SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Approximate neutrality of large-Z ions

LetN(Z) denote the number of electrons which a nucleus of chargeZ can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove thatN(Z)/Z1 asZ.Research partially supported by the NSERC under Grant NA7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01     

V4S9Br4: a novel high-spin vanadium cluster thiobromide with square-planar metal core

The novel vanadium thiobromide, V4S9Br4, with a square-planar metal cluster core was synthesized and characterized by single-crystal X-ray diffraction, measurements of magnetic properties and the heat capacity, and DFT calculations of the electronic structure. At the room temperature, the compound displays paramagnetic properties with an independent spin on each V atom and with a weak exchange constant (J approximately 10 cm(-1)). The paramagnetic state is transformed into a low-spin state (AF-type ordering) at low temperatures. This change is accompanied by a heat-capacity anomaly. The observed magnetic and heat-capacity anomalies can be explained by the thermal excitation of electrons on the closely spaced molecular energy levels in the presence of the Jahn-Teller effect.     

Construction of multiporphyrin arrays using ruthenium and rhodium coordination to phosphines

The synthesis of linear multiporphyrin arrays with mono- and bisphosphine-substituted porphyrins as ligand donors and ruthenium(II) or rhodium(III) porphyrins as ligand acceptors is described. With appropriate amounts of the building blocks mixed, linear dimeric and trimeric arrays have been synthesized and analyzed by (1)H NMR and (31)P NMR spectroscopy. The Ru/Rh acceptor porphyrins can be located either at the periphery or in the center of the array. Likewise, the monophosphine porphyrins can be positioned at the periphery, thus allowing a high degree of freedom in the overall composition of the arrays. This way, both donor and acceptor porphyrins can act as chain extenders or terminators. One of the trimeric complexes with two nickel and one ruthenium porphyrin has also been analyzed by X-ray crystallography. Attempts have also been made to synthesize higher order arrays by mixing appropriate amounts of the porphyrins; however, from the NMR data it cannot be concluded if monodisperse five, seven, or nine porphyrin arrays are present or if the solutions are composed of a statistical mixture of smaller and larger arrays.     

Adducts of Rh2[MTPA]4 with some phosphine chalcogenides: nature of binding and ligand exchange

Adducts of four phosphine chalcogenides with the chiral dirhodium complex ([Rh-Rh]) were investigated by variable-temperature 1H and 31P NMR spectroscopy in order to compare their properties as axial ligands. Whereas the selenide (1) and the sulfide (2) are strong ligands with electrostatic attraction and, in addition, a significant orbital (HOMO-LUMO) interaction, the phosphine oxide compounds (P=O) bind primarily via electrostatic attraction and are relatively weak donors. Moreover, the overall bond strength in these adducts depends on steric congestion around the P=O group.