Showing papers in "Acta Crystallographica Section B-structural Science in 2004"

Novel tools for visualizing and exploring intermolecular interactions in molecular crystals.

Abstract: A new way of exploring packing modes and intermolecular interactions in molecular crystals is described, using Hirshfeld surfaces to partition crystal space. These molecular Hirshfeld surfaces, so named because they derive from Hirshfeld's stockholder partitioning, divide the crystal into regions where the electron distribution of a sum of spherical atoms for the molecule (the promolecule) dominates the corresponding sum over the crystal (the procrystal). These surfaces reflect intermolecular interactions in a novel visual manner, offering a previously unseen picture of molecular shape in a crystalline environment. Surface features characteristic of different types of intermolecular interactions can be identified, and such features can be revealed by colour coding distances from the surface to the nearest atom exterior or interior to the surface, or by functions of the principal surface curvatures. These simple devices provide a striking and immediate picture of the types of interactions present, and even reflect their relative strengths from molecule to molecule. A complementary two-dimensional mapping is also presented, which summarizes quantitatively the types of intermolecular contacts experienced by molecules in the bulk and presents this information in a convenient colour plot. This paper describes the use of these tools in the compilation of a pictorial glossary of intermolecular interactions, using identifiable patterns of interaction between small molecules to rationalize the often complex mix of interactions displayed by large molecules.

Structures of stable and metastable Ge2Sb2Te5, an intermetallic compound in GeTe-Sb2Te3 pseudobinary systems.

Abstract: The most widely used memory materials for rewritable phase-change optical disks are the GeTe-Sb2Te3 pseudobinary compounds. Among these compounds, Ge2Sb2Te5 crystallizes into a cubic close-packed structure with a six-layer period (metastable phase) in the non-thermal equilibrium state, and a trigonal structure with a nine-layer period (stable phase) in the thermal equilibrium state. The structure of the stable phase has Ge/Sb layers in which Ge and Sb are randomly occupied, as does the structure of the metastable phase, while the conventionally estimated structure had separate layers of Ge and Te. The metastable and stable phases are very similar in that Te and Ge/Sb layers stack alternately to form the crystal. The major differences between these phases are: (i) the stable phase has pairs of adjacent Te layers that are not seen in the metastable phase and (ii) only the metastable phase contains vacancies of ca 20 at. % in the Ge/Sb layers.

Jahn–Teller distortions, cation ordering and octahedral tilting in perovskites

Abstract: In transition metal oxides, preferential occupation of specific d orbitals on the transition metal ion can lead to the development of a long-range ordered pattern of occupied orbitals. This phenomenon, referred to as orbital ordering, is usually observed indirectly from the cooperative Jahn-Teller distortions (CJTDs) that result as a consequence of the orbital ordering. This paper examines the interplay between orbital ordering, octahedral tilting and cation ordering in perovskites. Both ternary AMX(3) perovskites containing an active Jahn-Teller (J-T) ion on the octahedral site and quaternary A(2)MM'X(6) perovskites containing a J-T ion on one-half of the octahedral sites have been examined. In AMX(3) perovskites, the tendency is for the occupied 3d(3x2-r2) and 3d(3z2-r2) orbitals to order in the ac plane, as exemplified by the crystal structures of LaMnO(3) and KCuF(3). This arrangement maintains a favorable coordination environment for the anion sites. In AMX(3) perovskites, octahedral tilting tends to enhance the magnitude of the J-T distortions. In A(2)MM'X(6) perovskites, the tendency is for the occupied 3d(3z2-r2) orbitals to align parallel to the c axis. This pattern maintains a favorable coordination environment about the symmetric M'-cation site. The orbital ordering found in rock-salt ordered A(2)MM'X(6) perovskites is compatible with octahedral rotations about the c axis (Glazer tilt system a(0)a(0)c(-)) but appears to be incompatible with GdFeO(3)-type octahedral tilting (tilt system a(-)b(+)a(-)).

