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1.  Distinguishing tautomerism in the crystal structure of (Z)-N-(5-ethyl-2,3-di­hydro-1,3,4-thia­diazol-2-yl­idene)-4-methyl­benzene­sulfonamide using DFT-D calculations and 13C solid-state NMR 
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.
PMCID: PMC4174016  PMID: 25093360
crystal structure; powder diffraction; NMR analysis; amine–imine tautomerism; dispersion-corrected DFT
2.  The active site of hen egg-white lysozyme: flexibility and chemical bonding 
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.
PMCID: PMC3975892  PMID: 24699657
hen egg-white lysozyme; multipole model; multipole parameters
3.  Structure of Pigment Yellow 181 dimethylsulfoxide N-methyl-2-pyrrolidone (1:1:1) solvate from XRPD + DFT-D 
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.
PMCID: PMC4316649  PMID: 25643720
Pigment Yellow 181; X-ray powder diffraction; dispersion-corrected density functional theory
4.  Redetermination of Zn2Mo3O8  
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 [001] 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.
PMCID: PMC2969349  PMID: 21582645
5.  Structural basis for the transformation pathways of the sodium naproxen anhydrate–hydrate system 
IUCrJ  2014;1(Pt 5):328-337.
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.
PMCID: PMC4174875  PMID: 25295174
pharmaceutical; hydrate; X-ray diffraction; solid-state NMR; DFT-D
6.  Effects of Vacancy Cluster Defects on Electrical and Thermodynamic Properties of Silicon Crystals 
The Scientific World Journal  2014;2014:863404.
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%.
PMCID: PMC3913515  PMID: 24526923
7.  Crystal structure of lead(II) tartrate: a redetermination 
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 O 1,O 3:O 1′:O 2,O 4:O 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.
PMCID: PMC4331892
crystal structure; lead tartrate; gel growth; redetermination; O—H⋯O hydrogen bonds
8.  Hirshfeld atom refinement 
IUCrJ  2014;1(Pt 5):361-379.
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.
PMCID: PMC4174878  PMID: 25295177
aspherical atom partitioning; quantum mechanical molecular electron densities; X-ray structure refinement; hydrogen atom modelling; anisotropic displacement parameters
9.  Anharmonicity and isomorphic phase transition: a multi-temperature X-ray single-crystal and powder diffraction study of 1-(2′-aminophenyl)-2-methyl-4-nitroimidazole 
Iucrj  2014;1(Pt 2):110-118.
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.
PMCID: PMC4062092  PMID: 25075327
anharmonicity; isomorphic phase transition; experimental charge density; X-ray closed-circuit helium cryostat; Hansen–Coppens model; multiple-temperature powder diffraction
10.  CHARMM Additive All-Atom Force Field for Aldopentofuranoses, Methyl-Aldopentofuranosides and Fructofuranose 
The journal of physical chemistry. B  2009;113(37):12466-12476.
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.
PMCID: PMC2741538  PMID: 19694450
furanose; furanoside; aldopentose; carbohydrates; ribose; arabinose; fructose; empirical force field
11.  Polarizable atomic multipole X-ray refinement: application to peptide crystals 
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.
PMCID: PMC2733883  PMID: 19690373
scattering factors; aspherical; anisotropic; force fields; multipole; polarization; AMOEBA; bond density; direct summation; FFT; SGFFT; Ewald; PME
12.  The Potential Utility of Predicted One Bond Carbon-Proton Coupling Constants in the Structure Elucidation of Small Organic Molecules by NMR Spectroscopy 
PLoS ONE  2014;9(11):e111576.
NMR spectroscopy is the most popular technique used for structure elucidation of small organic molecules in solution, but incorrect structures are regularly reported. One-bond proton-carbon J-couplings provide additional information about chemical structure because they are determined by different features of molecular structure than are proton and carbon chemical shifts. However, these couplings are not routinely used to validate proposed structures because few software tools exist to predict them. This study assesses the accuracy of Density Functional Theory for predicting them using 396 published experimental observations from a diverse range of small organic molecules. With the B3LYP functional and the TZVP basis set, Density Functional Theory calculations using the open-source software package NWChem can predict one-bond CH J-couplings with good accuracy for most classes of small organic molecule. The root-mean-square deviation after correction is 1.5 Hz for most sp3 CH pairs and 1.9 Hz for sp2 pairs; larger errors are observed for sp3 pairs with multiple electronegative substituents and for sp pairs. These results suggest that prediction of one-bond CH J-couplings by Density Functional Theory is sufficiently accurate for structure validation. This will be of particular use in strained ring systems and heterocycles which have characteristic couplings and which pose challenges for structure elucidation.
