Using quaternions to calculate RMSD

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 x 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure.     

In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography

An ultrahigh-speed spectral domain optical coherence tomography (SD-OCT) system is presented that achieves acquisition rates of 29,300 depth profiles/s. The sensitivity of SD-OCT and time domain OCT (TD-OCT) are experimentally compared, demonstrating a 21.7-dB improvement of SD-OCT over TD-OCT. In vivo images of the human retina are presented, demonstrating the ability to acquire high-quality structural images with an axial resolution of 6 microm at ultrahigh speed and with an ocular exposure level of less than 600 microW.     

New oxidative tools for the functionalization of the cephalostatin north 1 hemisphere

Dimethyldioxirane (DMDO) C-H oxidation of ketone 17 to hemiketal 18 (82%), bis-dehydration to vinyl ether 21 (77%), and DMDO again provides C-23 axial alcohol 23 (99%). Routine processing, including a double-stereoselective Sharpless AD reaction (de >98%), gives alcohols 7 and 32. C-23 deoxy substrate 7 undergoes Suarez hypoiodite oxidative cyclization to (natural) beta spiroketal 34, but compound 32, bearing a C-23 silyl ether, generates unnatural spiroketal 33. [reaction: see text]     

Accelerating universe in two-dimensional noncommutative dilaton cosmology

We show that the phase transition from the decelerating universe to the accelerating universe, which is of relevance to the cosmological coincidence problem, is possible in the semiclassically quantized two-dimensional dilaton gravity by taking into account the noncommutative field variables during the finite time. Initially, the quantum-mechanically induced energy from the noncommutativity among the fields makes the early universe decelerate and subsequently the universe is accelerating because the dilaton driven cosmology becomes dominant later.     

In situ‐generated Ru(III)‐mediated ATRP from the polymeric Ru(III) complex in the absence of activator generation agents

Past research has examined the atom transfer radical polymerization (ATRP) with high oxidation state metal complexes and without the need for any additives such as reducing agent or free radical initiator. To extend this research, half‐metallocene ruthenium(III) (Ru(III)) catalysts were used for the polymerization of methyl methacrylate (MMA) for the first time. These catalysts were generated in situ simply by mixing phosphorus‐containing ligand and pentamethylcyclopentadienyl (Cp*) Ru(III) polymer ((Cp*RuCl₂)_n). The complexes in their higher oxidation state such as Cp*RuCl₂(PPh₃) were air‐stable, highly active, and removable catalysts for the ATRPs of MMA with both precision control of molecular weight and narrow polydispersity index. The addition of ppm amount of metal catalyst contributed to the formation of very well‐defined homopolymers and copolymers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

C60 as a chemical Faraday cage for three ferromagnetic Fe atoms

Based on calculations using density functional theory, we show that C₆₀ can act as a chemical Faraday cage in which a highly magnetic metal cluster with a high chemical reactivity can be encapsulated. As an example, we find that C₆₀ can encapsulate a Fe₃ cluster, while it is much less likely to encapsulate a Fe₂ cluster. Spin multiplicity (=9) of the Fe₃@C₆₀ is very high, being comparable to that (=11) of a free Fe₃ cluster. Geometrically, the triangular plane of the cluster is perpendicular to a S₆ axis of the fullerene.     

Preparation and characterization of branched and linear sulfonated poly(ether ketone sulfone) proton exchange membranes for fuel cell applications

Branched sulfonated poly(ether ketone sulfone)s (Br‐SPEKS) were prepared with bisphenol A, bis(4‐fluorophenyl)sulfone, 3,3′‐disodiumsulfonyl‐4,4′‐difluorobenzophenone, and THPE (1,1,1‐tris‐p‐hydroxyphenylethane), respectively, at 180 °C using potassium carbonate in NMP (N‐methylpyrrolidinone). THPE, as a branching agent, was used with 0.4 mol % of bisphenol A to synthesize branched copolymers. Copolymers containing 10–50 mol % disulfonated units were cast from dimethylsulfoxide solutions to form films. Linear sulfonated poly(ether ketone sulfone)s (SPEKS) were also synthesized without THPE. The films were converted from the salt to acid forms with dilute hydrochloric acid. A series of copolymers were studied by Fourier transform infrared, ¹H‐NMR spectroscopy, differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Sorption experiments were conducted to observe the interaction of sulfonated polymers with water and methanol. The ion‐exchange capacity (IEC), a measure of proton conductivity, was evaluated. The synthesized Br‐SPEKS and SPEKS membranes exhibit conductivities (25 °C) from 1.04 × 10^?3 to 4.32 × 10^?3 S/cm, water swell from 20.18 to 62.35%, IEC from 0.24 to 0.83 mequiv/g, and methanol diffusion coefficients from 3.2 × 10^?7 to 4.7 × 10^?7 cm²/S at 25 °C. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1792–1799, 2008     

2‐[(Diphenylphosphino)methyl]pyridine as ligand for iron‐based atom transfer radical polymerization

2‐[(Diphenylphosphino)methyl]pyridine (DPPMP) was successfully used as a bidentate ligand in the iron‐mediated atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) with various initiators and solvents. The effect of the catalytic system on ATRP was studied systematically. Most of the polymerizations with DPPMP ligand were well controlled with a linear increase in the number‐average molecular weights (M_n) versus conversion and relatively low molecular weight distributions (M_w/M_n = 1.10–1.3) being observed throughout the reactions, and the measured molecular weights matched the predicted values. Initially added iron(III) bromide improved the controllability of the polymerization reactions in terms of molecular weight control. The ratio of ligand to metal influenced the controllability of ATRP system, and the optimum ratio was found to be 2:1. It was shown that ATRP of MMA with FeX₂/DPPMP catalytic system (X = Cl, Br) initiated by 2‐bromopropionitrile (BPN) was controlled more effectively in toluene than in polar solvents. The rate of polymerization increased with increasing the polymerization temperature and the apparent activation energy was calculated to be 56.7 KJ mol^?1. In addition, reverse ATRP of MMA was able to be successfully carried out using AIBN in toluene at 80 °C. Polymerization of styrene (St) was found to be controlled well by using the PEBr/FeBr₂/DPPMP system in DMF at 110 °C. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2922–2935, 2008