New bond-valence parameters for lanthanides

Abstract: The bond-valence method, especially the valence-sum rule, is very useful for checking if the structures formed by trivalent lanthanides are correct. In this work bond-valence parameters (Rij), which connect bond valences and bond lengths, have been computed for a large number of bonds taken from the Cambridge Structural Database, Version 5.24 (2002) [Allen (2002). Acta Cryst. B58, 380-388]. The calculated values of bond-valence parameters for metal-organic compounds decrease with an increase in lanthanide atomic number; the Rij values are also smaller than bond-valence parameters calculated for inorganic compounds. A summary of bond-valence sums calculated for Rij given in this work and reported in the literature, and a functional correlation between lanthanide-oxygen distances and coordination number are presented.

New view of the high-pressure behaviour of GdFeO3-type perovskites

Abstract: Recent determinations of the structures of several GdFeO3-type orthorhombic perovskites (ABO3) show that the octahedra in some become more tilted with increasing pressure. In others the octahedra become less tilted and the structure evolves towards a higher-symmetry configuration. This variety of behaviour can be explained in terms of the relative compressibilities of the octahedral and dodecahedral cation sites in the perovskite structure. If the BO6 octahedra are less compressible than the AO12 sites then the perovskite will become more distorted with pressure, but the perovskite will become less distorted if the BO6 site is more compressible than the AO12 site. In this contribution we use the bond-valence concept to develop a model that predicts the relative compressibilities of the cation sites in oxide perovskites. We introduce the site parameter Mi defined in terms of the coordination number Ni, average bond length at room pressure Ri, and the bond-valence parameters R0 and B,M_i = ({R_i N_i }/ B)\exp [({{R_0 - R_i }) / B}].Mi represents the variation in the bond-valence sum at the central cation in a polyhedral site because of the change of the average bond distance. Experimental data suggest that the pressure-induced changes in the bond-valence sums at the two cation sites within any given perovskite are equal. With this condition we show that the ratio of cation-site compressibilities is given by \beta _B /\beta _A = M_A /M_B. This model, based only upon room-pressure bond lengths and bond-valence parameters, correctly predicts the structural behaviour and some physical properties of the oxide perovskites that have been measured at high pressure.

Structures of piperazine, piperidine and morpholine

Abstract: The crystal structures of piperazine, piperidine and morpholine have been determined at 150 K. All three structures are characterized by the formation of NH⋯N hydrogen-bonded chains. In piperazine these are linked to form sheets, but the chains are shifted so that the molecules interleave. In morpholine there are in addition weak CH⋯O interactions. Topological analyses show that these three structures are closely related to that of cyclohexane-II, which can be described in terms of a pseudo-cubic close-packed array of molecules in a familiar ABC layered arrangement. While the positions of the molecules within each layer are similar, hydrogen bonding occurs between the ABC layers and in order to accommodate this the molecules are rotated relative to those in cyclohexane-II. Piperidine and morpholine also adopt layered structures, with hydrogen-bonding or CH⋯O interactions between the layers. In these cases, however, the layering more resembles a hexagonal close-packed arrangement.

Space group Cc: an update.

Abstract: A recent survey of the Cambridge Structural Database, CSD [Allen (2002). Acta Cryst. B58, 380-388], shows that the percentage of incorrect assignments of the space group Cc has remained at about 10% since the last survey in 1997.

Isostructurality in one and two dimensions: isostructurality of polymorphs

Abstract: A set of polymorphic crystal structures was retrieved from the Cambridge Structural Database in order to estimate the frequency of isostructurality among polymorphs. Altogether, 50 structures, the polymorphs of 22 compounds, were investigated. It was found that one-, two- or three-dimensional isostructurality is exhibited by approximately half of the compounds analyzed. Among the isostructural polymorphs, the frequency of one-, two- and three-dimensional isostructurality is similar. From the examples, it appears that three-dimensional isostructurality is connected to the gradual ordering of crystal structures, while one- and two-dimensional isostructurality can often be related to specific packing interactions. The possibility of many similar interactions seems to decrease the probability of the occurrence of isostructural polymorphs. Conformational polymorphs do not exhibit isostructurality.

