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22 Ralf Steudel · Bodo Eckert Table 4 Molecular structure parameters of g-S7 and d-S7 at 163 K averaged for Cs symmetry. The numbering of the atoms is shown in Fig. 3. Note that the variation of geometrical pa- rameters of S7 deviating from Cs symmetry—which is not reported here—is in most of the cases larger than the experimental errors. More detailed structural data are given in ref. [20] Site symmetry of molecule Allotrope Bond lengths (pm)a S1-S2, S1-S3 S2-S4, S3-S5 S4-S6, S5-S7 S6-S7 Bond angles at indicated atom ()b S1 S2, S3 S4, S5 S6, S7 Torsion angles ( )c S1-S2, S1-S3 S2-S4, S3-S5 S4-S6, S5-S7 S6-S7 1C1 g-S7 204.8 209.9 199.8 217.5 104.97 102.12 105.34 107.43 ,+76.67 +,107.78 ,+83.23 0.43 d-S7 205.0 210.2 199.6 218.1 106.10 102.23 105.28 107.10 ,+5.20 +,107.45 ,+84.00 +1.35 a Standard deviations of the single bond values are 0.1 pm for g-S7 and 0.3–0.4 pm for d-S7 b Standard deviations are 0.05–0.06 for g-S7 and 0.1 for d-S7 c Standard deviations are 0.06–0.07 for g-S7 and 0.1 for d-S7 The geometry of the molecules of the well characterized allotropes (a-, b-, and g-S8) is almost the same, although the bond lengths, bond angles and torsion angles are influenced by the different packing environments of the actual crystal structures. The S8 molecule has a crown-shaped, puckered conformation; the dihedral angles alternate in sign so that a zig-zag ring with point symmetry D4d is obtained (see Fig. 4). Ring closure causes the bond angles and the dihedral angles to deviate from the unstrained, free chain values. The variation of bond lengths in g-S8 is larger than in a- and b-S8, whereas the range of valence angles is about the same. The torsion an- gles in g-S8 cover a closer range than in a- and b-S8. The molecular structure data of the three allotropes of the sulfur octamer are compared in Table 5. The strain energy of the S8 ring is typically within 2–3 kJ mol1 of zero which corresponds to the stability of the crown-shaped molecule [66]. In other words, the bond angles and the dihedral angles in S8 are close to the optimum values for a sulfur ring. Eight isomers of the crown-shaped S8 ring below the radical formation (~150 kJ mol1) and several interconversion pathways of low energy isomersPDF Image | Topics in Current Chemistry
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