Mn12O12(OMe)2(O2CPh)16(H2O)2]2- single-molecule magnets and other manganese compounds from a reductive aggregation procedure

A new synthetic procedure has been developed in Mn cluster chemistry involving reductive aggregation of permanganate (MnO4-) ions in MeOH in the presence of benzoic acid, and the first products from its use are described. The reductive aggregation of NBu(n)4MnO4 in MeOH/benzoic acid gave the new 4Mn(IV), 8Mn(III) anion [Mn12O12(OMe)2(O2CPh)16(H2O)2]2-, which was isolated as a mixture of two crystal forms (NBu(n)4)2[Mn12O12(OMe)2(O2CPh)16(H2O)2].2H2O.4CH2Cl2 (1a) and (NBu(n)4)2[Mn12O12(OMe)2(O2CPh)16(H2O)2].2H2O.CH2Cl2 (1b). The anion of 1 contains a central [Mn(IV)4(mu3-O)2(mu-O)2(mu-OMe)2]6+ unit surrounded by a nonplanar ring of eight Mn(III) atoms that are connected to the central Mn4 unit by eight bridging mu3-O2- ions. This compound is very similar to the well-known [Mn12O12(O2CR)16(H2O)4] complexes (hereafter called "normal Mn12"), with the main difference being the structure of the central cores. Longer reaction times (approximately 2 weeks) led to isolation of polymeric [Mn(OMe)(O2CPh)2]n2, which contains a linear chain of repeating [Mn(III)(mu-O2CPh)2(mu-OMe)Mn(III)] units. The chains are parallel to each other and interact weakly through pi-stacking between the benzoate rings. When KMnO4 was used instead of NBu(n)4MnO4, two types of compounds were obtained, [Mn12O12(O2CPh)16(H2O)4] (3), a normal Mn12 complex, and [Mn4O2(O2CPh)8(MeOH)4].2MeOH (4.2MeOH), a new member of the Mn4 butterfly family. The cyclic voltammogram of 1 exhibits three irreversible processes, two reductions and one oxidation. One-electron reduction of 1 by treatment with 1 equiv of I- in CH2Cl2 gave (NBu(n)4[Mn12O12(O2CPh)16(H2O)3].6CH2Cl2 (5.6CH2Cl2), a normal Mn12 complex in a one-electron reduced state. The variable-temperature magnetic properties of 1, 2, and 5 were studied by both direct current (dc) and alternating current (ac) magnetic susceptibility measurements. Variable-temperature dc magnetic susceptibility studies revealed that (i) complex 1 possesses an S = 6 ground state, (ii) complex 2 contains antiferromagnetically coupled chains, and (iii) complex 5 is a typical [Mn12]- cluster with an S = 19/2 ground state. Variable-temperature ac susceptibility measurements suggested that 5 and both isomeric forms of 1 (1a,b) are single-molecule magnets (SMMs). This was confirmed by the observation of hysteresis loops in magnetization vs dc field scans. In addition, 1a,b, like normal Mn12 clusters, display both faster and slower relaxing magnetization dynamics that are assigned to the presence of Jahn-Teller isomerism.     

Cationic fullerenes are effective and selective antimicrobial photosensitizers

Fullerenes are soccer ball-shaped molecules composed of carbon atoms, and, when derivatized with functional groups, they become soluble and can act as photosensitizers. Antimicrobial photodynamic therapy combines a nontoxic photosensitizer with harmless visible light to generate reactive oxygen species that kill microbial cells. We have compared the antimicrobial activity of six functionalized C(60) compounds with one, two, or three hydrophilic or cationic groups in combination with white light against gram-positive bacteria, gram-negative bacteria, and fungi. After a 10 min incubation, the bis- and tris-cationic fullerenes were highly active in killing all tested microbes (4-6 logs) under conditions in which mammalian cells were comparatively unharmed. These compounds performed significantly better than a widely used antimicrobial photosensitizer, toluidine blue O. The high selectivity and efficacy exhibited by these photosensitizers encourage further testing for antimicrobial applications.     

Imidoylketene-alpha-oxoketenimine and alpha-oxoketene-alpha-oxoketene rearrangements. 1,3-shifts of substituted phenyl groups

1,3-phenyl shifts interconvert imidoylketenes 1 and alpha-oxoketenimines 2 and, likewise, alpha-oxoketenes 3 automerize by this 1,3-shift. These rearrangements usually take place in the gas phase under conditions of flash vacuum thermolysis. Energy profiles calculated at the B3LYP/6-31G(d,p) and B3LYP/6311 + G(3df,2p)//B3LYP/6-31G(d,p) levels demonstrate that electron donating substituents (D) in the migrating phenyl group and electron withdrawing ones (W) in the non-migrating phenyl group, can stabilise the transition states TS1 and TS2 to the extent that activation barriers of ca. 100 kJ mol(-1) or less are obtained; i.e. enough to make these reactions potentially observable in solution at ordinary temperatures. The calculated transition state energies DeltaG(TS1) show an excellent correlation with the Hammett constants sigma(p)(W) and sigma(p+)(D).     

A Relativistic Hidden-Variable Interpretation for the Massive Vector Field Based on Energy-Momentum Flows

This paper is motivated by the desire to formulate a relativistically covariant hidden-variable particle trajectory interpretation of the quantum theory of the vector field that is formulated in such a way as to allow the inclusion of gravity. We present a methodology for calculating the flows of rest energy and a conserved density for the massive vector field using the time-like eigenvectors and eigenvalues of the stress-energy-momentum tensor. Such flows may be used to define particle trajectories which follow the flow. This work extends our previous work which used a similar procedure for the scalar field. The massive, spin-one, complex vector field is discussed in detail and the flows of energy-momentum are illustrated in a simple example of standing waves in a plane.     

Smoothness and absolute convergence of Fourier series in compact totally disconnected groups

In this paper we study in the context of compact totally disconnected groups the relationship between the smoothness of a function and its membership in the Fourier algebra $\text{G}$G. Specifically, we define a notion of smoothness which is natural for totally disconnected groups. This in turn leads to the notions of Lipshitz condition and bounded variation. We then give a condition on α which if satisfied implies Lip_α(G) ? $\text{R}$(G). On certain groups this condition becomes: $\text{α >}\text{1}\text{2}$ (Bernstein's theorem). We then give a similar condition on α which if satisfied implies that Lip_α(G) ∈ BV(G) ? $\text{R}$(G). On certain groups this condition becomes: α > 0 (Zygmund's theorem). Moreover we show that $\text{α >}\text{1}\text{2}$ is best possible by showing that $\text{Lip}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(G)}$ ? $\text{R}$(G).     

Monotone norms and tensor products

Various refinements of orthant monotonicity for norms are studied. A partial order is induced in the tensor product of two partially ordered vector spaces. The induced norm in the tensor product is shown to be orthant monotone in certain cases.     

Mechanics on manifolds and the incorporation of spin into Nelson's Stochastic mechanics

Nelson's theory of universal Brownian motion is generalized to manifold-valued processes with Hamiltonian of the form H=(p–A) ²+. It is shown that a spin model of Bopp & Haag is such a process. We show that, as the radius of the sphere of this model approaches zero, we recover the Pauli equation. We analyze further the case of no external field, singling out a continuous random variable which we call the angular momentum and showing that this random variable has the quantum mechanical expectation values. We also prove an ergodic theorem to the effect that the average value of the angular momentum equals its time average along trajectories.