Encapsulation of metal cations and anions within the cavity of bis(1,4,7-triazacyclononane) receptors

The synthesis and characterisation of a new bis([9]aneN3) ligand (L4) containing two [9]aneN3 macrocyclic moieties separated by a 2,6-dimethylenepyridine unit is reported. A potentiometric and 1H NMR study in aqueous solution reveals that ligand protonation occurs on the secondary amine groups and does not involve the pyridine nitrogen. The coordination properties toward Cu(II), Zn(II), Cd(II) and Pb(II) were studied by means of potentiometric and UV spectrophotometric measurements. The ligand can form mono- and binuclear complexes in aqueous solution. In the 1 : 1 complexes, the metal is sandwiched between the two [9]aneN3 moieties and the pyridine N-donor is coordinated to the metal, as actually shown by the crystal structure of the compound [ZnL4](NO3)2.CH3NO2. L4 shows a higher binding ability for Cd(II) with respect to Zn(II), probably due to a better fitting of Cd(II) ion inside the cavity generated by the two facing [9]aneN3 units. The formation of binuclear complexes is accompanied by the assembly of OH-bridged M2(OH)x (x = 1-3) clusters inside the cavity defined by the two facing [9]aneN3 units, and pyridine is not involved in metal coordination. A potentiometric and (1)H NMR study on the coordination of halogenide anions by L4 and its structural analogous L3 in which the two [9]aneN3 units are separated by a shorter quinoxaline linkage, shows that bromide is selectively recognised by L4, while chloride is selectively bound by L3. Such a behaviour is discussed in terms of dimensional matching between the spherical anions and the cavities generated by the two [9]aneN3 units of the receptors.     

Self-healing umbrella sampling: a non-equilibrium approach for quantitative free energy calculations

We propose a new approach for the umbrella sampling method in molecular dynamics simulations of complex systems. An accelerated sampling of the slow degrees of freedom is achieved by generating a single self-adaptive trajectory that tends to span uniformly the reaction coordinate using a time dependent bias potential derived from the preceding history of the system. To show the convergent behavior and the efficiency of the method, we present the free energy surface of alanine dipeptide in water as a function of the backbone dihedral angles.     

Rotational invariance and double frustration in the structures of gold clusters growing around the F(s)-defected MgO (100) surface

The interaction of small gold clusters (Au(n), n = 1-4, 20) and a gold monolayer with the MgO (100) surface surrounding a neutral oxygen vacancy (F(s) center) is investigated using density-functional (DF) calculations. It is found that the presence of the defect modifies the interaction of gold not only with the vacancy itself, but also with the oxygen and magnesium atoms around it by increasing both the adhesion energy and the equilibrium bond distances. This is at variance with the interaction of metal atoms with the regular MgO (100) surface or the F(s) defect itself, in which an increase of the adhesion energy is associated with a shortening of the metal-surface distance. The resulting double frustration and cylindrical invariance of the metal-surface interaction cause small gold clusters growing around an F(s) nucleation center to be highly fluxional in terms both of rotational freedom and of multiple competing structural motifs. Fragmentation energies of the gold clusters are also discussed, finding that the lowest-energy pathway corresponds to the detachment of a dimer.     

Thermodynamics, structure, and dynamics in room temperature ionic liquids: the case of 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF6])

A detailed investigation of the phase diagram of 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF(6)]) is presented on the basis of a wide set of experimental data accessing thermodynamic, structural, and dynamical properties of this important room temperature ionic liquid (RTIL). The combination of quasi adiabatic, continuous calorimetry, wide angle neutron and X-ray diffraction, and quasi elastic neutron scattering allows the exploration of many novel features of this material. Thermodynamic and microscopic structural information is derived on both glassy and crystalline states and compared with results that recently appeared in the literature allowing direct information to be obtained on the existence of two crystalline phases that were not previously characterized and confirming the view that RTILs show a substantial degree of order (even in their amorphous states), which resembles the crystalline order. We highlight a strong connection between structure and dynamics, showing the existence of three temperature ranges in the glassy state across which both the spatial correlation and the dynamics change. The complex crystalline polymorphism in [bmim][PF(6)] also is investigated; we compare our findings with the corresponding findings for similar RTILs. These results provide a strong experimental basis for the exploration of the features of the phase diagram of RTILs and for the further study of longer alkyl chain salts.     

Existence of tangent lines to Carnot–Carathéodory geodesics

We show that length minimizing curves in Carnot–Carathéodory spaces possess at any point at least one tangent curve (i.e., a blow-up in the nilpotent approximation) equal to a straight horizontal line.     

Eine Bemerkung über die Funktionalgleichungen der isomorphen Abbildung

Ohne Zusammenfassung     

3D model of rigid block with a rectangular base subject to pulse-type excitation

A model of 3D rigid body with a rectangular base, able to rock around a side or a vertex of the base is developed. Eccentricity of the center of mass with respect to the geometrical center of the body is also considered. The equations of motion are obtained through the general balance principle. A one-sine pulse base excitation is applied to the body in different directions. The analyses are conducted with the aim to highlight the role of the period, the amplitude and the direction of the external excitation. In significant ranges of the previous parameters, the results obtained with a bi-dimensional model, that does not consider the 3D rocking motions on a vertex of the base, are not in favor of safety. It is found, in fact, that in several conditions the overturning of the 3D block takes place for amplitudes of excitation smaller than those able to overturn the 3D block.