Structure of a high-pressure phase of vanadium pentoxide, β-V2O5

Abstract: A high-pressure phase of vanadium pentoxide, denoted β-V2O5, has been prepared at P = 6.0 GPa and T = 1073 K. The crystal structure of β-V2O5 has been studied by X-ray and neutron powder diffraction, and high-resolution transmission electron microscopy. The V atoms are six-coordinated within distorted VO6 octahedra. The structure is built up of quadruple units of edge-sharing VO6 octahedra linked by sharing edges along [010] and mutually connected by sharing corners along [001]. This arrangement forms layers of V4O10 composition in planes parallel to (100). The layers are mutually held together by weak forces. β-V2O5 is metastable and transforms to α-V2O5 at 643–653 K under ambient pressure. Structural relationships between β- and α-V2O5, and between β-V2O5 and B-Ta2O5-type structures are discussed. The high-pressure β-V2O5 layer structure can be considered as the parent of a new series of vanadium oxide bronzes with cations intercalated between the layers.

Octahedral tilting in cation-ordered perovskites--a group-theoretical analysis.

Abstract: Group-theoretical methods are used to enumerate the structures of ordered perovskites, in which 1:2 and 1:3 ordering of B and B′ cations is considered in combination with the ubiquitous BX6 (or B′X6) octahedral tilting The cation ordering on the B-cation site is described by irreducible representations of the Pm\bar 3m space group of the cubic aristotype: Λ1 (k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A3BB_2^{\prime}X9 and M_1^ + (k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A4BB_3^{\prime}X12 The octahedral tilting is mediated by the irreducible representations M_3^ + and R_4^ + Ten distinct structures have been identified in the 1:2 case and 11 structures for 1:3

Geometry of the 2-aminoheterocyclic–carboxylic acid R22(8) graph set: implications for crystal engineering

Abstract: The geometry of the R_2^2(8) graph set formed between a 2-aminoheterocyclic ring containing an Nsp2 atom (in the 1-position of the ring) and a carboxylic acid has been studied. Collating data from known co-crystal structures containing five- and six-membered heterocyclic rings from the Cambridge Structural Database revealed unexpected differences between two kinds of non-hydrogen contact distances, and between specific bond distances and angles of the heterocycle. Not only were the interatomic non-hydrogen distances between the N atoms (heterocycle) and O atoms (carboxylate) asymmetric, but also the 2-amino N atom (N21) to the heterocyclic C atom (C2) bond was shorter than the C2 to N1sp2 bond. However, this shortening of the C2—N21 bond was not observed in the examples where N21 was substituted with a non-H atom. For the six-membered rings the data also showed that as the C2—N21 bond shortened the N1—C2—N21 bond angle increased.

Experimental electron density study of the supramolecular aggregation between 4,4'-dipyridyl-N,N'-dioxide and 1,4-diiodotetrafluorobenzene at 90 K.

Abstract: The electron density of the halogen-bonded complex of 4,4′-dipyridyl-N,N′-dioxide (bpNO) with 1,4-diiodotetrafluorobenzene (F4dIb) at 90 K has been determined by X-ray diffraction and analysed. The nature of the I⋯O intermolecular bond connecting the bpNO and F4dIb molecules into one-dimensional infinite chains, as well as the other non-covalent interactions present in the crystal, such as C—H⋯O, C—H⋯F and C—H⋯I hydrogen bonds and C⋯C, C⋯N, C⋯I and F⋯F interactions, have been investigated. The integration of electron density over the atomic basins reveals the electrostatic nature of the I⋯O halogen bond, which is very similar to a previously analysed I⋯N halogen bond.

Structural study of Cu2−xSe alloys produced by mechanical alloying

Abstract: The crystalline structures of the superionic high-temperature copper selenides Cu2−xSe (0 < x < 0.25) produced using mechanical alloying were investigated using X-ray diffraction (XRD). The measured XRD patterns showed the presence of peaks corresponding to the crystalline superionic high-temperature α-Cu2Se phase in the as-milled sample, and its structural data were determined by means of a Rietveld refinement procedure. After heat treatment in argon at 473 K for 90 h, this phase transforms to the superionic high-temperature α-Cu1.8Se phase, whose structural data were also determined by Rietveld refinement. In this phase, a very low occupation of the trigonal 32(f) sites (∼ 3%) by Cu ions is found. In order to explain the evolution of the phases in the samples, two possible mechanisms are suggested: (i) the high mobility of Cu ions in superionic phases and (ii) the important diffusive processes in the interfacial component of samples produced by mechanical alloying.

