Practical applications of averages and differences of Friedel opposites

Absolute configuration of naturally occurring glabridin

The title compound {systematic name: 4-[(3R)-8,8-dimethyl-3,4-dihydro-2H-pyrano[2,3-f]chromen-3-yl]benzene-1,3-diol, commonly named glabridin}, C20H20O4, is a species-specific biomarker from the roots Glycyrrhiza glabra L. (European licorice, Fabaceae). In the present study, this prenylated isoflavan has been purified from an enriched CHCl3 fraction of the extract of the root, using three steps of medium-pressure liquid chromatography (MPLC) by employing HW-40F, Sephadex LH-20 and LiChroCN as adsorbents. Pure glabridin was crystallized from an MeOH-H2O mixture (95:5 v/v) to yield colorless crystals containing one molecule per asymmetric unit (Z' = 1) in the space group P212121. Although the crystal structure has been reported before, the determination of the absolute configuration remained uncertain. Stereochemical analysis, including circular dichroism, NMR data and an X-ray diffraction data set with Bijvoet differences, confirms that glabridin, purified from its natural source, is found only in a C3 R configuration. These results can therefore be used as a reference for the assignment of the configuration and enantiopurity of any isolated or synthetic glabridin sample.

TiGePt--a study of Friedel differences

The X-ray single-crystal diffraction intensities of the intermetallic compound TiGePt were analysed. These showed beyond doubt that the crystal structure is non-centrosymmetric. The analysis revolves around the resonant-scattering contribution to differences in intensity between Friedel opposites hkl and \bar h\bar k\bar l. The following techniques were used: R(merge) factors on the average (A) and difference (D) of Friedel opposites; statistical estimates of the resonant-scattering contribution to Friedel opposites; plots of 2A(obs) against 2A(model) and of D(obs) against D(model); the antisymmetric D-Patterson function. Moreover it was possible to show that a non-standard atomic model was unnecessary to describe TiGePt. Two data sets are compared. That measured with Ag Kα radiation at 295 K to a resolution of 1.25 Å(-1) is less conclusive than the one measured with Mo Kα radiation at 100 K to the lower resolution of 0.93 Å(-1). This result is probably due to the fact that the resonant scattering of Pt is larger for Mo Kα than for AgKα radiation.

Charge flipping for routine structure solution

Charge flipping can be routinely used for solving small-molecule structures measured at atomic resolution. It is shown by benchmark tests that its performance is at least equal to that of direct methods in terms of the speed of solution and the quality of the resulting structure. There are, however, cases where charge flipping may be more suitable than direct methods for solving structures,viz.where space-group symmetry is uncertain from the analysis of systematic extinct reflections. The latest charge-flipping enhancements, such as the minimum superposition map procedure and the AAR algorithm, are also tested against database structures and compared with the usual variant. Default parameters are determined which yield a maximum of solved structures.

Absolute-structure reports

All the 139 noncentrosymmetric crystal structures published inActa Crystallographica Section Cbetween January 2011 and November 2012 inclusive have been used as the basis of a detailed study of the reporting of absolute structure. These structure determinations cover a wide range of space groups, chemical composition and resonant-scattering contribution. DefiningAandDas the average and difference of the intensities of Friedel opposites, their level of fit has been examined using 2ADand selected-Dplots. It was found, regardless of the expected resonant-scattering contribution to Friedel opposites, that the Friedel-difference intensities are often dominated by random uncertainty and systematic error. An analysis of data collection strategy is provided. It is found that crystal-structure determinations resulting in a Flack parameter close to 0.5 may not necessarily be from crystals twinned by inversion. Friedifstatis shown to be a robust estimator of the resonant-scattering contribution to Friedel opposites, very little affected by the particular space group of a structure nor by the occupation of special positions. There is considerable confusion in the text of papers presenting achiral noncentrosymmetric crystal structures. Recommendations are provided for the optimal way of treating noncentrosymmetric crystal structures for which the experimenter has no interest in determining the absolute structure.<!?tpb=25.7pt>

