The accuracy of 215 experimental organic crystal structures from powder diffraction data is validated against a dispersion-corrected density functional theory method.
In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 Å for SX structures to 0.35 Å for XRPD structures; the grey area must be extended from 0.30 to 0.40 Å. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom.
dispersion-corrected density functional theory; powder data validation; energy mimimization
The crystal structure of (Z)-N-(5-ethyl-2,3-dihydro-1,3,4-thiadiazol-2-ylidene)-4-methylbenzenesulfonamide contains an imine tautomer, rather than the previously reported amine tautomer. The tautomers can be distinguished using dispersion-corrected density functional theory calculations and by comparison of calculated and measured 13C solid-state NMR spectra.
The crystal structure of the title compound, C11H13N3O2S2, has been determined previously on the basis of refinement against laboratory powder X-ray diffraction (PXRD) data, supported by comparison of measured and calculated 13C solid-state NMR spectra [Hangan et al. (2010 ▶). Acta Cryst. B66, 615–621]. The molecule is tautomeric, and was reported as an amine tautomer [systematic name: N-(5-ethyl-1,3,4-thiadiazol-2-yl)-p-toluenesulfonamide], rather than the correct imine tautomer. The protonation site on the molecule’s 1,3,4-thiadiazole ring is indicated by the intermolecular contacts in the crystal structure: N—H⋯O hydrogen bonds are established at the correct site, while the alternative protonation site does not establish any notable intermolecular interactions. The two tautomers provide essentially identical Rietveld fits to laboratory PXRD data, and therefore they cannot be directly distinguished in this way. However, the correct tautomer can be distinguished from the incorrect one by previously reported quantitative criteria based on the extent of structural distortion on optimization of the crystal structure using dispersion-corrected density functional theory (DFT-D) calculations. Calculation of the 13C SS-NMR spectrum based on the correct imine tautomer also provides considerably better agreement with the measured 13C SS-NMR spectrum.
crystal structure; powder diffraction; NMR analysis; amine–imine tautomerism; dispersion-corrected DFT
Chemical bonding at the active site of lysozyme is analyzed on the basis of a multipole model employing transferable multipole parameters from a database. Large B factors at low temperatures reflect frozen-in disorder, but therefore prevent a meaningful free refinement of multipole parameters.
Chemical bonding at the active site of hen egg-white lysozyme (HEWL) is analyzed on the basis of Bader’s quantum theory of atoms in molecules [QTAIM; Bader (1994 ▶), Atoms in Molecules: A Quantum Theory. Oxford University Press] applied to electron-density maps derived from a multipole model. The observation is made that the atomic displacement parameters (ADPs) of HEWL at a temperature of 100 K are larger than ADPs in crystals of small biological molecules at 298 K. This feature shows that the ADPs in the cold crystals of HEWL reflect frozen-in disorder rather than thermal vibrations of the atoms. Directly generalizing the results of multipole studies on small-molecule crystals, the important consequence for electron-density analysis of protein crystals is that multipole parameters cannot be independently varied in a meaningful way in structure refinements. Instead, a multipole model for HEWL has been developed by refinement of atomic coordinates and ADPs against the X-ray diffraction data of Wang and coworkers [Wang et al. (2007), Acta Cryst. D63, 1254–1268], while multipole parameters were fixed to the values for transferable multipole parameters from the ELMAM2 database [Domagala et al. (2012), Acta Cryst. A68, 337–351] . Static and dynamic electron densities based on this multipole model are presented. Analysis of their topological properties according to the QTAIM shows that the covalent bonds possess similar properties to the covalent bonds of small molecules. Hydrogen bonds of intermediate strength are identified for the Glu35 and Asp52 residues, which are considered to be essential parts of the active site of HEWL. Furthermore, a series of weak C—H⋯O hydrogen bonds are identified by means of the existence of bond critical points (BCPs) in the multipole electron density. It is proposed that these weak interactions might be important for defining the tertiary structure and activity of HEWL. The deprotonated state of Glu35 prevents a distinction between the Phillips and Koshland mechanisms.