Water molecules insert into N—H⋯Cl—M hydrogen bonds while M—Cl⋯X—C halogen bonds remain intact in dihydrates of halopyridinium hexachloroplatinates

Abstract: The crystal structures of the 3-halopyridinium hexachloroplatinate(IV) dihydrates (HPyX-3)2[PtCl6]·2H2O [(1), X = Br; (2a), (2b), X = I] comprise networks in which the molecular components are linked via N—H⋯O and O—H⋯Cl—Pt hydrogen bonds and Pt—Cl⋯X—C halogen bonds (X = Br, I). The iodo derivative has been isolated in two polymorphic forms. Of particular interest to the understanding of the utility of the hydrogen bonds and M—X⋯X′—C halogen bonds that propagate the networks in anhydrous salts of this type is that the water molecules insert exclusively into the putative N—H⋯Cl—Pt hydrogen bonds, while the Pt—Cl⋯X′—C halogen bonds remain undisrupted by the presence of water molecules.

Torsional vibration and central bond length of N-benzylideneanilines.

Abstract: The crystal structures of N-benzylideneaniline (1), N-benzylidene-4-carboxyaniline (2), N-(4-methylbenzylidene)-4-nitroaniline (3), N-(4-nitrobenzylidene)-4-methoxyaniline (4), N-(4-nitrobenzylidene)-4-methylaniline (5), N-(4-methoxybenzylidene)aniline (6) and N-(4-methoxybenzylidene)-4-methylaniline (7) were determined by X-ray diffraction analyses at various temperatures. In the crystal structures of all the compounds, an apparent shortening of the central C=N bond was observed at room temperature. As the temperature was lowered, the observed bond lengths increased to approximately 1.28 A at 90 K, irrespective of substituents in the molecules. The shortening and the temperature dependence of the C=N bond length are interpreted in terms of an artifact caused by the torsional vibration of the C-Ph and N-Ph bonds in the crystals. In the crystal structures of (1) and (7), a static disorder around the C=N bond was observed, which is also responsible for the apparent shortening of the C=N bond.

Structure for perovskites with layered ordering of A-site cations.

Abstract: The structure of La1/3NbO3 is that of a perovskite with La3+ cations ordered into alternate layers of perovskite A-sites. This is the description of a tetragonal structure and yet the room-temperature structure shows an orthorhombic distortion. The structure of La2/3TiO3 shows similar features. It has been recognized only very recently that the ortho­rhombic distortion in both these compounds is due to octahedral tilting. It seems clear from the literature that Ce2/3TiO3, Pr2/3TiO3, Nd2/3TiO3 and Ce1/3NbO3 adopt the same structure. Structures of other perovskites, such as Ln2/3TiO3, Ln1/3NbO3 and Ln1/3TaO3 (Ln = lanthanoid), when orthorhombically distorted, may be similar.

Ab initio structure determination of the hygroscopic anhydrous form of α-lactose by powder X-ray diffraction

Abstract: Annealing of α-lactose monohydrate at 408 K yielded a mixture of this compound with hygroscopic anhydrous α-lactose. A powder X-ray diffraction pattern of this mixture was recorded at room temperature. The starting structural model of hygroscopic α-lactose was found by a Monte Carlo simulated-annealing method. The final structure was obtained through Rietveld refinements, with soft restraints on inter­atomic bond lengths and bond angles, and crystalline energy minimization to locate the H atoms of the hydroxy groups. The crystalline cohesion is achieved by networks of O—H⋯O hydrogen bonds that differ from those of the monohydrate phase. The width of the Bragg peaks is interpreted by a phenomenological microstructural approach in terms of isotropic size effects and anisotropic strain effects.

