On outer automorphism groups of coxeter groups

Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ ₁ andΠ ₂ any two bases of the root system ofW, thenΠ ₂ = ±ωΠ ₁ for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett. This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

THE MOLECULAR WEIGHT OF HAEMATOPORPHYRIN DERIVATIVE, ITS GEL COLUMN FRACTIONS and SOME OF ITS COMPONENTS IN AQUEOUS SOLUTION

Abstract— The average molecular weights of haematoporphyrin derivative (HPD), the fractions of HPD that can he obtained by gel chromatography and of purified haematoporphyrin and protoporphyrin in aqueous solution have been determined by ultracentrifugation. The results show that HPD contains polymeric material with the excluded fraction from the gel column (HPD aggregate) having an average molecular weight of greater than 20000. The two remaining gel column fractions of HPD have lower molecular weights and their similarity indicates that these fractions do not separate because of molecular weight differences. Purified haematoporphyrin has a comparatively low molecular weight in aqueous solution but the data is not capable of discriminating between monomer, dimer or slightly higher oligomer. In contrast, protoporphyrin sediments to the bottom of the centrifuge tube under the conditions of sedimentation equilibrium indicating that it has an average molecular weight considerably greater than that of HPD aggregate.     

Ground vs. excited state electron transfer: adsorbed monolayers and trimers in solution

Transient emission spectroscopy has been used to probe the rate of photoinduced electron transfer between metal centres within a novel trimeric complex [[Os(bpy)2(bpe)2][Os(bpy)2Cl]2]4+, where bpy is 2,2'-bipyridyl and bpe is trans-1,2-bis-(4-pyridyl)ethylene. Transient emission experiments on the trimer, and on [Os(bpy)2 (bpe)2]2+ in which the [Os(bpy)2 Cl]+ quenching moieties are absent, reveal that the rate of photoinduced electron transfer (PET) across the bpe bridge is 1.3 +/- 0.1 x 10(8) s(-1). Investigations into the driving forces for oxidation and reduction of the electronically excited state within the trimer indicate that quenching of the [Os(bpy)2 (bpe)2]2+ centre within the trimer involves electron transfer from the [bpe Os(bpy)2 Cl]+ centres to the electronically excited state with a driving force of -0.3 eV. Monolayers of the complex, [Os(bpy)2 bpe pyridine]2+, have been formed by spontaneous adsorption onto platinum microelectrodes and used to probe the dynamics of electron transfer across the trans-1,2-bis-(4-pyridyl)ethylene bridge in the ground state. These monolayers are stable and exhibit well defined voltammetric responses for the Os2+/3+ redox reaction. Cyclic voltammograms recorded at high scan rates can be accurately modelled according to a non-adiabatic electron transfer model based on the Marcus theory using a standard heterogeneous electron transfer rate constant, k(o), of 3.1 +/- 0.2 x 10(4) s(-1) and a reorganization energy of 0.4 +/- 0.1 eV. This rate constant is a factor of approximately two orders of magnitude smaller than that found for photoinduced electron transfer across the same bpe bridge for identical driving forces. This significant difference is interpreted in terms of both the nature of the orbitals involved in electrochemically and optically driven electron transfer, as well as the strength of electronic coupling between two molecular components as opposed to a molecular component and a metal electrode.