hen egg-white lysozyme; multipole model; multipole parameters
The crystal structure of dizinc trimolybdenum(IV) octaoxide, Zn2Mo3O8, has been redetermined from single-crystal X-ray data. The structure has been reported previously based on neutron powder diffraction data [Hibble et al. (1999 ▶). Acta Cryst. B55, 683-697] and single-crystal data [McCarroll et al. (1957 ▶). J. Am. Chem. Soc.
79, 5410–5414; Ansell & Katz (1966 ▶) Acta Cryst.
21, 482–485]. The results of the current redetermination show an improvement in the precision of the structural and geometric parameters with all atoms refined with anisotropic displacement parameters. The crystal structure consists of distorted hexagonal-close-packed oxygen layers with stacking sequence abac along  and is held together by alternating zinc and molybdenum layers. The Zn atoms occupy both tetrahedral and octahedral interstices with a ratio of 1:1. The Mo atoms occupy octahedral sites and form strongly bonded triangular clusters involving three MoO6 octahedra that are each shared along two edges, forming a Mo3O13 unit. All atoms lie on special positions. The Zn atoms are in 2b Wyckoff positions with 3m. site symmetry, the Mo atoms are in 6c Wyckoff positions with . m. site symmetry and the O atoms are in 2a, 2b and 6c Wyckoff positions with 3m. and . m. site symmetries, respectively.
The redetermination of the crystal structure of lead tartrate from crystals grown in a gel medium confirmed the previous powder X-ray diffraction study in the space group P212121 with higher precision. Contradictions in the literature regarding space group and water content could be clarified.
Single crystals of poly[μ4-tartrato-κ6
4′-lead], [Pb(C4H4O6)]n, were grown in a gel medium. In comparison with the previous structure determination of this compound from laboratory powder X-ray diffraction data [De Ridder et al. (2002 ▸). Acta Cryst. C58, m596–m598], the redetermination on the basis of single-crystal data reveals the absolute structure, all atoms with anisotropic displacement parameters and a much higher accuracy in terms of bond lengths and angles. It could be shown that a different space group or incorporation of water as reported for similarly gel-grown lead tartrate crystals is incorrect. In the structure, each Pb2+ cation is bonded to eight O atoms of five tartrate anions, while each tartrate anion links four Pb2+ cations. The resulting three-dimensional framework is stabilized by O—H⋯O hydrogen bonds between the OH groups of one tartrate anion and the carboxylate O atoms of adjacent anions.
crystal structure; lead tartrate; gel growth; redetermination; O—H⋯O hydrogen bonds
The relatively complex structure of a triclinic disolvate was solved from low-resolution laboratory powder diffraction data through the intermediate use of dummy atoms and the combination with quantum-mechanical calculations.
With only a 2.6 Å resolution laboratory powder diffraction pattern of the θ phase of Pigment Yellow 181 (P.Y. 181) available, crystal-structure solution and Rietveld refinement proved challenging; especially when the crystal structure was shown to be a triclinic dimethylsulfoxide N-methyl-2-pyrrolidone (1:1:1) solvate. The crystal structure, which in principle has 28 possible degrees of freedom, was determined in three stages by a combination of simulated annealing, partial Rietveld refinement with dummy atoms replacing the solvent molecules and further simulated annealing. The θ phase not being of commercial interest, additional experiments were not economically feasible and additional dispersion-corrected density functional theory (DFT-D) calculations were employed to confirm the correctness of the crystal structure. After the correctness of the structure had been ascertained, the bond lengths and valence angles from the DFT-D minimized crystal structure were fed back into the Rietveld refinement as geometrical restraints (‘polymorph-dependent restraints’) to further improve the details of the crystal structure; the positions of the H atoms were also taken from the DFT-D calculations. The final crystal structure is a layered structure with an elaborate network of hydrogen bonds.