A new polymorph of ortho-ethoxy-trans-cinnamic acid: single-to-single-crystal phase transformation and mechanism

Abstract: The α-polymorph of ortho-ethoxy-trans-cinnamic acid (OETCA) undergoes a reversible single-crystal-to-single-crystal phase transformation at 333 K. The new high-temperature polymorph (α′-OETCA) is stable between 333 and 393 K with three molecules in the asymmetric unit (Z′ = 3), space group P\bar 1. Unlike the other polymorphs (and solvate) of OETCA recently reported, two of the molecules in α′-OETCA deviate significantly from planarity. This conformational change results in the corrugated sheet-type structure of α′-OETCA. The sheets are made up of ribbons, each composed of R_2 ^2 (8) hydrogen-bonded pairs (via the —COOH groups), which are further connected by CH⋯O interactions. When exposed to UV radiation the α′-OETCA polymorph can be stabilized below 333 K with ca 8% of the monomer converted into the photodimer. The crystal structures of α′-OETCA are reported at two temperatures above the phase transition point (at 345 and 375 K) as well as the stabilized forms at 173 and 293 K. A mechanism for the phase transition involving a cooperative conformational transformation coupled with a shift of layers of OETCA molecules is proposed. The α′-OETCA polymorph is also an example of a cinnamic acid derivative where two different potentially photoreactive environments exist in one crystal in which each unit cell has two non-centrosymmetric predimer sites and one centrosymmetric predimer site.

Synchrotron X-ray and ab initio studies of β-Si3N4

Abstract: Almost absorption- and extinction-free single-crystal synchrotron X-ray diffraction data were measured at 150, 200 and 295 K for β-Si3N4, silicon nitride, at a wavelength of 0.7 A. The true symmetry of this material has been the subject of minor controversy for several decades. No compelling evidence favouring the low-symmetry P63 model was identified in this study.

Structural chemistry of new lithium bis(oxalato)borate solvates.

Abstract: Recently lithium bis(oxalato)borate, LiB(C2O4)2, has been proposed as an alternative lithium salt for the electrolyte in rechargeable batteries that do not contain explosive perchlorate, reactive fluoride or toxic arsenic. This lithium salt crystallizes in the form of solvates from such solvents as water, acetonitrile, acetone, dimethoxyethane, 1,3-dioxolane and ethylene carbonate. Their crystal structures were determined in order to explore the crystal chemistry of this lithium salt. It was found that most of the solvents consist of a lithium bis(oxalato)borate dimer in which the ligand acts as both a chelating and a bridging agent. Lithium has octahedral coordination that typically includes one or, less commonly, two solvent molecules. An exception to this rule is the ethylene carbonate solvate where the lithium is tetrahedrally surrounded exclusively by the solvent and bis(oxalato)borate plays the role of counter-ion only. The ethylene carbonate solvates were also studied for LiPF6 and LiAsF6 salts and they have similar structures to the bis(oxalato)borate tetrahedral complexes.

Photodimerization of the α'-polymorph of ortho-ethoxy-trans-cinnamic acid in the solid state. I. Monitoring the reaction at 293 K

Abstract: Structural changes that occur during the [2 + 2] photodimerization of the metastable α′-polymorph of ortho-ethoxy-trans-cinnamic acid at 293 K are presented here. Crystals of the α′-polymorph were first stabilized by exposing the α-polymorph to UV light for a short period of time at 343 K. The photodimerization reaction was then carried out at 293 K and observed in situ by single-crystal X-ray diffraction. The α′-polymorph contains three molecules in the asymmetric unit, labelled A, B and C, which are arranged to form two potential reaction sites. The intermolecular distance between the C=C bonds of molecules A and B (making up the AB site) is 3.6 A, and these were observed to undergo photodimerization at 293 K. The corresponding distance between centrosymmetrically related C=C bonds in the CC site (made up of C molecules) is 4.6 A, and these remain unreacted even after 60 h irradiation at 293 K. The crystal of the final product, which corresponds to a 66.7% conversion (only two out of three molecules in the asymmetric unit take part in the photodimerization reaction at 293 K), contains an ordered arrangement of the photodimer and unreacted monomer. The crystal retains many structural features of the original monomer crystal, including carboxylic acid hydrogen bonds and C—H⋯O interactions. Single-crystal X-ray diffraction was used to monitor changes in the unit-cell parameters, reacting molecules and molecular conformations as the reaction progressed. The conformation of the photodimer obtained from the solid-state reaction differs from that of the photodimer obtained by recrystallization from solution.

Atomic volumes and charges in a system with a strong hydrogen bond: L-tryptophan formic acid.

