Synthesis of a molecular Mo2Fe6S9 cluster with the topology of the PN cluster of nitrogenase by rearrangement of an edge-bridged Mo2Fe6S8 double cubane

The structures of the P cluster and cofactor cluster of nitrogenase are well-defined crystallographically. They have been obtained only by biosynthesis; their chemical synthesis remains a challenge. Synthetic routes are sought to the P cluster in the P(N) state in which two cuboidal Fe(3)S(3) units are connected by a mu(6)-S atom and two Fe-(mu(2)-S(Cys))-Fe bridges. A reaction scheme affording a Mo(2)Fe(6)S(9) cluster in molecular form having the topology of the P(N) cluster has been devised. Reaction of the single cubane [(Tp)MoFe(3)S(4)Cl(3)](1)(-) with PEt(3) gives [(Tp)MoFe(3)S(4)(PEt(3))(3)](1+) (2), which upon reduction with BH(4)(-) affords the edge-bridged all-ferrous double cubane [(Tp)(2)Mo(2)Fe(6)S(8)(PEt(3))(4)] (4) (Tp = tris(pyrazolylhydroborate(1-)). Treatment of 4 with 3 equiv of HS(-) produces [(Tp)(2)Mo(2)Fe(6)S(9)(SH)(2)](3)(-) (7) as the Et(4)N(+) salt in 86% yield. The structure of 7 is built of two (Tp)MoFe(3)(mu(3)-S)(3) cuboidal fragments bridged by two mu(2)-S atoms and one mu(6)-S atom in an arrangement of idealized C(2) symmetry. The cluster undergoes three one-electron oxidation reactions and is oxidatively cleaved by p-tolylthiol to [(Tp)MoFe(3)S(4)(S-p-tol)(3)](2)(-) and by weak acids to [(Tp)MoFe(3)S(4)(SH)(3)](2-). The cluster core of 7 has the bridging pattern [Mo(2)Fe(6)(mu(2)-S)(2)(mu(3)-S)(6)(mu(6)-S)](1+) with the probable charge distribution [Mo(3+)(2)Fe(2+)(5)Fe(3+)S(9)](1+). Cluster 7 is a topological analogue of the P(N) cluster but differs in having two heteroatoms and two Fe-(mu(2)-S)-Fe instead of two Fe-(mu(2)-S(Cys))-Fe bridges. A best-fit superposition of the two cluster cores affords a weighted rms deviation in atom positions of 0.38 A. Cluster 7 is the first molecular topological analogue of the P(N) cluster. This structure had been prepared previously only as a fragment of complex high-nuclearity Mo-Fe-S clusters.     

On [Fe4S4]2+ -(mu2-SR)-M II bridge formation in the synthesis of an A-cluster analogue of carbon monoxide dehydrogenase/acetylcoenzyme A synthase

The construction of a synthetic analogue of the A-cluster of carbon monoxide dehydrogenase/acetylcoenzyme synthase, the site of acetylcoenzyme A formation, requires as a final step the formation of an unsupported [Fe(4)S(4)]-(mu(2)-SR)-Ni(II) bridge to a preformed cluster. Our previous results (Rao, P. V.; Bhaduri, S.; Jiang, J.; Holm, R. H. Inorg. Chem. 2004, 43, 5833) and the work of others have addressed synthesis of dinuclear complexes relevant to the A-cluster. This investigation concentrates on reactions pertinent to bridge formation by examining systems containing dinuclear and mononuclear Ni(II) complexes and the 3:1 site-differentiated clusters [Fe(4)S(4)(LS(3))L'](2-) (L' = TfO(-) (14), SEt (15)). The system 14/[{Ni(L(O)-S(2)N(2))}M(SCH(2)CH(2)PPh(2))](+) results in cleavage of the dinuclear complex and formation of [{Ni(L(O)-S(2)N(2))}Fe(4)S(4)(LS(3))]- (18), in which the Ni(II) complex binds at the unique cluster site with formation of a Ni(mu(2)-SR)(2)Fe bridge rhomb. Cluster 18 and the related species [{Ni(phma)}Fe(4)S(4)(LS(3))](3)- (19) are obtainable by direct reaction of the corresponding cis-planar Ni(II)-S(2)N(2) complexes with 14. The mononuclear complexes [M(pdmt)(SEt)]- (M = Ni(II), Pd(II)) with 14 in acetonitrile or Me(2)SO solution react by thiolate transfer to give 15 and [M(2)(pdmt)(2)]. However, in dichloromethane the Ni(II) reaction product is interpreted as [{Ni(pdmt)(mu(2)-SEt)}Fe(4)S(4)(LS(3))](2-) (20). Reaction of Et(3)NH(+) and 15 affords the double cubane [{Fe(4)S(4)(LS(3))}(2)(mu(2)-SEt)](3-) (21). Cluster 18 contains two mutually supportive Fe-(mu(2)-SR)-Ni(II) bridges, 19 exhibits one strong and one weaker bridge, 20 has one unsupported bridge (inferred from the (1)H NMR spectrum), and 21 has one unsupported Fe-(mu(2)-SR)-Fe bridge. Bridges in 18, 19, and 21 were established by X-ray structures. This work demonstrates that a bridge of the type found in the enzyme A-clusters is achievable by synthesis and implies that more stable, unsupported single thiolate bridges may require reinforcement by an additional covalent linkage between the Fe(4)S(4) and nickel-containing components. (LS(3) = 1,3,5-tris((4,6-dimethyl-3-mercaptophenyl)thio)-2,4,6-tris(p-tolylthio)benzene(3-); L(O)-S(2)N(2) = N,N'-diethyl-3,7-diazanonane-1,9-dithiolate(2-); pdmt = pyridine-2,6-methanedithiolate(2-); phma = N,N'-1,2-phenylenebis(2-acetylthio)acetamidate(4-); TfO = triflate.).     