Pigment Yellow 181; X-ray powder diffraction; dispersion-corrected density functional theory
Multi-temperature single-crystal and powder diffraction experiments on 1-(2′-aminophenyl)-2-methyl-4-nitroimidazole show that this crystal undergoes an isomorphic phase transition with the coexistence of two phase domains over a wide temperature range. The anharmonic approach was the only way to model the resulting disorder.
The harmonic model of atomic nuclear motions is usually enough for multipole modelling of high-resolution X-ray diffraction data; however, in some molecular crystals, such as 1-(2′-aminophenyl)-2-methyl-4-nitro-1H-imidazole [Paul, Kubicki, Jelsch et al. (2011 ▶). Acta Cryst. B67, 365–378], it may not be sufficient for a correct description of the charge-density distribution. Multipole refinement using harmonic atom vibrations does not lead to the best electron density model in this case and the so-called ‘shashlik-like’ pattern of positive and negative residual electron density peaks is observed in the vicinity of some atoms. This slight disorder, which cannot be modelled by split atoms, was solved using third-order anharmonic nuclear motion (ANM) parameters. Multipole refinement of the experimental high-resolution X-ray diffraction data of 1-(2′-aminophenyl)-2-methyl-4-nitro-1H-imidazole at three different temperatures (10, 35 and 70 K) and a series of powder diffraction experiments (20 ≤ T ≤ 300 K) were performed to relate this anharmonicity observed for several light atoms (N atoms of amino and nitro groups, and O atoms of nitro groups) to an isomorphic phase transition reflected by a change in the b cell parameter around 65 K. The observed disorder may result from the coexistence of domains of two phases over a large temperature range, as shown by low-temperature powder diffraction.
anharmonicity; isomorphic phase transition; experimental charge density; X-ray closed-circuit helium cryostat; Hansen–Coppens model; multiple-temperature powder diffraction
Relationships between the crystal structures of two polymorphs of sodium naproxen dihydrate and its monohydrate and anhydrate phases provide a basis to rationalize the observed transformation pathways in the sodium (S)-naproxen anhydrate–hydrate system.
Crystal structures are presented for two dihydrate polymorphs (DH-I and DH-II) of the non-steroidal anti-inflammatory drug sodium (S)-naproxen. The structure of DH-I is determined from twinned single crystals obtained by solution crystallization. DH-II is obtained by solid-state routes, and its structure is derived using powder X-ray diffraction, solid-state 13C and 23Na MAS NMR, and molecular modelling. The validity of both structures is supported by dispersion-corrected density functional theory (DFT-D) calculations. The structures of DH-I and DH-II, and in particular their relationships to the monohydrate (MH) and anhydrate (AH) structures, provide a basis to rationalize the observed transformation pathways in the sodium (S)-naproxen anhydrate–hydrate system. All structures contain Na+/carboxylate/H2O sections, alternating with sections containing the naproxen molecules. The structure of DH-I is essentially identical to MH in the naproxen region, containing face-to-face arrangements of the naphthalene rings, whereas the structure of DH-II is comparable to AH in the naproxen region, containing edge-to-face arrangements of the naphthalene rings. This structural similarity permits topotactic transformation between AH and DH-II, and between MH and DH-I, but requires re-organization of the naproxen molecules for transformation between any other pair of structures. The topotactic pathways dominate at room temperature or below, while the non-topotactic pathways become active at higher temperatures. Thermochemical data for the dehydration processes are rationalized in the light of this new structural information.
