ChemInform Abstract: s‐Tetrazine as Ligand for Monomeric and Bridged Macrocyclic Metal Complexes.

Abstract

The bridged complexes (Ia) and (Ic) are prepared by reaction of the monomeric phthalocyaninato‐ or naphthalocyaninatometal compounds with a small excess of s‐tetrazine at 70 ° or 50 °C in CHCl3 for one or two days.

Torus Quantization for Spinning Particles

“…For the spin rotation angle α L we find α L = 2π for any spherically symmetric system [14]. Intriguingly, for the relativistic Kepler problem α r is also given by 2π!…”

“…Condition (14) plays the same role as the condition {A j , A k } = 0 does in the scalar case; it guarantees that all skew products Y cl t j commute [14]. Under these conditions we are able to prove the following theorem.…”

“…We remark that analogous quantization conditions can be derived for the Pauli equation [14]. There we can also choose to describe particles with arbitrary spin s ∈ 1 2 N 0 by replacing the Pauli matrices σ with a higher dimensional irreducible representation of su (2).…”

“…The proof of this theorem will be given elsewhere [14]. The geometry of the the invariant sets T θ is illustrated in figure 1: a Liouville-Arnold torus is sketched as a 2-torus; at two different points we show the attached sphere together with the local axes n and a corresponding parallel of latitude.…”

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

“…Further conditions needed to arrive at (14) are hyperbolicity of the translational dynamics and the mixing property of the skew product of translational and spin dynamics, see [7] for details. We remark that the last condition can be weakened to ergodicity; this result will be presented elsewhere [16]. Introducing an auxiliary variable s ′ , the contributions r ν (s, I), ν = 0, can be written as derivatives,…”