Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational

We prove that the Reidemeister zeta functions of automorphisms of crystallographic groups with diagonal holonomy ?₂ are rational. As a result, we obtain that Reidemeister zeta functions of automorphisms of almost-crystallographic groups up to dimension 3 are rational.     

A footnote to The crisis in contemporary mathematics

We examine the preparation and context of the paper “The Crisis in Contemporary Mathematics” by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as ‘a debasement of meaning.’ The ‘debasement’ comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the ‘debasement’ comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.     

Effects of Lewis acids on higher order, mixed cuprate couplings

The presence of BF₃·Et₂O in reactions of R₂Cu(CN)Li₂ and R_T(2-thienyl)Cu(CN)Li₂ with epoxides and ,β-unsaturated ketones leads to dramatic enhancements in reaction rates and/or product yields relative to those observed in the absence of this lewis Acid.     

Synthetic studies toward phenoxan analogs

We developed two reactions needed for a total synthesis of phenoxan, a naturally occurring compound with anti-HIV activity. In this Note, we further examined these two issues: metallation of a 2-methyl-oxazole and formation of a pyran-4-one. We employed these methods for the preparation of a phenoxan analog.     

Stereochemistry of epimeric 1-hydroxy-N-methylquinolizidinium iodides

The methiodides of epimeric 1-hydroxy, 1-hydroxy-1-phenyl, and 1-hydroxy-1-methylquinolizidines were prepared from their respective bases. The previously described but not separated epimeric 1-hydroxy-1-methylquinolizidines were prepared and their configurations elucidated by the use of nuclear magnetic resonance (NMR) and infrared data. Structural assignments of the quinolizidinium iodides were made on the basis of NMR data.     

External electric field will control the selectivity of enzymatic-like bond activations

Controlling the selectivity of a chemical reaction is a Holy Grail in chemistry. This paper reports theoretical results of unprecedented effects induced by moderately strong electric fields on the selectivity of two competing nonpolar bond activation processes, C-H hydroxylation vs C=C epoxidation, promoted by an active species that is common to heme-enzymes and to metallo-organic catalysts. The molecular system by itself shows no selectivity whatsoever. However, the presence of an electric field induces absolute selectivity that can be controlled at will. Thus, the choice of the orientation and direction of the field vis-à-vis the molecular axes drives the reaction in the direction of complete C-H hydroxylation or complete C=C epoxidation.     

Is the ruthenium analogue of compound I of cytochrome p450 an efficient oxidant? A theoretical investigation of the methane hydroxylation reaction

High-valent metal-oxo complexes catalyze C-H bond activation by oxygen insertion, with an efficiency that depends on the identity of the transition metal and its oxidation state. Our study uses density functional calculations and theoretical analysis to derive fundamental factors of catalytic activity, by comparison of a ruthenium-oxo catalyst with its iron-oxo analogue toward methane hydroxylation. The study focuses on the ruthenium analogue of the active species of the enzyme cytochrome P450, which is known to be among the most potent catalysts for C-H activation. The computed reaction pathways reveal one high-spin (HS) and two low-spin (LS) mechanisms, all nascent from the low-lying states of the ruthenium-oxo catalyst (Ogliaro, F.; de Visser, S. P.; Groves, J. T.; Shaik, S. Angew. Chem. Int. Ed. 2001, 40, 2874-2878). These mechanisms involve a bond activation phase, in which the transition states (TS's) appear as hydrogen abstraction species, followed by a C-O bond making phase, through a rebound of the methyl radical on the metal-hydroxo complex. However, while the HS mechanism has a significant rebound barrier, and hence a long lifetime of the radical intermediate, by contrast, the LS ones are effectively concerted with small barriers to rebound, if at all. Unlike the iron catalyst, the hydroxylation reaction for the ruthenium analogue is expected to follow largely a single-state reactivity on the LS surface, due to a very large rebound barrier of the HS process and to the more efficient spin crossover expected for ruthenium. As such, ruthenium-oxo catalysts (Groves, J. T.; Shalyaev, K.; Lee, J. In The Porphyrin Handbook; Biochemistry and Binding: Activation of Small Molecules, Vol. 4; Kadish, K. M., Smith, K. M., Guilard, R., Eds.; Academic Press: New York, 2000; pp 17-40) are expected to lead to more stereoselective hydroxylations compared with the corresponding iron-oxo reactions. It is reasoned that the ruthenium-oxo catalyst should have larger turnover numbers compared with the iron-oxo analogue, due to lesser production of suicidal side products that destroy the catalyst (Ortiz de Montellano, P. R.; Beilan, H. S.; Kunze, K. L.; Mico, B. A. J. Biol. Chem. 1981, 256, 4395-4399). The computations reveal also that the ruthenium complex is more electrophilic than its iron analogue, having lower hydrogen abstraction barriers. These reactivity features of the ruthenium-oxo system are analyzed and shown to originate from a key fundamental factor, namely, the strong 4d(Ru)-2p(O,N) overlaps, which produce high-lying pi(Ru-O), sigma(Ru-O), and sigma(Ru-N) orbitals and thereby to lead to a preference of ruthenium for higher-valent oxidation states with higher electrophilicity, for the effectively concerted LS hydroxylation mechanism, and for less suicidal complexes. As such, the ruthenium-oxo species is predicted to be a more robust catalyst than its iron-oxo analogue.