Abstract: A high-resolution X-ray diffraction data set was collected within 48 h at 100 K with synchrotron radiation and area detection. A full topological analysis was applied to the resulting electron-density model. This analysis was followed by a Bader partitioning making use of the zero-flux surfaces of the electron-density gradient vector field. The atomic and bonding properties obtained were compared with the results of previous experimental studies, and with theoretical calculations for the title complex and free tryptophan as reported in the literature. The agreement between experiment and theory is similar to the agreement between different theoretical calculations. There is no charge transfer via the strong hydrogen bond; however, its strength is indicated by the very small atomic volume of the H atom involved.

Calcium-lead fluoro-vanadinite apatites. II. Equilibrium structures

Abstract: The synthetic vanadinites (Pb(x)Ca(10-x))(VO4)6F2delta, 1 < x < 9, adopt a P6(3)/m apatite structure with 9.7590 (1) < or = a < or = 10.1179 (1) A and 7.0434 (3) < or = c < or = 7.4021 (1) A. The partitioning of calcium and lead over the AI(4f) and AII(6h) positions is nonstoichiometric with lead preferentially entering the larger AII site. High-resolution electron microscopy showed that samples annealed for 10 h at 1073 K are in disequilibrium with calcium- and lead-rich microdomains co-existing at unit-cell scales. For (Pb5Ca5)(VO4)6F2delta, sintering in excess of 2 weeks is required for the metals to order macroscopically. As annealing progresses, c/a, the partitioning coefficient kPb(AI/AII) and the AIO6 metaprism twist angle (phi) adjust cooperatively to enlarge the apatite channel, and thereby accommodate higher lead content. These results demonstrate that phi is a sensitive measure of disequilibrium and a useful device for monitoring changes in apatite topology as a function of composition.

30 Space-group corrections: two examples of false polymorphism and one of incorrect interpretation of the fine details of an IR spectrum

Abstract: Revised structures are reported for 30 crystalline compounds, based on space groups of higher symmetry than originally reported. In 18 cases the Laue class is revised, in seven cases the center of symmetry is added, in two cases the Laue class change is coupled with the addition of the center of symmetry, in two cases the addition of the center of symmetry also requires the addition of systematic absences and, finally, one case of the addition of systematic absences without changing the Laue group is reported. Two examples (CSD refcodes: DAMLIM and ABPZCU01) of false polymorphism and one (PAVJUR) of the erroneous interpretation of the fine details of IR spectra, owing to incorrect space-group determination, have been detected.

Structures and phase transitions of trigonal ZrMo2O8 and HfMo2O8.

Abstract: This paper describes the structures, thermal-expansion properties and phase transitions of the trigonal forms of ZrMo(2)O(8) and HfMo(2)O(8). Both phases adopt a P(-)3m structure at room temperature and show positive thermal expansion. Both phases also undergo a displacive phase transition at high temperature (ZrMo(2)O(8) at 487 K and HfMo(2)O(8) at 463 K) to a higher-symmetry structure that has lower thermal expansion. The structure of the high-temperature alpha'-AMo(2)O(8) form (A = Zr and Hf) has been refined from powder diffraction data in space group P(-)3m1.

Structural manifestations of proton transfer in complexes of 2,6-dichlorophenols with pyridines.

Abstract: DFT B3LYP/6-31G(d,p) calculations were performed to describe the proton transfer reaction pathway in the 2,6-dichlorophenolate of pyridine The aim of these calculations was to establish the character of the dependence of the structure parameters on the proton transfer and comparing the results with known structures, eg the 2,6-dichloro-4-nitro- and pentachlorophenolates of pyridines To make this comparison more reliable, the calculations were repeated with the use of a reaction-field correction with the Onsager radius and electric permittivity taken from the solid-state measurements The calculations show that the second approach gives a better description of the structural modifications during the proton transfer

Model for the crystal packing and conformational changes of biphenyl in incommensurate phase transitions.

