Volume 212, Issue 5

We have studied the structure of the clean and Cs covered Ag(001) surface, using surface X-ray diffraction. For the clean unreconstructed Ag(001) surface the analysis of the integer-order crystal truncation rods gives evidence for a compression of the first interlayer spacing relative to the bulk by Δ d 12 / d bulk = −0.8(8)%, whereas for the second interlayer spacing we obtain an expansion of Δ d 23 / d bulk = 1.0(8)%. For the first two Ag layers we observe enhanced thermal disorder as expressed by the isotropic mean-squared displacement amplitude, U = 0.011(1) Å 2 at 340 K relative to the bulk value of 0.009 Å 2 at this temperature. Our X-ray results for Ag(001) are in good agreement with previous experimental and theoretical results. The adsorption of 0.25 ML (1 ML = 1.25 × 10 15 adatoms/cm 2 ) Cs on the Ag(001) surface at 170 K leads to the formation of a c (2 × 4) superstructure. The Cs atoms are found to occupy fourfold hollow sites at d Cs = 2.49(20) Å above the Ag(001) surface thereby shifting the underlying Ag atoms laterally by 0.029(5) Å from their bulk positions. From the adsorption height we derive an effective Cs radius of 1.78(16) Å. Large anisotropic disorder is observed for the Cs adatoms. Within the harmonic approximation we derive mean-squared displacement amplitudes of U 11 = 0.08(1) Å 2 , U 22 = 0.10(1) Å 2 and U 33 = 0.27(3) Å 2 . An alternative model, suggested by the very large value of U 33 , was also tried, in which there are 15% of Ag vacancies in the top layer and a lower Cs site. This ‘unusual’ model is discussed in the context of current theories of alkali metal induced reconstructions.

Certain rules are developed in 3D geometry to study the structure of mathematical expressions. A general formula for multiple helices has been found. Using the exponential scale we describe interpenetrating structures and the corresponding nodal surfaces. The rules of the structure of mathematical expressions found are used to describe complex chemical structures.

In the crystal systems where two crystallographic axes are related by symmetry, there are certain centrosymmetric space groups which do not include a two-fold rotation that interchanges the two said axes and inverts the third, or, in rhombohedral cases, interchanges two and inverts all the three axes. When the set of atomic coordinates describing a structure with any one of such space groups is transformed by such a two-fold rotation, not present in the space group, a different set of coordinates, equally valid but unrelated to the first set by any operation of the space group, is obtained. Thus one is confronted with the apparently paradoxical situation that depending on the choice of the positive direction of a crystallographic axis, two different descriptions (four in certain cubic cases) may exist even for a centrosymmetric structure. Since such a situation is particularly confusing when isostructurality of crystals is investigated, it has been considered worthwhile to compile a list of all the centrosymmetric space groups where this complication may arise.

Anomalous dispersion of X-ray diffraction from bovine trypsin has been measured at three wavelengths near the K -absorption edge of sulphur ( λ K = 5.02 Å) which are characteristic of sulphur in methionine and the cystine disulphide bridges. The feasibility of phasing by means of the dispersion analysis is demonstrated in two steps: 1. Scaling of the experimental data and calculation of the anomalous difference Patterson map, showing the correlation between sulphur atoms. 2. Using the measured dispersion to calculate phases based on the known sulphur sites of the refined trypsin model. Although the resulting electron density map of 5 Å resolution is calculated from 600 unique reflections only, there is a reasonable agreement with the superimposed molecular model.

Single crystal structure determinations of the complexes of 4,7,13,16,21,24-hexaoxa-1,10-diazabicyclo-[8.8.8]hexacosane, C 18 H 36 N 2 O 6 (= C222), with AgClO 4 (1) [ R 32, a = 8.589(2) Å, c = 27.553(11) Å, T = 92K] and NaIO 4 (2) [ Pccn , a = 10.402(5) Å, b = 13.452(9) Å, c = 17.172(9) Å, T = 293 K] were performed. The cell constants of the cryptates Ag(C222)X (X = NO 3 − , ClO 3 − , BrO 3 − , ClO 4 − , IO 4 − , ReO 4 − , BF 4 − , PF 6 − , AsF 6 − ) and of Na(C222)ClO 4 were determined from powder difraction data, and are all isotypic to (1). Indexing of the powder spectrum of Na(C222)ReO 4 resulted in an orthorhombic unit cell comparable to that of (2), but with a c -axis reduced by one half. In these compounds the metal cations lying at the centres of the ligand cavities are clearly separated from the anions [>5.4 Å]. In both the AgClO 4 and NaIO 4 complexes the metal cations have coordination numbers of 8, but the coordination types are quite different: Whereas the Ag + ion prefers N to O coordination [2 × Ag … N 2.372(3) Å, 6 × Ag … O 2.834(3) Å], at the Na+ ion the situation is inverted [2 × Na … N 2.710(5) Å, 6 × Na … O 2.403(4) Å–2.529(4) Å]. The metal–ligand distances and the conformational changes of the C222 ligand are discussed taking as a basis the data of all known crystal structures containing this ligand.

