Duality Functors for Triple Vector Bundles

We calculate the group of dualization operations for triple vector bundles, showing that it has order 96 and not 72 as given in Mackenzie’s original treatment. The group is a nonsplit extension of S ₄ by the Klein group. Dualization operations are interpreted as functors on appropriate categories and are said to be equal if they are naturally isomorphic. The method set out here will be applied in a subsequent paper to the case of n-fold vector bundles.     

Real radiation at next-to-next-to-leading order in QCD: e+e- --> 2 jets through O(alpha2s)

We present a calculation of the differential two-jet cross section in e(+)e(-) annihilation through next-to-next-to-leading order (NNLO) in the strong coupling constant alpha(s). The calculation is performed using a new method for dealing with real radiation suggested recently by us. For the first time, the two-jet event rate is computed directly, without any reference to the inclusive cross section e(+)e(-)-->hadrons. We also calculate the energy distribution of the leading jet in e(+)e(-)-->2 jets and find significant modifications of the shape of this distribution at NNLO.     

Empirical and DFT GIAO quantum‐mechanical methods of 13C chemical shifts prediction: competitors or collaborators?

The accuracy of ¹³C chemical shift prediction by both DFT GIAO quantum‐mechanical (QM) and empirical methods was compared using 205 structures for which experimental and QM‐calculated chemical shifts were published in the literature. For these structures, ¹³C chemical shifts were calculated using HOSE code and neural network (NN) algorithms developed within our laboratory. In total, 2531 chemical shifts were analyzed and statistically processed. It has been shown that, in general, QM methods are capable of providing similar but inferior accuracy to the empirical approaches, but quite frequently they give larger mean average error values. For the structural set examined in this work, the following mean absolute errors (MAEs) were found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm and MAE(QM) = 3.29 ppm. A strategy of combined application of both the empirical and DFT GIAO approaches is suggested. The strategy could provide a synergistic effect if the advantages intrinsic to each method are exploited. Copyright © 2010 John Wiley & Sons, Ltd.     

NMR‐based analysis of structure of heteroleptic triple‐decker (phthalocyaninato) (porphyrinato) lanthanides in solutions

A novel approach for the structural analysis of heteroleptic triple‐decker (porphyrinato)(phthalocyaninato) lanthanides(III) in solutions is developed. The developed approach consists in molecular mechanics (MM+) optimization of the geometry of the complex taking into account the lanthanide‐induced shift (LIS) datasets. LISs of the resonance peaks in ¹H NMR spectra of a series of symmetric complexes [An₄P]Ln[(15C5)₄Pc]Ln[An₄P], where An₄P^2? is 5,10,15,20‐tetrakis(4‐methoxyphenyl)porphyrinato‐dianion, [(15C5)₄Pc]^2? is 2,3,9,10,16,17,24,25‐tetrakis(15‐crown‐5)phthalocyaninato‐dianion and Ln = La, Ce, Pr, Nd, Sm, Eu, are analyzed. Analysis of LISs showed two sets of protons in the molecule with opposite signs of shift. Two‐nuclei analysis of LISs testifies isostructurality of the whole series of investigated complexes in solution despite contraction of the lanthanide ions. Model‐free separation of contact and dipolar contributions of LISs was performed with one‐nucleus technique and did not show changes in contact and dipolar terms within the investigated series. MM+ optimization of the molecular structure allowed the interpretation of features of LIS for each particular group of protons. Parameterization of MM + ‐optimized model of molecule with values of structure‐dependent dipolar contributions of LIS allows the development of the precise structural model of the triple‐decker complex in solution. This approach allows the determination of the geometry and structure of the sandwich macrocyclic tetrapyrrolic complexes together with conformational analysis of flexible peripheral substituents in solutions. The developed method can be applied with minor modifications for the determination of structural parameters of other types of lanthanides(III) complexes with tetrapyrrolic ligands and also supramolecular systems based on them. Copyright © 2010 John Wiley & Sons, Ltd.     

Biomimetic synthesis of the pyrrolobenzoxazine core of paeciloxazine

Starting from a protected L-tryptophan derivative the pyrrolobenzoxazine core unit of paeciloxazine can be synthesized in two oxidation steps.     

