Extended Hu ¨ckel, DFT, and ab initio MP2 calculations have been carried out to rationalize the unprecedented structural characteristics of the recently synthesized complex (µ-η 1 -S 2 ) 3 (Fe-TACN) 2 (TACN ) triazacyclononane). The orbital interaction diagram between the metal-macrocycle dimer and the three disulfide ligands accounts for some of the observed properties of the complex: diamagnetism, existence of an Fe-Fe single bond, nucleophilicity of the terminal sulfur atoms. The unprecedented occurrence of a M 2 S 6 core, as the very unusual µ-η 1 coordination of the S 2 ligands, however, requires further analysis. It was assumed that the key to the structural singularities of this complex should be sought in the network of intramolecular H‚‚‚S bonds revealed by the crystallographic analysis and involving all six NH groups and all three terminal S atoms. We therefore report the first quantitative theoretical investigation of the energetics of intramolecular H‚‚‚S bonds. Geometry optimizations have been carried out by means of the Density Functional Theory (DFT) on two configurations of (µ-η 1 -S 2 ) 3 (Fe-TACN) 2 deduced one from another by inverting the pyramidality at the proximal sulfur atoms. The experimental conformation 1, characterized by six "strong" N-H‚‚‚S bonds (d H‚‚‚S ) 2.31 Å), is more stable by 10.0 kcal‚mol -1 than the hypothetic structure 2 with "weak" hydrogen bonds (d H‚‚‚S ) 2.65 Å). Replacing persulfide by sulfoxide ligands leads to a similar energy difference (11.4 kcal‚mol -1 ), despite the well-documented tendency to obtain stronger H bonds with oxygen than with sulfur. Those results are rationalized by means of a systematic investigation, at the DFT and MP2 levels, of the N-H‚‚‚S and N-H‚‚‚O interactions in the model systems C 2 H 4 SX‚‚‚HNH 2 (X ) S, O). The strength of the N-H‚‚‚X interaction is shown to be highly dependent on the directionality of the hydrogen bond characterized by the angle θ ) H-X-S. For X ) S, the optimal interaction is obtained for θ ∼ 80°, which almost exactly reproduces the angular parameter optimized in 1 (76.7°). For X ) O, the interaction is most favorable for higher values of θ (∼115°) which cannot be obtained in the hypothetic compound (µη 1 -SO) 3 (Fe-TACN) 2 because of structural constraints. Finally, varying the H‚‚‚X distance in the models shows that those interactions are extremely far-reaching. The energy difference between conformations 1 and 2 then accounts for only a small part of the global stabilization assigned to the hydrogen bond network, which could hence represent the key to the stabilization of the Fe 2 S 6 core.
Environmental health studies commonly quantify subjects' pollution exposure in their neighborhood. How this neighborhood is defined can vary, however, leading to different approaches to quantification whose impacts on exposure levels remain unclear. We explore the relationship between neighborhood definition and exposure assessment. NO2, benzene, PM10 and PM2.5 exposure estimates were computed in the vicinity of 10,825 buildings using twelve exposure assessment techniques reflecting different definitions of "neighborhood". At the city scale, its definition does not significantly influence exposure estimates. It does impact levels at the building scale, however: at least a quarter of the buildings' exposure estimates for a 400 m buffer differ from the estimated 50 m buffer value (±1.0 μg/m(3) for NO2, PM10 and PM2.5; and ±0.05 μg/m(3) for benzene). This variation is significantly related to the definition of neighborhood. It is vitally important for investigators to understand the impact of chosen assessment techniques on exposure estimates.
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