored by short bonds (202 pm) and associated with the small- est dihedral angle of the molecule (66). Therefore, the molecular symmetry is actually C2. This long bond may explain the low thermal stability of the molecule which decomposes in solution at room temperature (but not in the solid state). The molecular structure parameters are summarized in Table 16. Although the S20 rings are relatively flat the space required by the mole- cules and the unfavorable packing in the crystal result in a low density of crystalline S20. 2.2.2 Isomers of the Sulfur Homocycles Theoretical studies have demonstrated that small sulfur molecules can exist as various isomers corresponding to local minima on the potential energy hypersurface. Naturally, the S8 molecule has been studied most extensively and at the highest level of theory, and at least nine isomers have been report- ed. Both ab initio MO and density functional theory (DFT) calculations have been published [69, 79, 105]. Unfortunately, the energies obtained by DFT calculations are not very reliable in the case of sulfur-rich compounds al- though the geometries are well reproduced at the B3LYP/6–31G(2df) level, for example. In Fig. 15 are nine isomeric forms of S8 shown which represent local minima. Their relative energies are given in Table 17. The reliability of the energies in Table 17 follows from the good agree- ment between the experimental SS bond dissociation enthalpy of 150€2 kJ mol1 and the relative enthalpy calculated for the eight-atomic S8 chain in its triplet ground state which is 154 kJ mol1 at 298 K [79]. To a certain extend isomers of other sulfur rings have also been discov- ered by theoretical methods. However, as far as known the activation ener- gies for the transformation of the ground state conformation into the next most stable structure are quite high (>25 kJ mol1) [69, 105]. An exceptionPDF Image | Topics in Current Chemistry
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