Anomalous (S2 → S0) luminescence of some derivatives of triphenylmethane dyes and their complexes with rare earth metals

Anomalous S₂ → S₀ fluorescence and T₂ → S₀ phosphorescence have been found in several triphenylmethane derivatives. This phenomenon can be explained by a large energy gap between the S₂ and S₁ levels, approximately 14000 cm^?1. Some of the investigated compounds exhibit also a normal long-wave fluorescence in spite of the fact, that the S₂ ? S₁ energy gap does not change significantly. However, in these cases absorption spectra reveal a high oscillator strength of the S₁ → S₀ transition. The coordination of a lanthanide ion quenches in several cases the normal S₁ → S₀ fluorescence whereas the S₂ → S₀ one is not affected significantly.     

Some remarks on dynamical semigroups

We deal with time evolution of a finite quantum system given by a dynamical semigroup Λ_t. For the semigroup we define and give some properties of the convex Λ_t-invariant subset of states “pathological” in some aspect evolving in strictly reversible manner independently of the stochastic surroundings of the system.     

Ellipsoidal space-times,sources for the Kerr metric

The paper develops a systematic derivation of the Kerr metric and its possible sources in a clear geometric manner. It starts with a concise account of previous attempts at constructing an interior Kerr solution. Then a treatment of stationary-axisymmetric spacetimes, specially fitted to the needs of the following analysis, is presented. A new notion of an ellipsoidal space-time is introduced: it is a space-time in which local rest 3-spaces of some observers split naturally into congruences of concentric and coaxial ellipsoids. It is shown that these 3-spaces are natural spaces to consider the ellipsoidal figures of equilibrium. The investigation is carried out in detail for axially symmetric oblate confocal ellipsoids, but possible generalizations are indicated. The Kerr metric is found to be an ellipsoidal space-time of this special kind. Some remarks concerning an (unfound) explicit interior Kerr solution conclude the paper.     

Refinement of the crystal structure of acetylacetonatodicarbonylrhodium(I)

The structure of acetylacetonatodicarbonylrhodium(I), Rh(acac)(CO)₂, has been refined from three-dimensional X-ray diffractometer data. The complex crystallises in the triclinic space groupP¯1 with two molecules in a unit cell of dimensionsa = 6.5189(5),b = 7.7614(8),c = 9.2049(12)Å, = 106.04(1), = 91.15(1), = 100.21(1) °. Full-matrix least-squares refinement, using 1456 independent reflections, has reachedR = 0.038.The rhodium atom has a square-planar coordination with two Rh-O(acac) distances of 2.040 and 2.044Å, and two Rh-C(carbonyl) distances both equal to 1.831Å, the O-Rh-O angle is 90.8 ° and the C-Rh-C angle is 88.9 °. All twelve non-hydrogen atoms are closely planar, with an average deviation of 0.003Å, and a maximum deviation of 0.006Å, from the least-squares plane through the molecule. A second non-crystallographic plane of symmetry bisects the molecule, which therefore has essentiallymm2 (C _2v ) point symmetry. The molecules stack in such a way that the rhodium atoms of neighbouring molecules occupy the two remaining pseudo-octahedral positions, with Rh...Rh distances of 3.253 and 3.271Å.     

Gaussian geminal basis set optimization with crude SCF reference state

Gaussian geminal basis functions for second-order correlation energy calculations according to the Sinanogˇlu method are optimized with reference to rather crude SCF functions. The optimized geminal basis set is then used in a one-step calculation of the correlation energy with respect to the near-Hartree-Fock reference State. The numerical results for the beryllium atom indicate the usefulness of the proposed technique.