Symmetry old and new: Some recent examples of the role of symmetry in X-ray analysis

Two recent examples in X-ray structure analysis at opposite ends of the molecular weight range, in which very careful consideration of space group and diffraction symmetry was necessary to resolve all the associated problems, are described. Case 1 involves the structures of (1) transdiBromo (1,4,8,11-tetraazacyclotetradecane) chromium (III) bromide and (2) the corresponding trans-bromo-chloro compound. Both crystallise in space groupP4₂/m with unit cell dimensions sufficiently close to suggest that the structures are isomorphous. It is shown however that the structures are not superimposable or even related by simple rotation or inversion, but that it is necessary to apply a hypothetical glide operation in order to bring the structures into coincidence. The organic moieties are thus structural enantiomorphs in spite of existing in a centrosymmetric space group. Case 2 involves studies on a co-crystallised derivative of the enzyme RNase with deoxycytidylyl-3–5-deoxyguanosine (dCpdG). Preliminary X-ray precession photographs, from low quality crystals, indicated an orthogonal C-centred unit cell, but were unable to define the true diffraction symmetry, which wasnot orthorhombic. The true symmetry was discovered only after solving the structure in a second (erroneous) cell and careful inspection of the lattice and diffraction symmetry from the measured intensity values.     

Crystal and molecular structure of 4,17a-methy1-4, 17a-diaza-5α-androstane (HS353): An intermediate in the design of azasteroid neuromuscular blocking agents

The crystal and molecular structure of 4, 17a-methyl-4, 17a-diaza-5-androstane (HS353), C₂₀N₂H₃₆ has been determined by direct methods and successive electron density calculations. The crystals are triclinic,a=7.419(2),b=20.300(4),c=12.866(2)Å,=105.91(2),=76.33(2),=99.32(2)°, space groupP1,Z=4. Block-matrix least-squares refinement converged toR=0.0660 for 3243 reflections withI3I (CuK radiation). The four independent molecules show only minor conformational variations, all rings being trans-connected chairs. Introduction of N at positions 4 and 17a of ringsA andD creates asymmetry in both conformation and bond angles, producing outward bending of the C-N side groups at both ends of all four molecules.Steroids and related studies, Part 83.     

Approximate Solutions of Continuous Dispersion Problems

The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate that, as p increases, it becomes dramatically more expensive to compute solutions of the exact formulation than to compute solutions of the approximate formulation.     

Molecular structure of an ancient folk medicine: Berberine hydrogen sulfate

The crystal structure of the versatile folk medicine berberine hydrogen sulfate, (C₂₀H₁₈NO₄)⁺HSO ₄ ^– , has been determined by the heavy-atom method and refined by blocked full-matrix least-squares refinement. The crystals are triclinic, space groupF¯1,a=20.370(5),b=7.435(2),c=27.427(6) Å,=97.700(9),=116.222(9),=85.456.(8)°,Z=8,D _x =1.556 g cm^–3,D _m =1.549(5) g cm^–3. The structure refined toR=0.070 for 1659 observed reflections withI(hkl)2.5[I(hkl)]. The ring system of the berberine molecule is approximately planar, with both –OCH₃ groups twisted slightly out of the plane. Heterocyclic ringB has a half-chair conformation with a pseudo-two-fold axis bisecting the bonds C(9)-C(10) and C(7)-C(8), diagonal to the isoquinoline groupAB. The five-membered ringE has an envelope conformation, the apical atom C(1) being out of plane.     

Volume effects in the thermodynamics of binary substitutional solid solutions at high temperatures

Recent measurements of the variation with temperature and composition of the elastic properties of Fe-based solid solution containing the substitutional solutes Mn, Ni and Cr have enabled calculations to be made of the effect of the composition-dependent variation of the specific volume of the lattice upon the partial thermodynamic functions of the solute species. The calculations show that, in contrast to the case of binary interstitial solid solutions, the effects are of the same order, or less, as the normal uncertainty in the experimental determination of the partial thermodynamic functions of solid solutions at high temperatures (1273 K).     

Aflavinine,a novel indole-mevalonate metabolite from tremorgen-producing aspergillusflavus species

The structure of aflavanine, a new diterpene indole from $\text{A}$. $\text{flavus}$, is presented.