The crystal structures of three diaza crowns-18, namely 1,4,10,13-tetraoxa-7,16-diazacyclooctadecane (crown 1), 1,4,10,13-tetraoxa-7,16-diazacyclooctadecane-7,16-diacetonitrile (crown 2) and N,N′-(1,4,10,13-tetraoxa-7,16-diazacyclooctadecane-7,16-diyldi-2,1-ethanediyl)bis-[4-methyl-benzenesulfonamide] (crown 3) have the following space groups and unit cell parameters: crown 1(C 12 H 26 N 2 O 4 ), monoclinic, P 2 1 / c , Z = 2, a = 10.207(3) Å, b = 8.494(3) Å, c = 8.942(3) Å, β = 109.39(3)°; crown 2(C 16 H 28 N 4 O 4 ), triclinic, P [unk], Z = 1, a = 6.226(3) Å, b = 8.367(4) Å, c = 9.323(4) Å, α = 74.13(3)°, β = 74.66(2)°, γ = 81.56(2)°; and crown 3 (C 30 H 48 N 4 O 8 S 2 ), triclinic, P [unk], Z = 1, a = 7.880(3) Å, b = 10.559(4) Å, c = 10.984(4) Å, α = 72.63(3)°, β = 77.67(3)°, γ = 71.87(3)°. The structures were solved using direct methods and refined by full-matrix least-squares techniques to R 1 of 0.039, 0.045 and 0.055, respectively. Geometry of the 18-membered ring of the crowns studied, in the neat state and engaged in complexes with alkali metals, has been thoroughly examined in order to reveal similarities and differences between them, relations between constitution and ability to interaction, as well as possibilities of selective complexation of metal cations.

M r = 273.164, orthorhombic, P 2 1 2 1 2 1 , a = 12.075(2) Å, b = 13.694(2) Å, c = 9.610(1) Å, V = 1589(3) Å 3 , Z = 4, D x = 1.141, D m = 1.115g cm −3 , λ (Mo K α ) = 0.7107 Å, μ = 0.91 cm −1 , F (000) = 592, R = 0.049 for 717 unique reflections with I > 2 σ ( I ). The interaction compound is formed by the tetrapropylammonium cation and the tetrafluoroborate anion. The remarkable features of this crystal at room temperature are: i) the non centrosymmetric structure; ii) the ordered distribution of the fluoroborate tetrahedra, also confirmed by NMR measurements, iii) the partial disorder of the n -propylammonium cations, which are statistically arranged in two orientations symmetrical to a mirror plane.

The crystal structures of two borines were solved by direct methods and refined by full-matrix least-squares procedure. 6-methyl-4-phenyl-1,3,2-(2 H )-2,2-difluorodioxaborine, C 10 H 9 BF 2 O 2 (compound 1 ): orthorhombic, space group Pnma , a = 12.534(2) Å, b = 7.109(2) Å, c = 10.933(2) Å, V = 974.2(3) Å 3 , Z = 4 and d = 1.43Mg m −3 , R = 0.039 ( Rw = 0.036) for 88 parameters and 752 observations with I > 3 σ ( I ). 4-( p -anisyl)-6-methyl-1,3,2-(2 H )-2,2-difluorodioxaborine, C 11 H 11 BF 2 O 3 (compound 2 ): monoclinic, space group P 2 1 / m , a = 6.8889(8) Å, b = 7.071(1) Å, c = 11.695(2) Å, β = 98.55(1)°, V = 563.3(9) Å 3 , Z = 2 and d = 1.42Mg m −3 , R = 0.039 ( Rw = 0.036) for 100 parameters and 1003 observations with I > 3 σ ( I ). The crystal structure analysis of compound 1 and 2 reveals that the difference in their absorption and fluorescence spectra, by going from solution to the solid state, reflects their packing in the crystal lattice which enables a charge transfer process to be developed between two planar molecules at ca. 3.5 Å from each other in two different but parallel planes.

2,10 Dichloro 6-(2,3 dimethylphenoxy) dibenzo [ d . g ] [1,3.6,2] dioxathiaphosphocin 6-sulphide (C 20 H 15 Cl 2 O 3 PS) crystallizes in the triclinic system, P [unk] with a = 7.845(3) Å, b = 11.720(2) Å, c = 11.871(2) Å, a = 88.5(2)°, β = 73.6(2)°, γ = 89.1(2)°, V = 1046.7(4) Å3, Z = 2, D c = 1.489M gm −3 , (Mo K α ) = 0.71069 Å, F (000) = 480 and T = 293 K. The crystal structure was solved by direct methods and refined by full matrix least-squares method to a final R = 0.0345 for 2701 unique observed reflections [ I ≥ 2 σ ( I )]. The chlorobenzene rings A & B which are at 68.8° to each other, are oriented respectively at 19.9° and 61.6° to the phenyl ring and both are at 36.5° to the best plane of the heterocyclic ring. The heterocyclic ring adopts a distorted boat chair conformation.