David Hull

Journal of Optimization Theory and Applications -     

George Leitmann

Journal of Optimization Theory and Applications -     

Fluorescent macrocyclic chemosensor for Zn(II) detection at alkaline pH values

ABSTRACT

The new macrocyclic ligand L (28,29-dimethoxy-27-oxa-8,11,14,17,25,26-hexaazatetracyclo[22.2.1.1(2,6).1(19,23)]nonacosa-2,4,6(28),19,21,23(29),24,26(1)-octaene) has been synthesised. It contains a tetramine chain and the 2,5-bis(2-methoxy-3-metyl-phenyl)-1,3,4-oxadiazole (PPD-OMe) chromophore, acting as coordinating and sensing units, respectively.

The fluorescent emission of L depends on the pH being highly fluorescent at pH = 2 and not emitting from pH >10. The studies highlighted that L is a PET mediated emitting chemosensor, being the PET effect regulated by the degree of the tetraamine protonation.

L coordinates metal ions (Cu(II), Zn(II) and Cd(II)) in water giving rise to an OFF-ON fluorescent response for the presence of Zn(II) ion thus signalling its presence in the medium. This response is particularly notable at pH = 9 allowing to extend the Zn(II) sensing also in the alkaline pH field.     

pH-Dependent Hydration Change in a Gd-Based MRI Contrast Agent with a Phosphonated Ligand

The heptadentate ligand L was shown to form an extremely stable Gd complex at neutral pH with a pGd value of 18.4 at pH 7.4. The X-ray crystal structures of the complexes formed with Gd and Tb displayed two very different coordination behaviors being, respectively, octa- and nonacoordinated. The relaxometric properties of the Gd complex were studied by field-dependent relaxivity measurements at various temperatures and by ¹⁷O NMR spectroscopy. The pH-dependence of the longitudinal relaxivity profile indicated large changes around neutral pH leading to a very large value of 10.1 mm ⁻¹⋅s⁻¹ (60 MHz, 298 K) at pH 4.7. The changes were attributed to an increase of the hydration number from one water molecule in basic conditions to two at acidic pH. A similar trend was observed for the luminescence of the Eu complex, confirming the change in hydration state. DOSY experiments were performed on the Lu analogue, pointing to the absence of dimers in solution in the considered pH range. A breathing mode of the complex was postulated, which was further supported by ¹H and ³¹P NMR spectroscopy of the Yb complex at varying pH and was finally modeled by DFT calculations.     

The Skew Normal multivariate risk measurement framework

Computational Management Science - In this paper, we consider a random vector $$X=\left( X_1,X_2\right) $$ following a multivariate Skew Normal distribution and we provide an explicit formula for...     

Spin polarisation in dual catalysts for the oxygen evolution and reduction reactions

Strongly correlated catalysts can be understood from precise quantum approximations. Incorporating properly electronic correlations thus let’s define Spin rules in catalysis, opening a new door towards optimum compositions for the most important reactions for a sustainable future.     

Dedication

Journal of Optimization Theory and Applications -     

Relaxation Dynamics and Magnetic Anisotropy in a Low‐Symmetry DyIII Complex

The magnetic behaviour of a Dy(LH)₃ complex (LH^? is the anion of 2‐hydroxy‐N′‐[(E)‐(2‐hydroxy‐3‐methoxyphenyl)methylidene]benzhydrazide) was analysed in depth from both theoretical and experimental points of view. Cantilever torque magnetometry indicated that the complex has Ising‐type anisotropy, and provided two possible directions for the easy axis of anisotropy due to the presence of two magnetically non‐equivalent molecules in the crystal. Ab initio calculations confirmed the strong Ising‐type anisotropy and disentangled the two possible orientations. The computed results obtained by using ab initio calculations were then used to rationalise the composite dynamic behaviour observed for both pure Dy^III phase and Y^III diluted phase, which showed two different relaxation channels in zero and non‐zero static magnetic fields. In particular, we showed that the relaxation behaviour at the higher temperature range can be correctly reproduced by using a master matrix approach, which suggests that Orbach relaxation is occurring through a second excited doublet.     

Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.