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128 Ralf Steudel et al. formed by direct combination of two Sn·· diradicals. The conformation of this S7=S species observed after 933 fs is, however, different from the cluster structures mentioned above [67, 68]. Nevertheless, evidence is accumulating that branched sulfur rings and chains are present in liquid sulfur as well as in sulfur vapor at high temperatures [68]. The formation of chain-like sulfur diradicals by homolytic ring opening re- actions of S8, S7, and S6 in liquid sulfur requires enthalpies of 150, 127, and 124 kJ mol1, respectively (€5 kJ mol1 each; 298 K). While the S8 value was obtained from temperature dependent ESR [16, 17] and magnetic susceptibili- ty measurements [18], the data for S6 and S7 were estimated from the S8 value using simple thermodynamic cycles and certain assumptions [71]. For com- parison, the dissociation enthalpy of the central S-S bond of chain-like organic tetrasulfanes (e.g., Me2S4) amounts to 142€16 kJ mol€1 in the gas phase [72]. Since the entropies of the chain-like sulfur molecules obtained by homolytic ring opening were not known until recently, the equilibrium concentration of such chains in liquid and gaseous sulfur could not be calculated accurately. However, it is generally believed [73] that their equilibrium concentration near 160 C becomes high enough to trigger the well-known ring-opening po- lymerization of liquid sulfur which can best be recognized from the sudden increase of the viscosity by three orders of magnitude [74]. High-level ab ini- tio MO calculations based on the G3X(MP2) method have now provided the Gibbs energy of the ring opening reaction of cyclo-S8 at 298 K as 129 kJ mol1 and DH298=154 kJ mol1 [68] in excellent agreement with the experimental data. If the temperature dependence of this enthalpy as well as mixing effects are neglected the molar ratio of catena-S8 to cyclo-S8 can be calculated as 7·1017 at 393 K (melting point of sulfur) and as 4·1010 at 718 K (boiling point) [68]. While the direct experimental evidence for such diradical-chains in liquid sulfur comes from the cited ESR spectroscopic and magnetic suscep- tibility measurements, no comparable investigations have been made in the case of sulfur vapor. Therefore, high-level ab initio MO calculations have been carried out to determine the relative energies and enthalpies of all triplet di- radical chains of molecular size 2–10 [53]. These data are given in Table 6. As expected, the homolytic ring opening of the S8 molecule requires the highest Table 6 Calculated [G3X(MP2)] energy differences (kJ mol1) between the global minimum structures and the chain-like triplet diradicals of Sn molecules (n=3–10). All species are of C2 symmetry except S3·· and S4·· which both are of C2v symmetry [53] Sn·· species S3·· S4·· S5·· S6·· S7·· S8·· S9·· S10·· DE0 DH298 DG298 96 96 92 49 50 43 109 111 99 117 120 101 135 138 121 151 154 129 134 137 115 133 136 111PDF Image | Topics in Current Chemistry
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