pharmaceutical; hydrate; X-ray diffraction; solid-state NMR; DFT-D
A first-principle plane-wave pseudopotential method based on the density function theory (DFT) was employed to investigate the effects of vacancy cluster (VC) defects on the band structure and thermoelectric properties of silicon (Si) crystals. Simulation results showed that various VC defects changed the energy band and localized electron density distribution of Si crystals and caused the band gap to decrease with increasing VC size. The results can be ascribed to the formation of a defect level produced by the dangling bonds, floating bonds, or high-strain atoms surrounding the VC defects. The appearance of imaginary frequencies in the phonon spectrum of defective Si crystals indicates that the defect-region structure is dynamically unstable and demonstrates phase changes. The phonon dispersion relation and phonon density of state were also investigated using density functional perturbation theory. The obtained Debye temperature (θD) for a perfect Si crystal had a minimum value of 448 K at T = 42 K and a maximum value of 671 K at the high-temperature limit, which is consistent with the experimental results reported by Flubacher. Moreover, the Debye temperature decreased with increases in the VC size. VC defects had minimal effects on the heat capacity (Cv) value when temperatures were below 150 K. As the temperature was higher than 150 K, the heat capacity gradually increased with increasing temperature until it achieved a constant value of 11.8 cal/cell·K. The heat capacity significantly decreased as the VC size increased. For a 2 × 2 × 2 superlattice Si crystal containing a hexagonal ring VC (HRVC10), the heat capacity decreased by approximately 17%.
An additive all-atom empirical force field for aldopentofuranoses, methyl-aldopentofuranosides (Me-aldopentofuranosides) and fructofuranose carbohydrates, compatible with existing CHARMM carbohydrate parameters, is presented. Building on existing parameters transferred from cyclic ethers and hexopyranoses, parameters were further developed using target data for complete furanose carbohydrates as well as O-methyl tetrahydrofuran. The bond and angle equilibrium parameters were adjusted to reproduce target geometries from a survey of furanose crystal structures, and dihedral parameters were fit to over 1700 quantum mechanical (QM) MP2/cc-pVTZ//MP2/6-31G(d) conformational energies. The conformational energies were for a variety of complete furanose monosaccharides, and included two-dimensional ring pucker energy surfaces. Bonded parameter optimization led to the correct description of the ring pucker for a large set of furanose compounds, while furanose-water interaction energies and distances reproduced QM HF/6-31G(d) results for a number of furanose monosaccharides, thereby validating the nonbonded parameters. Crystal lattice unit cell parameters and volumes, aqueous-phase densities, and aqueous NMR ring pucker and exocyclic data were used to validate the parameters in condensed-phase environments. Conformational sampling analysis of the ring pucker and exocyclic group showed excellent agreement with experimental NMR data, demonstrating that the conformational energetics in aqueous solution are accurately described by the optimized force field. Overall, the parameters reproduce available experimental data well and are anticipated to be of utility in future computational studies of carbohydrates, including in the context of proteins, nucleic acids and/or lipids when combined with existing CHARMM biomolecular force fields.
furanose; furanoside; aldopentose; carbohydrates; ribose; arabinose; fructose; empirical force field
A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors via fast Fourier transformation is described for the first time.
Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered R
free by 20–40% relative to the original spherically symmetric scattering model.
scattering factors; aspherical; anisotropic; force fields; multipole; polarization; AMOEBA; bond density; direct summation; FFT; SGFFT; Ewald; PME
The structure of the O-methyl glycoside of the naturally
C10H18O8, has been determined by X-ray
crystallography at 100 K, supplementing the previously determined structure
obtained at 293 K (Acta Cryst., 1996, C52, 2285-2287). Molecular dynamics
simulations of this glycoside were performed in the crystal environment with
different numbers of units cells included in the primary simulation system at
both 100 K and 293 K. The calculated unit cell parameters and the
intra-molecular geometries (bonds, angles, and dihedrals) agree well with
experimental results. Atomic fluctuations, including B-factors and anisotropies,
are in good agreement with respect to the relative values on an atom-by-atom
basis. In addition, the fluctuations increase with increasing simulation system
size, with the simulated values converging to values lower than those observed
experimentally indicating that the simulation model is not accounting for all
possible contributions to the experimentally observed B-factors which may be
related to either the simulation time scale or size. In the simulations the
hydroxyl group of O7 is found to form bifurcated hydrogen bonds with O6 and O8
of an adjacent molecule, with the interactions dominated by the HO7-O6
interaction. Quantum mechanical calculations support this observation.
