A dysprosium single molecule magnet outperforming current pseudocontact shift agents

A common criterion for designing performant single molecule magnets and pseudocontact shift tags is a large magnetic anisotropy. In this article we present a dysprosium complex chemically designed to exhibit strong easy-axis type magnetic anisotropy that is preserved in dichloromethane solution at room temperature. Our detailed theoretical and experimental studies on the magnetic properties allowed explaining several features typical of highly performant SMMs. Moreover, the NMR characterization shows remarkably large chemical shifts, outperforming the current state-of-the art PCS tags.

A robust dysprosium(iii) single molecule magnet with large uniaxial magnetic anisotropy induces pseudocontact shifts at almost doubled distance compared to standard shift agents.     

Jahn-Teller distortion and dissociation of CCl4+ by transient X-ray spectroscopy simultaneously at the carbon K- and chlorine L-edge

X-ray Transient Absorption Spectroscopy (XTAS) and theoretical calculations are used to study CCl₄⁺ prepared by 800 nm strong-field ionization. XTAS simultaneously probes atoms at the carbon K-edge (280–300 eV) and chlorine L-edge (195–220 eV). Comparison of experiment to X-ray spectra computed by orbital-optimized density functional theory (OO-DFT) indicates that after ionization, CCl₄⁺ undergoes symmetry breaking driven by Jahn–Teller distortion away from the initial tetrahedral structure (T_d) in 6 ± 2 fs. The resultant symmetry-broken covalently bonded form subsequently separates to a noncovalently bound complex between CCl₃⁺ and Cl over 90 ± 10 fs, which is again predicted by theory. Finally, after more than 800 fs, L-edge signals for atomic Cl are observed, indicating dissociation to free CCl₃⁺ and Cl. The results for Jahn–Teller distortion to the symmetry-broken form of CCl₄⁺ and formation of the Cl–CCl⁺₃ complex characterize previously unobserved new species along the route to dissociation.

Dynamics of CCl₄⁺ prepared by 800 nm strong-field ionization, as studied with X-ray transient absorption spectroscopy (XTAS) and quantum chemical calculations.     

A variational approach to chaotic dynamics in periodically forced nonlinear oscillators

We prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multibump type heteroclinic solutions to periodic orbits by the use of global variational methods.     

An identity for T-ordered exponentials with applications to quantum mechanics

The solution of the Cauchy problem for Liouville's equation φ_xy = e^φ is shown to be equivalent to the calculation of a T-ordered exponential of a two-dimensional variable matrix. This gives rise to an identity for the T-ordered exponential involving two arbitrary functions. The formalism is applied to the time evolution of a magnetic dipole in a time dependent magnetic field and to the one-dimensional Dirac equation with external potential $\text{V(x) = (n +}\text{1}\text{2}\text{)λ}$ tanh λx which is relevant for field theoretic applications. A generalization to n-dimensional matrices is also given.     

Equazioni quasi ellittiche e spaziL p, θ (ω, δ) (I)

Summary Regularity theorems inL ^{2, θ} (ω, δ) spaces are proved for weak solutions of quasielliptic differential equations. In particular, regularization results are obtained in the class of holder continuous functions (with respect to a suitable metric related to the operator). As a consequence, we obtain results and estimates in L^p andL ^{p, θ} spaces for the solution of the Dirichlet problem.

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Lavoro eseguito nell’ambito del Gruppo di Ricerca n^o 46 del Comitato per la Matematica del C N.R.