Arnout Ceulemans

Symmetry-induced formation of antivortices in mesoscopic superconductors.

Recent progress in nanotechnology has stimulated interest in mesoscopic superconductors as components for quantum computing and cryoelectronics. The critical parameters for superconductivity (current and field) of a mesoscopic sample are determined by the pattern of vortices in it, which in turn is controlled by the symmetry imposed by the shape of the sample (see ref. 1 and references therein). Hitherto it has been unclear what happens when the number of vortices is not consistent with the natural symmetry. Here we show that additional vortex–antivortex pairs nucleate spontaneously so as to preserve the symmetry of the sample. For example, in a square with three vortices, the spontaneously generated pair, along with the original three vortices, distribute themselves so that the four vortices sit in the four corners, with the antivortex in the centre. The measured superconducting phase boundary (of superconducting transition temperature Tc versus magnetic field strength) is in very good agreement with the calculations, giving direct experimental evidence for these symmetry-induced vortex–antivortex pairs. Vortex entry into the sample is also changed: vortices enter a square in fours, with antivortices generated to preserve the imposed vorticity. The symmetry-induced nucleation of antivortices is not restricted to superconductors, but should also apply to symmetrically confined superfluids and Bose–Einstein condensates.

Magnetic dipole transitions as standards for Judd–Ofelt parametrization in lanthanide spectra

It is shown that the sum of the intensities for magnetic dipole transitions between crystal‐field components of two free‐ion levels in lanthanide spectra is almost independent of the symmetry of the environment. A mean theoretical sum value of 18×10−7D2, 94×10−7D2, and 9×10−7D2 for, respectively, the 5 D 1←7 F 0, 5 D 0←7 F 1, and 5 D 2←7 F 1 dipole strengths has been found. Experimental values of the dipole strength for Eu3+ in different lattices support within reasonable limits the theoretically derived sum rule. We therefore propose to use these magnetic dipole transitions in the Eu3+ spectrum as standards for further Judd–Ofelt parametrization.

Room-temperature magnetic anisotropy of lanthanide complexes: A model study for various coordination polyhedra

The dependence of the room-temperature magnetic anisotropy Δχ of lanthanide complexes on the type of the coordination polyhedron and on the nature of the lanthanide ion is quantitatively analyzed in terms of a model approach based on numerical calculations. The aim of this study is to establish general regularities in the variation of the sign and magnitude of the magnetic anisotropy of lanthanide complexes at room-temperature and to estimate its maximal value. Except for some special cases, the variation of the sign of the magnetic anisotropy over the series of isostructural lanthanide complexes is found to obey a general sign rule, according to which Ce(III), Pr(III), Nd(III), Sm(III), Tb(III), Dy(III), and Ho(III) complexes have one sign of Δχ and Eu(III), Er(III), Tm(III), and Yb(III) complexes have the opposite sign. Depending on the specific coordination polyhedron, a maximal magnetic anisotropy is observed for Tb(III), Dy(III), or Tm(III) complexes, and its absolute value can reach 50 000×10−6 cm3 ...

The Jahn–Teller instability of fivefold degenerate states in icosahedral molecules

The linear H⊗(g⊕2h) Jahn–Teller problem, relevant to the instability of icosahedral molecules in fivefold degenerate states, is analyzed in detail for the first time. The method of the isostationary function is used to identify all the extrema of the corresponding potential energy surface. Depending on one single mode‐splitting parameter, two different coupling regimes are possible, favoring either pentagonal or trigonal minima. The saddle points on interconversion paths between equivalent minima are identified and the topology of the low‐energy regions of the surface is determined. The results are found to be in agreement with the epikernel principle. In addition the symmetry characteristics of the principal warping term under the SO(5) symmetry group of electronic space are assigned.

Disk Aromaticity of the Planar and Fluxional Anionic Boron Clusters B20−/2−

The presence of excess electrons modifies the structural landscape and tends to extend the planarity of boron clusters. While the neutral B(20) is tubular, both the anion and dianion B(20)(-/2-) become planar. Geometrical features of the stable anions suggest the existence of a new type of cluster that is planar and doubly cyclic with one atom located at the center (see figure), as well as being fluxional.