Spectroscopic and photophysical properties of hexanuclear rhenium(III) chalcogenide clusters

The electronic, vibrational, and excited-state properties of hexanuclear rhenium(III) chalcogenide clusters based on the [Re(6)(mu(3)-Q)(8)](2+) (Q = S, Se) core have been investigated by spectroscopic and theoretical methods. Ultraviolet or visible excitation of [Re(6)Q(8)](2+) clusters produces luminescence with ranges in maxima of 12 500-15 100 cm(-)(1), emission quantum yields of 1-24%, and emission lifetimes of 2.6-22.4 microseconds. Nonradiative decay rate constants and the luminescence maxima follow the trend predicted by the energy gap law (EGL). Examination of 24 clusters in solution and 14 in the solid phase establish that exocluster ligands engender the observed EGL behavior; clusters with oxygen- or nitrogen-based apical ligands achieve maximal quantum yields and the longest lifetimes. The excited-state decay mechanism was investigated by applying nonradiative decay models to temperature-dependent emission experiments. Solid-state Raman spectra were recorded to identify vibrational contributions to excited-state deactivation; spectral assignments were enabled by normal coordinate analysis afforded from Hartree-Fock and DFT calculations. Excited-state decay is interpreted with a model where normal modes largely centered on the [Re(6)Q(8)](2+) core induce nonradiative relaxation. Hartree-Fock and DFT calculations of the electronic structure of the hexarhenium family of compounds support such a model. These experimental and theoretical studies of [Re(6)Q(8)](2+) luminescence provide a framework for elaborating a variety of luminescence-based applications of the largest series of isoelectronic clusters yet discovered.     

Imine Derivatives of Fumaraldehyde From Oxidation of A β-Aziridinyl Alcohol

Oxidation of a β-aziridinyl alcohol with tetrapropylammonium perruthenate yields a pyrrole and two unusual imine derivatives of fumaraldehyde.     

The Preparation of Substituted Hydroxyphenyl-pyridyl-ethanols and α-Hydroxyphenyl-α-methylpyridineethanols by the Condensation of 2-, 3-, or 4-Picolyllithium with Select Hydroxy-benzaldehydes and 4-Hydroxyacetophenone

2-, 3-, or 4-Picolyllithium was prepared in excess lithium diiso-propylamide and condensed with several hydroxy-benzaldehydes and 4-hydroxy-acetophenone to afford substituted hydroxyphenyl-pyridyl-ethanols and α-hydroxyphenyl-α-methylpyridineethanols. In two instances. 3-picolyllithium condensed with aldehydes to presumably form the hydroxyphenyl-pyridyl-ethanol, which underwent linear dehydration to the substituted pyridyl-ethylenyl-phenol.     

Extending the hydrophobic cavity of β-cyclodextrin results in more negative heat capacity changes but reduced binding affinities

The formation of inclusion complexes of hydroxypropylated β-cyclodextrins (CDs) with three bile salts are investigated to shed light on the role played by the hydroxypropyl (HP) substituents. The HP-chains are situated at the rim of the CD and may thus extend the hydrophobic cavity of the CD. Calorimetric titrations in a broad temperature range and molecular dynamics simulations confirm previous speculations that the HP-chains cause an increase in dehydrated nonpolar surface area upon formation of the complexes. This additional burial of nonpolar surface area, 12–16 Å² per HP-chain according to the MD simulations, results in more negative values of ΔC _p °, which are in quantitative agreement with what is expected for hydrophobic dehydration. Although these observations support the picture of an extended hydrophobic cavity, HPβCD complexes were less stable than their unsubstituted counterparts. This indicates that increased hydrophobic contacts are not always accompanied by increased binding strength. The linear dependence of ΔC _p °, ΔH° and ΔS° on the number of HP-chains give rise to isoentropic and isoenthalpic temperatures at which ΔH° and ΔS° are independent of the number of HP-chains on the host CD (but depend on the type of bile salt). Interestingly, these convergence temperatures are close to what is observed for unfolding of proteins and may be a common feature of hydrophobic dehydration.     

A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

Variational inequality theory facilitates the formulation of equilibrium problems in economic networks. Examples of successful applications include models of supply chains, financial networks, transportation networks, and electricity networks. Previous economic network equilibrium models that were formulated as variational inequalities only included linear constraints; in this case the equivalence between equilibrium problems and variational inequality problems is achieved with a standard procedure because of the linearity of the constraints. However, in reality, often nonlinear constraints can be observed in the context of economic networks. In this paper, we first highlight with an application from the context of reverse logistics why the introduction of nonlinear constraints is beneficial. We then show mathematical conditions, including a constraint qualification and convexity of the feasible set, which allow us to characterize the economic problem by using a variational inequality formulation. Then, we provide numerical examples that highlight the applicability of the model to real-world problems. The numerical examples provide specific insights related to the role of collection targets in achieving sustainability goals.