CHARMM force field; carbohydrates; molecular dynamics simulation; molecular modeling; monosaccharides
The new automated iterative Hirshfeld atom refinement method is explained and validated through comparison of structural models of Gly–l-Ala obtained from synchrotron X-ray and neutron diffraction data at 12, 50, 150 and 295 K. Structural parameters involving hydrogen atoms are determined with comparable precision from both experiments and agree mostly to within two combined standard uncertainties.
Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly–l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree–Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints – even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu’s), all other structural parameters agree within less than 2 csu’s. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å2 as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements – an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.
aspherical atom partitioning; quantum mechanical molecular electron densities; X-ray structure refinement; hydrogen atom modelling; anisotropic displacement parameters
An improved crystal structure of the title compound, C30H30O8 (systematic name: 1,1′,6,6′,7,7′-hexahydroxy-5,5′-diisopropyl-3,3′-dimethyl[2,2′-binaphthalene]-8,8′-dicarbaldehyde), was determined based on modern CCD data. Compared to the previous structure [Talipov et al. (1985). Khim. Prirod. Soedin. (Chem. Nat. Prod.), 6, 20–24], geometrical precision has been improved (typical C—C bond-distance s.u. = 0.002 Å in the present structure compared to 0.005 Å in the previous structure) and the locations of several H atoms have been corrected. The gossypol molecules are in the aldehyde tautomeric form and the dihedral angle between the naphthyl fragments is 80.42 (4)°. Four intramolecular O—H⋯O hydrogen bonds are formed. In the crystal, inversion dimers with graph-set motif R
2(20) are formed by pairs of O—H⋯O hydrogen bonds; another pair of O—H⋯O hydrogen bonds with the same graph-set motif links the dimers into  chains. The packing of such chains in the crystal leads to the formation of channels (diameter = 5–8 Å) propagating in the  direction. The channels presumably contain highly disordered solvent molecules; their contribution to the scattering was removed with the SQUEEZE [Spek (2015). Acta Cryst. C71, 9–18] routine in PLATON and the stated molecular mass, density etc., do not take them into account.
crystal structure; redetermination; gossypol; polymorph; hydrogen bonding
The crystal structure of the title compound, 4-hydroxy-2-pyridone, C5H5NO2, which has been the subject of several determinations using X-rays and neutron diffraction, was first reported by Low & Wilson [Acta Cryst. (1983). C39, 1688–1690]. It has been redetermined, providing a significant increase in the precision of the derived geometric parameters. The asymmetric unit comprises a planar 4-enol tautomer having some degree of delocalization of π-electron density through the molecule. In the crystal structure, the molecules are connected into chains by two strong O—H⋯O and N—H⋯O hydrogen bonds between the OH and NH groups and the carbonyl O atom.
The crystal structure of the title compound, [ZnCl2(C15H11N3)], was redetermined based on modern CCD data. In comparison with the previous determination from photographic film data [Corbridge & Cox (1956 ▶). J. Chem. Soc.
159, 594–603; Einstein & Penfold (1966 ▶). Acta Cryst.