The epikernel principle

An epikernel is an intermediate subgroup in the decomposition scheme of a given point group. The epikernel principle states that the preferred distortions of Jahn-Teller unstable molecules are directed towards the maximal allowed epikernels of the undistorted parent group. The group theoretical foundations of this principle are explained, and a wide variety of applications in different areas of chemistry is discussed.

The structure of jahn-teller surfaces

In chemical applications of the Jahn–Teller effect, the shape of the adiabatic potential near the instability point is of primary importance. The present article examines this shape, both in the usual representation in the space of the nuclear configurations and in the less current projective representation in the space of the electronic functions. The general structural aspects of these representations are viewed as the results of a symmetry breaking process, starting at the continuous invariance group of the degenerate coupling limit, and ending with the finite point group of the representation space. The various vibronic coupling mechanisms involved in this process are characterized by irreducible tensor functions of the full orthogonal groups. The leading tensorial rank of the unequal linear coupling mechanism is shown to be four, while the bilinear coupling mechanism also involves an irreducible component of the sixth rank. This tensorial analysis provides a grouptheoretical foundation for the recent...

On the magnetic anisotropy of lanthanide-containing metallomesogens

A general theoretical model of the origin of the magnetic anisotropy in paramagnetic metal-containing liquid crystals is developed. General relations between the molecular magnetic anisotropy of mesogenic lanthanide complexes and the macroscopic magnetic anisotropy of these liquid crystals in the mesophase are obtained. The net magnetic anisotropy of a real metallomesogen is shown to be the result of a complex interplay between the molecular magnetic anisotropy, orientation of the long molecular axis, and disorder effects. The sign of the magnetic anisotropy Δχ depends not only on the anisotropy of the tensor of molecular magnetic susceptibility, but also on the orientation of the long molecular axis of rodlike lanthanide complexes with respect to the principal magnetic axes of the molecular tensor of magnetic susceptibility. The influence of micro- and macroscopic disorder in real liquid crystals is discussed. Numerical parametric calculations were used to rationalize the variation of the magnitude and s...

Structure-Based Site of Metabolism Prediction for Cytochrome P450 2D6

Realistic representation of protein flexibility in biomolecular simulations remains an unsolved fundamental problem and is an active area of research. The high flexibility of the cytochrome P450 2D6 (CYP2D6) active site represents a challenge for accurate prediction of the preferred binding mode and site of metabolism (SOM) for compounds metabolized by this important enzyme. To account for this flexibility, we generated a large ensemble of unbiased CYP2D6 conformations, to which small molecule substrates were docked to predict their experimentally observed SOM. SOM predictivity was investigated as a function of the number of protein structures, the scoring function, the SOM-heme cutoff distance used to distinguish metabolic sites, and intrinsic reactivity. Good SOM predictions for CYP2D6 require information from the protein. A critical parameter is the distance between the heme iron and the candidate site of metabolism. The best predictions were achieved with cutoff distances consistent with the chemistry relevant to CYP2D6 metabolism. Combination of the new ensemble-based docking method with estimated intrinsic reactivities of substrate sites considerably improved the predictivity of the model. Testing on an independent set of substrates yielded area under curve values as high as 0.93, validating our new approach.

The electronic structure of polyhex carbon tori

The π-orbital electronic structure of polyhex carbon tori constructed from bent individual single-wall nanotubes is investigated within the tight-binding approach. Analytical solutions for tori from nanotubes of arbitrary radius, length, chirality, and twisting angle are derived using simple geometrical and band-structure arguments. Vanishing of the gap between highest occupied and lowest unoccupied molecular orbitals for a torus imposes divisibility by 3 on the indices of chiral and twisting vectors, which translates into one graph-theoretical condition: a metallic polyhex torus is constructible as a leapfrog transformation of a smaller polyhex torus.