HMBC‐1,1‐ADEQUATE via generalized indirect covariance: a high sensitivity alternative to n,1‐ADEQUATE

1,1‐ADEQUATE and the related long‐range 1,n‐ and n,1‐ADEQUATE variants were developed to provide an unequivocal means of establishing ²J_CH and the equivalent of ⁿJ_CH correlations where n = 3,4. Whereas the 1,1‐ and 1,n‐ADEQUATE experiments have two simultaneous evolution periods that refocus the chemical shift and afford net single quantum evolution for the carbon spins, the n,1‐variant has a single evolution period that leaves the carbon spin to be observed at the double quantum frequency. The n,1‐ADEQUATE experiment begins with an HMBC‐type ⁿJ_CH magnetization transfer, which leads to inherently lower sensitivity than the 1,1‐ and 1,n‐ADEQUATE experiments that begin with a ¹J_CH transfer. These attributes, in tandem, serve to render the n,1‐ADEQUATE experiment less generally applicable and more difficult to interpret than the 1,n‐ADEQUATE experiment, which can in principle afford the same structural information. Unsymmetrical and generalized indirect covariance processing methods can complement and enhance the structural information encoded in combinations of experiments e.g. HSQC‐1,1‐ or ?1,n‐ADEQUATE. Another benefit is that covariance processing methods offer the possibility of mathematically combining a higher sensitivity 2D NMR spectrum with for example 1,1‐ or 1,n‐ADEQUATE to improve access to the information content of lower sensitivity congeners. The covariance spectrum also provides a significant enhancement in the F₁ digital resolution. The combination of HMBC and 1,1‐ADEQUATE spectra is shown here using strychnine as a model compound to derive structural information inherent to an n,1‐ADEQUATE spectrum with higher sensitivity and in a more convenient to interpret single quantum presentation. Copyright © 2012 John Wiley & Sons, Ltd.     

Polar Red‐Emitting Rhodamine Dyes with Reactive Groups: Synthesis,Photophysical Properties,and Two‐Color STED Nanoscopy Applications

The synthesis, reactivity, and photophysical properties of new rhodamines with intense red fluorescence, two polar residues (hydroxyls, primary phosphates, or sulfonic acid groups), and improved hydrolytic stability of the amino‐reactive sites (NHS esters or mixed N‐succinimidyl carbonates) are reported. All fluorophores contain an N‐alkyl‐1,2‐dihydro‐2,2,4‐trimethylquinoline fragment, and most of them bear a fully substituted tetrafluoro phenyl ring with a secondary carboxamide group. The absorption and emission maxima in water are in the range of 635–639 and 655–659 nm, respectively. A vastly simplified approach to red‐emitting rhodamines with two phosphate groups that are compatible with diverse functional linkers was developed. As an example, a phosphorylated dye with an azide residue was prepared and was used in a click reaction with a strained alkyne bearing an N‐hydroxysuccinimid (NHS) ester group. This method bypasses the undesired activation of phosphate groups, and gives an amphiphilic amino‐reactive dye, the solubility and distribution of which between aqueous and organic phases can be controlled by varying the pH. The presence of two hydroxyl groups and a phenyl ring with two carboxyl residues in the dyes with another substitution pattern is sufficient for providing the hydrophilic properties. Selective formation of a mono‐N‐hydroxysuccinimidyl ester from 5‐carboxy isomer of this rhodamine is reported. The fluorescence quantum yields varied from 58 to 92 % for free fluorophores, and amounted to 18–64 % for antibody conjugates in aqueous buffers. The brightness and photostability of these fluorophores facilitated two‐color stimulated emission depletion (STED) fluorescence nanoscopy of biological samples with high contrast and minimal background. Selecting a pair of fluorophores with absorption/emission bands at 579/609 and 635/655 nm enabled two‐color channels with low cross‐talk and negligible background at approximately 40 nm resolution.     

Long‐Lived Spin States for Low‐Field Hyperpolarized Gas MRI

Parahydrogen induced polarization was employed to prepare a relatively long‐lived correlated nuclear spin state between methylene and methyl protons in propane gas. Conventionally, such states are converted into a strong NMR signal enhancement by transferring the reaction product to a high magnetic field in an adiabatic longitudinal transport after dissociation engenders net alignment (ALTADENA) experiment. However, the relaxation time T₁ of ～0.6 s of the resulting hyperpolarized propane is too short for potential biomedical applications. The presented alternative approach employs low‐field MRI to preserve the initial correlated state with a much longer decay time T_LLSS=(4.7±0.5) s. While the direct detection at low‐magnetic fields (e.g. 0.0475 T) is challenging, we demonstrate here that spin‐lock induced crossing (SLIC) at this low magnetic field transforms the long‐lived correlated state into an observable nuclear magnetization suitable for MRI with sub‐millimeter and sub‐second spatial and temporal resolution, respectively. Propane is a non‐toxic gas, and therefore, these results potentially enable low‐cost high‐resolution high‐speed MRI of gases for functional imaging of lungs and other applications.