20, 924–926], all non-H atoms were refined with anisotropic displacement parameters, leading to a much higher precision in terms of bond lengths and angles [e.g. Zn—Cl = 2.2684 (8) and 2.2883 (11) compared to 2.25 (1) and 2.27 (1) Å]. In the title molecule, the ZnII atom is five-coordinated in a distorted square-pyramidal mode by two Cl atoms and by the three N atoms from the 2,2′:6′,2′′-terpyridine ligand. The latter is not planar and shows dihedral angles between the least-squares planes of the central pyridine ring and the terminal rings of 3.18 (8) and 6.36 (9)°. The molecules in the crystal structure pack with π–π interactions [centroid–centroid distance = 3.655 (2) Å] between pyridine rings of neighbouring terpyridine moieties. These, together with intermolecular C—H⋯Cl interactions, stablize the three-dimensional structure.
crystal structure; redetermination; 2,2′:6′,2′′-terpyridine; zinc complex; π–π interactions
Alkali metal atoms are frequently
used for simple yet efficient
n-type doping of organic semiconductors and as an ingredient of the
recently discovered polycyclic aromatic hydrocarbon superconductors.
However, the incorporation of dopants from the gas phase into molecular
crystal structures needs to be controlled and well understood in order
to optimize the electronic properties (charge carrier density and
mobility) of the target material. Here, we report that potassium intercalation
into the pristine 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA)
monolayer domains on a Ag(111) substrate induces distinct stoichiometry-dependent
structural reordering processes, resulting in highly ordered and large
KxPTCDA domains. The emerging structures
are analyzed by low-temperature scanning tunneling microscopy, scanning
tunneling hydrogen microscopy (ST[H]M), and low-energy electron diffraction
as a function of the stoichiometry. The analysis of the measurements
is corroborated by density functional theory calculations. These turn
out to be essential for a correct interpretation of the experimental
ST[H]M data. The epitaxy types for all intercalated stages are determined
as point-on-line. The K atoms adsorb in the vicinity of the oxygen
atoms of the PTCDA molecules, and their positions are determined with
sub-Ångström precision. This is a crucial prerequisite
for the prospective assessment of the electronic properties of such
composite films, as they depend rather sensitively on the mutual alignment
between donor atoms and acceptor molecules. Our results demonstrate
that only the combination of experimental and theoretical approaches
allows for an unambiguous explanation of the pronounced reordering
of KxPTCDA/Ag(111) upon changing the K
potassium intercalation; self-assembled nanostructures; low-temperature scanning
tunneling microscopy (LT-STM); scanning tunneling hydrogen
microscopy (STHM); density functional
theory (DFT); low-energy electron diffraction (LEED)
A brief overview, with examples, of the evolution of molecular-replacement methods and models over the past few years is presented.
The ‘phase problem’ in crystallography results from the inability to directly measure the phases of individual diffracted X-ray waves. While intensities are directly measured during data collection, phases must be obtained by other means. Several phasing methods are available (MIR, SAR, MAD, SAD and MR) and they all rely on the premise that phase information can be obtained if the positions of marker atoms in the unknown crystal structure are known. This paper is dedicated to the most popular phasing method, molecular replacement (MR), and represents a personal overview of the development, use and requirements of the methodology. The first description of noncrystallographic symmetry as a tool for structure determination was explained by Rossmann and Blow [Rossmann & Blow (1962 ▶), Acta Cryst.
15, 24–31]. The term ‘molecular replacement’ was introduced as the name of a book in which the early papers were collected and briefly reviewed [Rossmann (1972 ▶), The Molecular Replacement Method. New York: Gordon & Breach]. Several programs have evolved from the original concept to allow faster and more sophisticated searches, including six-dimensional searches and brute-force approaches. While careful selection of the resolution range for the search and the quality of the data will greatly influence the outcome, the correct choice of the search model is probably still the main criterion to guarantee success in solving a structure using MR. Two of the main parameters used to define the ‘best’ search model are sequence identity (25% or more) and structural similarity. Another parameter that may often be undervalued is the quality of the probe: there is clearly a relationship between the quality and the correctness of the chosen probe and its usefulness as a search model. Efforts should be made by all structural biologists to ensure that their deposited structures, which are potential search probes for future systems, are of the best possible quality.
molecular replacement; models; accuracy; quality
An extension is proposed to the rigid-bond description of atomic thermal motion in crystals.
