Analysis of paramagnetic NMR spectra of triple-helical lanthanide complexes with 2,6-dipicolinic acid revisited: a new assignment of structural changes and crystal-field effects 25 years later

Variable-temperature (1)H and (13)C NMR measurements of the D(3)-symmetrical triple-helical complexes [Ln(L1-2H)(3)](3)(-) (L1 = pyridine-2,6-dicarboxylic acid; Ln = La-Lu) show evidence of dynamic intermolecular ligand-exchange processes whose activation energies depend on the size of the metal ion. At 298 K, the use of diastereotopic probes in [Ln(L3-2H)(3)](3)(-) (L3 = 4-ethyl-pyridine-2,6-dicarboxylic acid) shows that fast intramolecular P <==> M interconversion between the helical enantiomers occurs on the NMR time scale. Detailed analyses of the paramagnetic NMR hyperfine shifts according to crystal-field independent techniques demonstrate the existence of two different helical structures, one for large lanthanides (Ln = La-Eu) and one for small lanthanides (Ln = Tb-Lu), in complete contrast with the isostructurality proposed 25 years ago. A careful reconsideration of the original crystal-field-dependent analysis shows that an abrupt variation of the axial crystal-field parameter A(0)2 parallels the structural change leading to some accidental compensation effects that prevent the detection of structural variations according to the classical one-nucleus method. Crystal structures in the solid state and density functional theory calculations in the gas phase provide structural models that rationalize the paramagnetic NMR data. A regular triple-helical structure is found for small lanthanides (Ln = Tb-Lu) in which the terdentate chelating ligands are rigidly tricoordinated to the metals. A flexible and distorted structure is evidenced for Ln = La-Eu in which the central pyridine rings interact poorly with the metal ion. The origin of the simultaneous variation of structural parameters and crystal-field and hyperfine constants near the middle of the lanthanide series is discussed together with the use of crystal-field-independent techniques for the interpretation of paramagnetic NMR spectra in axial lanthanide complexes.     

The first self-assembled trimetallic lanthanide helicates driven by positive cooperativity

The segmental tris-tridentate ligand L7 reacts with stoichiometric quantities of Ln(III) (Ln=La-Lu) in acetonitrile to give the complexes [Ln(2)(L7)(3)](6+) and [Ln(3)(L7)(3)](9+). Formation constants point to negligible size-discriminating effects along the lanthanide series, but Scatchard plots suggest that the self-assembly of the trimetallic triple-stranded helicates [Ln(3)(L7)(3)](9+) is driven to completion by positive cooperativity, despite strong intermetallic electrostatic repulsions. Crystallization provides quantitatively [Ln(3)(L7)(3)](CF(3)SO(3))(9) (Ln=La, Eu, Gd, Tb, Lu) and the X-ray crystal structure of [Eu(3)(L7)(3)](CF(3)SO(3))(9).(CH(3)CN)(9).(H(2)O)(2) (Eu(3)C(216)H(226)N(48)O(35)F(27)S(9), triclinic, P1, Z=2) shows the three ligand strands wrapped around a pseudo-threefold axis defined by the three metal ions rigidly held at about 9 A. Each metal ion is coordinated by nine donor atoms in a pseudo-trigonal prismatic arrangement, but the existence of terminal carboxamide units in the ligand strands differentiates the electronic properties of the terminal and the central metallic sites. Photophysical data confirm that the three coordination sites possess comparable pseudo-trigonal symmetries in the solid state and in solution. High-resolution luminescence analyses evidence a low-lying LMCT state affecting the central EuN(9) site, so that multi-metal-centered luminescence is essentially dominated by the emission from the two terminal EuN(6)O(3) sites in [Eu(3)(L7)(3)](9+). New multicenter equations have been developed for investigating the solution structure of [Ln(3)(L7)(3)](9+) by paramagnetic NMR spectroscopy and linear correlations for Ln=Ce-Tb imply isostructurality for these larger lanthanides. NMR spectra point to the triple helical structure being maintained in solution, but an inversion of the magnitude of the second-rank crystal-field parameters, obtained by LIS analysis, for the LnN(6)O(3) and LnN(9) sites with respect to the parameters extracted for Eu(III) from luminescence data, suggests that the geometry of the central LnN(9) site is somewhat relaxed in solution.     

On the role of leptonic CPV phases in cLFV observables

The European Physical Journal C - We argue that high-quality data on the reaction $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ will allow one to determine the doubly-virtual form factor $$\eta...     

A possible connection between neutrino mass generation and the lightness of a NMSSM pseudoscalar

One of the interesting properties of the NMSSM is that it can accommodate a light pseudoscalar of order 10 GeV. However, such scenarios are challenged by several experimental constraints, especially those related to the fermionic decays of the pseudoscalar. In this Letter, we extend the NMSSM field content by two gauge singlets, with lepton numbers +1 and −1. This serves the twin purpose of generating neutrino masses via the inverse seesaw mechanism and keeping the option of a very light pseudoscalar experimentally viable by opening dominant invisible decay channels of the pseudoscalar which help it evade the existing bounds.     

Isoscalar NN spin-orbit potential from a Skyrme model with scalar mesons

As a first step toward circumventing the difficulty to obtain an attractive isospin-independent NN spin-orbit force from Skyrme-type models involving only pions, we investigate an improved Skyrme Lagrangian that incorporates the scalar-isoscalar meson ε which can be viewed as the cause behind the enhancement of the ππ S-wave. We find that at large distances, the main contribution to the spin-orbit potential comes from the scalar Lagrangian and it is found to be attractive. We briefly discuss how to pursue this work to finally obtain a medium-range attractive interaction.     

Impulsive semilinear neutral functional differential inclusions with multivalued jumps

In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.     

Nonlinear impulsive partial functional differential inclusions with state-dependent delay and multivalued jumps

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined impulsive semilinear functional differential inclusions with state-dependent delay in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators.