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.     

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.     

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.     

Dilepton rapidity distribution in the Drell-Yan process at next-to-next-to-leading order in QCD

We compute the rapidity distribution of the virtual photon produced in the Drell-Yan process through next-to-next-to-leading order in perturbative QCD. We introduce a powerful new method for calculating differential distributions in hard scattering processes. This method is based upon a generalization of the optical theorem; it allows the integration-by-parts technology developed for multiloop diagrams to be applied to noninclusive phase-space integrals, and permits a high degree of automation. We apply our results to the analysis of fixed-target experiments.     

Determining Liquid Structure from the Tail of the Direct Correlation Function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the tail of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the out projection of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.     

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.