The rigid-bond model [Hirshfeld (1976 ▶). Acta Cryst. A32, 239–244] states that the mean-square displacements of two atoms are equal in the direction of the bond joining them. This criterion is widely used for verification (as intended by Hirshfeld) and also as a restraint in structure refinement as suggested by Rollett [Crystallographic Computing (1970 ▶), edited by F. R. Ahmed et al., pp. 167–181. Copenhagen: Munksgaard]. By reformulating this condition, so that the relative motion of the two atoms is required to be perpendicular to the bond, the number of restraints that can be applied per anisotropic atom is increased from about one to about three. Application of this condition to 1,3-distances in addition to the 1,2-distances means that on average just over six restraints can be applied to the six anisotropic displacement parameters of each atom. This concept is tested against very high resolution data of a small peptide and employed as a restraint for protein refinement at more modest resolution (e.g. 1.7 Å).
rigid-bond test; refinement restraints; anisotropic displacement parameters
Liquid-phase bonding is a technologically important method to fabricate high-performance metal/ceramic heterostructures used for power electronic devices. However, the atomic-scale mechanisms of how these two dissimilar crystals specifically bond at the interfaces are still not well understood. Here we analyse the atomically-resolved structure of a liquid-phase bonded heterointerface between Al alloy and AlN single crystal using aberration corrected scanning transmission electron microscopy (STEM). In addition, energy-dispersive X-ray microanalysis, using dual silicon drift X-ray detectors in STEM, was performed to analyze the local chemistry of the interface. We find that a monolayer of MgO is spontaneously formed on the AlN substrate surface and that a polarity-inverted monolayer of AlN is grown on top of it. Thus, the Al alloy is bonded with the polarity-inverted AlN monolayer, creating a complex atomic-scale layered structure, facilitating the bonding between the two dissimilar crystals during liquid-phase bonding processes. Density-functional-theory calculations confirm that the bonding stability is strongly dependent on the polarity and stacking of AlN and MgO monolayers. Understanding the spontaneous formation of layered transition structures at the heterointerface will be key in fabricating very stable Al alloy/AlN heterointerface required for high reliability power electronic devices.
The title complex, [Cu(C17H13N2O2)2], crystallizes with two independent molecules in the asymmetric unit. Each CuII atom has a distorted ocahedral coordination environment defined by two N atoms and four O atoms from two tridentate 1-[(E)-(2-methoxyphenyl)diazenyl]naphthalen-2-olate ligands. In the crystal, the two molecules are linked via weak C—H⋯O hydrogen bonds which in turn stack parallel to . A region of disordered electron density, most probably disordered methanol solvent molecules, was corrected for using the SQUEEZE routine in PLATON [Spek (2015). Acta Cryst. C71, 9–18]. Their formula mass and unit-cell characteristics were not taken into account during refinement.
crystal structure; naphthalen-2-olate; copper(II) complex; octahedral coordination; azo compounds
Diffuse scattering from PZN (PbZn1/3Nb2/3O3) has been analysed by combining the average structure revealed by Bragg diffraction with the requirements of the bond-valence sum. This goes beyond previous models, which are more prescriptive and artificial in nature, although not all key aspects of the short-range order can be shown to arise ‘naturally’ out of the modelled interactions.
This work extends previous efforts to model diffuse scattering from PZN (PbZn1/3Nb2/3O3). Earlier work [Welberry et al. (2005 ▶). J. Appl. Cryst.