Abstract: Standard atom-atom potentials for hydrocarbons and a torsional potential to account for the pi-electron conjugation energy were used to model the crystal structures and phase transitions of biphenyl. The model describes the high-temperature phase (I) with its planar molecule as a stationary point of the energy hypersurface. Phase I represents a low-energy barrier between the symmetry minima of the ground state (phase III), in which the molecule is twisted with torsion angles of opposite sign. Global-energy minimization was carried out by considering both regular structures, with one or two independent molecules, and quasi-one-dimensional superstructures built of N cells (N up to 16) of the high-temperature structure. The various energy-minimized biphenyl structures demonstrate remarkable similarity in their crystal packing; in particular, there are characteristic rows of cooperatively twisted molecules parallel to the superstructure dimension b. The structures built of centrosymmetric rows (P1, Z = 4 and 8) are almost as low in energy as the basic structure (an N = 2 superstructure, Pa, Z = 4); moreover, one of them is isostructural with the low-temperature p-quaterphenyl structure. With N > 8, structures of lower energy than that of the basic structure (N = 2) were found; their common feature is an M-fold modulation of the twist angle over the supercell period, with M smaller than N and generally not a simple fraction of it. The global minimum was found to conform to the ratio k = M/N = 6/14, which is close to the experimentally observed k = 6/13 in the incommensurate phase III. Enthalpy minimization showed an overall decrease in the magnitude of the twist angle down to tau approximately 0 degrees, as well as the evolution of the modulated structures towards the high-temperature structure with increasing pressure, in agreement with evidence for the high-pressure limit of the incommensurate biphenyl phases.

Crystal structure of the supramolecular linear polymer formed by the self-assembly of mono-6-deoxy-6-adamantylamide-β-cyclodextrin

Abstract: Mono-6-deoxy-6-adamantylamide-β-cyclodextrin–dimethyl­form­amide–15H2O, C53H85NO35·C3H7NO·15H2O, crystallizes in the orthorhombic space group P212121. The adamantyl group is inserted into the cyclodextrin cavity of the adjacent molecule, entering by the side of the secondary hydroxy rim, thus forming a supramolecular linear polymer by self-assembly. Adjacent macrocycles are linked into columns by hydrogen bonds involving the nearest glucose residues, and the structure is further stabilized by their involvement in hydrogen bonding with water molecules which reside in channels surrounding the polymer columns, thus acting as bridges between the cyclodextrin units. The centroid of the adamantyl group lies below the plane formed by the seven glycosidic O atoms of the host cyclodextrin, excluding water molecules from the secondary side of β-cyclodextrin (β-CD). Between the adamantyl group and the primary hydroxy rim of the cyclodextrin cavity lies a dimethylformamide molecule, which shields the hydrophobic adamantyl group from the primary hydroxy rim of its carrying β-CD and excludes water molecules from the primary side of the β-CD cavity.

Conformational change of N-benzylideneanilines in crystals.

Abstract: The crystal structures of N-(4-nitrobenzylidene)aniline (1), N-(4-chlorobenzylidene)-4-methylaniline (2) and N-(4-methylbenzylidene)-4-methylaniline (3) were determined by X-ray diffraction analyses at various temperatures. A dynamic disorder was observed in the crystal structures of all compounds. The dynamic disorder is accounted for in terms of a conformational change involving a pedal motion in the crystals.

X-ray diffraction and packing analysis on vintage crystals: Wilhelm Koerner's nitrobenzene derivatives from the School of Agricultural Sciences in Milano.

Abstract: The crystal structures of six nitrotoluene derivatives, synthesized by Wilhelm Koerner about a century ago and retrieved from a depository at the University of Milano, were determined. The correct assignment of molecular structures is verified. The geometry of the nitro groups and factors affecting the orientation of nitro groups with respect to the benzene ring are discussed, also using an auxiliary set of crystal structures retrieved from the Cambridge Structural Database. The crystal packings have been analyzed, and lattice energies have been calculated by atom–atom potential methods and by the newly proposed Pixel method. This method allows a more complete description of intermolecular potentials in terms of the interaction between molecular electron densities and separate Coulombic, polarization, dispersion and overlap repulsion energies. Lattice vibrations and external entropies were calculated by lattice-dynamical procedures. The results of the Pixel energy calculations allow a reliable, quantitative assessment of the relative importance of stacking interactions and hydrogen bonding in the rationalization of the recognition modes of nitrobenzene derivatives, which is impossible to attain using only qualitative atom– atom geometry concepts.