A Porphyrin Coordination Cage Assembled from Four Silver(I) Triazolyl‐Pyridine Complexes

The synthesis of a zinc(II) porphyrin 1 with four appended triazolyl–pyridine chelates is reported. Complexation of the porphyrin peripheral ligands with Ag^I ions in a 1:2 binding stoichiometry afforded quantitatively the coordination cage [Ag₄( 1 )₂]⁴⁺. The assembly and disassembly processes of the cage were investigated in solution using UV/Vis spectroscopy. The mathematical analysis of the data obtained in the UV/Vis titration of 1 with Ag^I confirmed the assembly in CH₂Cl₂/MeOH (90:10) solution of a species having a 1:2 porphyrin/silver stoichiometry and assigned to it an overall stability constant of 5.0×10²⁶ M ^?5. The use of a model system allowed an independent assessment of a microscopic binding constant value (K_m) for the interaction between the triazolyl‐pyridine ligand and Ag^I. The coincidence that existed between the K_m values extracted from the model system and the titration of 1 provided an indication of the quality and fit of the data analysis. It also allowed the calculation of the average effective molarity (EM) value for the three intramolecular processes that led to the cage assembly as 2.6 mM . Simulated speciation profiles supported the conclusion that at millimolar concentration and working under strict stoichiometric control of the silver/porphyrin ratio, the cage [Ag₄( 1 )₂]⁴⁺ was the species exclusively assembled in solution. On the other hand, when the concentration of added Ag^I was approximately 2.6 mM , 50 % of the coordination cage disassembled into open aggregates.     

Weak C-H/pi interaction participates in the diastereoselectivity of a host-guest complex in the presence of six strong hydrogen bonds

[structure: see text] We report a study of the interaction between methylmethanetriacetic acid (MMTA) and a tripodal amidopyridine receptor 1, where the geometry of the binding is in part governed by a weak C-H/pi interaction in the presence of six strong N(O)-H.O(N) hydrogen bonds. There are two possible binding geometries for the 1:1 complex 1.MMTA; combining computational and experimental evidence we demonstrate that the endo binding mode is more favorable as the result of a C-H/pi interaction.     

Self‐Sorting of Cyclic Peptide Homodimers into a Heterodimeric Assembly Featuring an Efficient Photoinduced Intramolecular Electron‐Transfer Process

We describe the thermodynamic characterisation of the self‐sorting process experienced by two homodimers assembled by hydrogen‐bonding interactions through their cyclopeptide scaffolds and decorated with Zn–porphyrin and fullerene units into a heterodimeric assembly that contains one electron‐donor (Zn–porphyrin) and one electron‐acceptor group (fullerene). The fluorescence of the Zn–porphyrin unit is strongly quenched upon heterodimer formation. This phenomenon is demonstrated to be the result of an efficient photoinduced electron‐transfer (PET) process occurring between the Zn–porphyrin and the fullerene units of the heterodimeric system. The recombination lifetime of the charge‐separated state of the heterodimer complex is in the order of 180 ns. In solution, both homo‐ and heterodimers are present as a mixture of three regioisomers: two staggered and one eclipsed. At the concentration used for this study, the high stability constant determined for the heterodimer suggests that the eclipsed conformer is the main component in solution. The application of the bound‐state scenario allowed us to calculate that the heterodimer exists mainly as the eclipsed regioisomer (75–90 %). The attractive interaction that exists between the donor and acceptor chromophores in the heterodimeric assembly favours their arrangement in close contact. This is confirmed by the presence of charge‐transfer bands centred at 720 nm in the absorption spectrum of the heterodimer. PET occurs in approximately 75 % of the chromophores after excitation of both Zn–porphyrin and fullerene chromophores. Conversely, analogous systems, reported previously, decorated with extended tetrathiafulvalene and fullerene units showed a PET process in a significantly reduced extent (33 %). We conclude that the strength (stability constant (K)×effective molarity (EM)) of the intramolecular interaction established between the two chromophores in the Zn–porphyrin/fullerene cyclopeptide‐based heterodimers controls the regioisomeric distribution and regulates the high extent to which the PET process takes place in this system.     

Embeddings of SL(2; ?) into the cremona group

Geometric and dynamic properties of embeddings of SL(2; ℤ) into the Cremona group are studied. Infinitely many nonconjugate embeddings that preserve the type (i.e., that send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many nonconjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2; ℤ), preserves an elliptic curve and all its elements of infinite order are hyperbolic.     

Dynamics and kinetics of the S + HO2 reaction: A theoretical study

We report a quasi‐classical trajectory study of the S + HO₂ reaction using a previously reported global potential energy surface for the ground electronic state of HSO₂. Zero‐point energy leakage is approximately accounted for by using the vibrational energy quantum mechanical threshold method. Calculations are carried out both for specific ro‐vibrational states of the reactants and thermalized ones, with rate constants being reported as a function of temperature. The results suggest that the title reaction is capture type, with OH and SO showing as the most favorable products. The internal energy distribution of such products and the reaction mechanism are also investigated. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 533–540, 2008     

The Dirichlet Problem for the Total Variation Flow

We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L¹ for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions.     

Nature of Noncovalent Carbon‐Bonding Interactions Derived from Experimental Charge‐Density Analysis

In an effort to better understand the nature of noncovalent carbon‐bonding interactions, we undertook accurate high‐resolution X‐ray diffraction analysis of single crystals of 1,1,2,2‐tetracyanocyclopropane. We selected this compound to study the fundamental characteristics of carbon‐bonding interactions, because it provides accessible σ holes. The study required extremely accurate experimental diffraction data, because the interaction of interest is weak. The electron‐density distribution around the carbon nuclei, as shown by the experimental maps of the electrophilic bowl defined by a (CN)₂C?C(CN)₂ unit, was assigned as the origin of the interaction. This fact was also evidenced by plotting the Δ²ρ(r) distribution. Taken together, the obtained results clearly indicate that noncovalent carbon bonding can be explained as an interaction between confronted oppositely polarized regions. The interaction is, thus electrophilic–nucleophilic (electrostatic) in nature and unambiguously considered as attractive.     

Quantification of aromaticity in oxocarbons: the problem of the fictitious "nonaromatic" reference system

Despite the extensive research reported in the literature, the concept of aromaticity has eluded rigorous quantification. The main reason for this undesirable reality is the fact that aromaticity is a differential property. While bond orders, atomic charges and electronegativity differences are properties of the molecule under analysis, the aromaticity concept often refers to the difference between some property of the molecule and that of an artificial "nonaromatic" reference system. A rigorous definition of such a reference system is non-existing and therefore constituting the main barrier to obtain a satisfactory quantification of the aromatic concept. Oxocarbon acids and their anions are examples where the criteria of aromaticity that use reference systems are unsuccessful, only NICS criterion gives satisfactory results. Wiberg bond indexes and 17O NMR chemical shifts are also useful to study such compounds.