Use of intensity quotients and differences in absolute structure refinement

Several methods for absolute structure refinement were tested using single-crystal X-ray diffraction data collected using Cu Kα radiation for 23 crystals with no element heavier than oxygen: conventional refinement using an inversion twin model, estimation using intensity quotients in SHELXL2012, estimation using Bayesian methods in PLATON, estimation using restraints consisting of numerical intensity differences in CRYSTALS and estimation using differences and quotients in TOPAS-Academic where both quantities were coded in terms of other structural parameters and implemented as restraints. The conventional refinement approach yielded accurate values of the Flack parameter, but with standard uncertainties ranging from 0.15 to 0.77. The other methods also yielded accurate values of the Flack parameter, but with much higher precision. Absolute structure was established in all cases, even for a hydrocarbon. The procedures in which restraints are coded explicitly in terms of other structural parameters enable the Flack parameter to correlate with these other parameters, so that it is determined along with those parameters during refinement.

Analysing Friedel averages and differences

Various practical applications of the average (A) and difference (D) of Friedel opposites are described. Techniques based on the resonant-scattering contribution to Friedel differences are applied to see whether a crystal is centrosymmetric or not, and to determine the point group of the crystal. For the validation of a structural study, plots of A(obs) against A(model), and D(obs) against D(model) are used extensively. Moreover, it is useful to display both plots on the same graph. Intensity measurements on a crystal of NaClO(3) were made at three different speeds, with two different radiations and two different diffractometers, and treated with two different software packages and four different absorption corrections. The evaluation of these numerous data sets reveals underlying deficiencies. For comparison, plots of A(obs) against A(model), and D(obs) against D(model) are presented for two centrosymmetric crystals.

Chirality and diastereoselection of Δ/Λ-configured tetrahedral zinc complexes through enantiopure Schiff base complexes: combined vibrational circular dichroism, density functional theory, 1H NMR, and X-ray structural studies

The metal-centered Δ/Λ-chirality of four-coordinated, nonplanar Zn(A(^)B)(2) complexes is correlated to the chirality of the bidentate enantiopure (R)-A(^)B or (S)-A(^)B Schiff base building blocks [A(^)B = (R)- or (S)-N-(1-(4-X-phenyl)ethyl)salicylaldiminato-κ(2)N,O with X = OCH(3), Cl, Br]. In the solid-state the (R) ligand chirality induces a Λ-M configuration and the (S) ligand chirality quantitatively gives the Δ-M configuration upon crystallization as deduced from X-ray single crystal studies. The diastereoselections of the pseudotetrahedral zinc-Schiff base complexes in CDCl(3) solution were investigated by (1)H NMR and by vibrational circular dichroism (VCD) spectroscopy. The appearance of two signals for the Schiff-base -CH═N- imine proton in (1)H NMR indicates an equilibrium of both Δ- and Λ-diastereomers with a diastereomeric ratio of roughly 20:80% for all three ligands. VCD proved to be very sensitive to the metal-centered Δ/Λ-chirality because of a characteristic band representing coupled vibrations of the two ligand's C═N stretch modes. The absolute configuration was assigned on the basis of agreement in sign with theoretical VCD spectra from Density Functional Theory calculations.

Plumeridoid C from the Amazonian traditional medicinal plant Himatanthus sucuuba

The stereochemistry of the iridoid plumeridoid C, C(15)H(18)O(7), was established by X-ray single-crystal structure analysis, giving (2'R,3R,4R,4aS,7aR)-methyl 3-hydroxy-4'-[(S)-1-hydroxyethyl]-5'-oxo-3,4,4a,7a-tetrahydro-1H,5'H-spiro[cyclopenta[c]pyran-7,2'-furan]-4-carboxylate. The absolute structure of the title compound was determined on the basis of the Flack x parameter and Bayesian statistics on Bijvoet differences. The hydrogen-bond donor and acceptor functions of the two hydroxy groups are employed in the formation of O-H···O-bonded helical chains.

CRYSTALSenhancements: absolute structure determination

A summary of the features for investigating absolute structure available in the crystallographic refinement programCRYSTALSis presented, together with the results of analyses of 150 light-atom structures collected with molybdenum radiation carried out with these tools. The results confirm that the Flack and Hooft parameters are strongly indicative, even when the standard uncertainties are large compared to the thresholds recommended by Flack & Bernardinelli [J. Appl. Cryst.(2000),33, 1143–1148].