Supramolecular coordination complexes as building blocks for porous and magnetic materials

In this work, new coordination polymers based on two different classes of synthons are presented. In addition, manganese-based metallacrowns of magnetic interest are studied, both in the solid state and in solution. Firstly, functionalized bispyrazolylmethane derivatives are employed as bridging ligands for the establishment of silver-based coordination polymers; the influence of the substituent groups and of the counterions on the supramolecular packing is also investigated. Secondly, the use of metallacrown (MC) complexes as building blocks for porous coordination polymers is discussed. The design of a new metallacrown species is presented, which shows the tendency of aggregating in the solid state to form coordination polymers. Two new coordination polymers are indeed reported, of which one is the first MC-based permanently porous coordination network ever presented. The solid resists solvent evacuation and exhibits gas uptake ability. Furthermore, the isolation and characterization of a new metallacryptate species based on manganese ions is described. The metal-rich structure comprises nine Mn(II)/Mn(III) ions and presents an inverse metallacrown core subunit that binds a μ3-O2- ion. The metallacryptate is isolated in high yields and stable in solution. Lastly, a family of 3d-4f heterometallic metallacrowns is characterized in solution by means of UV-Vis spectrophotometry and of paramagnetically shifted 1H-NMR. The lanthanide-induced shifts observed in the spectra are employed to describe the molecules behaviour in solution and are qualitatively related to the magnetic properties of the compounds.

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.