38, 639–647; Welberry et al. (2006 ▶). Phys. Rev. B, 74, 224108] is highly prescriptive, using Monte Carlo simulation with very artificial potentials to induce short-range-order structures which were deduced as necessary from inspection of the data. While this gives valid results for the nature of the local structure, it does not strongly relate these structures to underlying crystal chemistry. In that work, the idea of the bond-valence sum was used as a guide to the expected behaviour of the atoms. This paper extends the use of the bond-valence sum from a qualitative guide to becoming a key aspect of the potential experienced by the atoms, through the idea of the global instability index, whose square has been shown to be proportional to the density functional theory energy of some systems when close to the minimum energy configuration.
neutron scattering; X-ray scattering; relaxor ferroelectrics; single crystals; short-range order; diffuse scattering; PZN
Single crystals of silver(I) polyphosphate(V), AgPO3, were prepared via a phosphoric acid melt method using a solution of Ag3PO4 in H3PO4. In comparison with the previous study based on single-crystal Weissenberg photographs [Jost (1961 ▶). Acta Cryst. 14, 779–784], the results were mainly confirmed, but with much higher precision and with all displacement parameters refined anisotropically. The structure is built up from two types of distorted edge- and corner-sharing [AgO5] polyhedra, giving rise to multidirectional ribbons, and from two types of PO4 tetrahedra linked into meandering chains (PO3)n spreading parallel to the b axis with a repeat unit of four tetrahedra. The calculated bond-valence sum value of one of the two AgI ions indicates a significant strain of the structure.
When refining the fit of component atomic structures into electron microscopic reconstructions, use of a resolution-dependent atomic density function makes it possible to jointly optimize the atomic model and imaging parameters of the microscope. Atomic density is calculated by one-dimensional Fourier transform of atomic form factors convoluted with a microscope envelope correction and a low-pass filter, allowing refinement of imaging parameters such as resolution, by optimizing the agreement of calculated and experimental maps. A similar approach allows refinement of atomic displacement parameters, providing indications of molecular flexibility even at low resolution. A modest improvement in atomic coordinates is possible following optimization of these additional parameters. Methods have been implemented in a Python program that can be used in stand-alone mode for rigid-group refinement, or embedded in other optimizers for flexible refinement with stereochemical restraints. The approach is demonstrated with refinements of virus and chaperonin structures at resolutions of 9 through 4.5 Å, representing regimes where rigid-group and fully flexible parameterizations are appropriate. Through comparisons to known crystal structures, flexible fitting by RSRef is shown to be an improvement relative to other methods and to generate models with all-atom rms accuracies of 1.5–2.5 Å at resolutions of 4.5–6 Å.
Fitting; Optimization; Structure; Resolution; Restraint; B-factor; Flexibility
The title compound, Na(C2H10N2)[Co(C2O4)(C2H8N2)2]4[H5(P2W18O62)2]·14H2O, prepared under hydrothermal conditions, consists of two Dawson-type [P2W18O62]6− anions, four isolated [Co(en)2(ox)]+ cations (en = ethylenediamine and ox = oxalate), one Na+ cation, one [H2en]2+ cation, and a number of ordered (14) and disordered solvent water molecules. The [P2W18O62]6− polyoxidometalate anion has site symmetry 1 and contains two structurally distinct types of W atoms: viz. six W atoms on vertical pseudo-mirror planes grouped in two sets of three, and 12 equatorial W atoms that do not lie in the pseudo-mirror planes grouped in two sets of six. In each [Co(en)2(ox)]+ cation, the CoIII ion is coordinated by four N atoms from two en ligands and two O atoms from the ox ligands, completing a distorted octahedral structure. The sodium cation lies on an inversion centre and additionally links the complex cations and anions. In the crystal, the various units are linked by N—H⋯O and O—H⋯O hydrogen bonds, which together with C—H⋯O hydrogen bonds form a three-dimensional structure. The contribution of a region of disordered electron density, possibly highly disordered solvent water molecules, to the scattering was removed with the SQUEEZE option of PLATON [Spek (2009 ▶). Acta Cryst. D65, 148–155]. To equilibrate the charges five H+ ions have been added to the polyoxidometalate. These H+ ions and the disordered solvent contribution were not included in the reported molecular weight and density.