PMCID: PMC4218771  PMID: 25365289
13.  Bifurcated Hydrogen Bonding and Asymmetric Fluctuations in a Carbohydrate Crystal Studied via X-ray Crystallography and Computational analysis 
The journal of physical chemistry. B  2013;117(25):7546-7553.
The structure of the O-methyl glycoside of the naturally occurring 6-O-[(R)-1-carboxyethyl]-α-d-galactopyranose, 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.
PMCID: PMC3771504  PMID: 23738792
CHARMM force field; carbohydrates; molecular dynamics simulation; molecular modeling; monosaccharides
14.  Atomic modeling of cryo-electron microscopy reconstructions – Joint refinement of model and imaging parameters 
Journal of structural biology  2013;182(1):10-21.
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.
PMCID: PMC3662558  PMID: 23376441
Fitting; Optimization; Structure; Resolution; Restraint; B-factor; Flexibility
15.  Cage-Forming Compounds in the Ba–Rh–Ge System: From Thermoelectrics to Superconductivity 
Inorganic Chemistry  2013;52(2):931-943.
Phase relations and solidification behavior in the Ge-rich part of the phase diagram have been determined in two isothermal sections at 700 and 750 °C and in a liquidus projection. A reaction scheme has been derived in the form of a Schulz–Scheil diagram. Phase equilibria are characterized by three ternary compounds: τ1-BaRhGe3 (BaNiSn3-type) and two novel phases, τ2-Ba3Rh4Ge16 and τ3-Ba5Rh15Ge36-x, both forming in peritectic reactions. The crystal structures of τ2 and τ3 have been elucidated from single-crystal X-ray intensity data and were found to crystallize in unique structure types: Ba3Rh4Ge16 is tetragonal (I4/mmm, a = 0.65643(2) nm, c = 2.20367(8) nm, and RF = 0.0273), whereas atoms in Ba5Rh15Ge36–x (x = 0.25) arrange in a large orthorhombic unit cell (Fddd, a = 0.84570(2) nm, b = 1.4725(2) nm, c = 6.644(3) nm, and RF = 0.034). The body-centered-cubic superstructure of binary Ba8Ge43□3 was observed to extend at 800 °C to Ba8Rh0.6Ge43□2.4, while the clathrate type I phase, κI-Ba8RhxGe46–x–y□y, reveals a maximum solubility of x = 1.2 Rh atoms in the structure at a vacancy level of y = 2.0. The cubic lattice parameter increases with increasing Rh content. Clathrate I decomposes eutectoidally at 740 °C: κI ⇔ (Ge) + κIX + τ2. A very small solubility range is observed at 750 °C for the clathrate IX, κIX-Ba6RhxGe25–x (x ∼ 0.16). Density functional theory calculations have been performed to derive the enthalpies of formation and densities of states for various compositions Ba8RhxGe46–x (x = 0–6). The physical properties have been investigated for the phases κI, τ1, τ2, and τ3, documenting a change from thermoelectric (κI) to superconducting behavior (τ2). The electrical resistivity of κI-Ba8Rh1.2Ge42.8□2.0 increases almost linearly with the temperature from room temperature to 730 K, and the Seebeck coefficient is negative throughout the same temperature range. τ1-BaRhGe3 has a typical metallic electrical resistivity. A superconducting transition at TC = 6.5 K was observed for τ2-Ba3Rh4Ge16, whereas τ3-Ba5Rh15Ge35.75 showed metallic-like behavior down to 4 K.
Phase equilibria in the Ba−Rh−Ge system are characterized by three ternary cage compounds: τ 1-BaRhGe3 (BaNiSn3-type) and two novel phases with unique structures, τ 2-Ba3Rh4Ge16 and τ 3-Ba5Rh15Ge36−x, besides κI-Ba8RhxGe46−x−y□y (x ≤ 1.2 and y ≥ 2.0). Density functional theory calculations for the enthalpies of formation and density of states for various compositions Ba8RhxGe46−x (x = 0−6) demonstrate a strong stabilizing influence of Ge/Rh substitution. The physical properties have been investigated for κI, τ 1, τ 2, and τ 3, documenting a change from n-type thermoelectric (κI) to superconducting behavior (τ 2; TC = 6.5 K).
PMCID: PMC3557931  PMID: 23286379
16.  Redetermination of 3-deaza­uracil 
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.
PMCID: PMC2961372  PMID: 21202619
17.  The Catalytic Mn2+ Sites in the Enolase-Inhibitor Complex - Crystallography, Single Crystal EPR and DFT Calculations 
Crystals of Zn2+ / Mn2+ yeast enolase with the inhibitor PhAH (phosphonoacetohydroxamate) were grown under conditions with a slight preference for binding of Zn2+ at the higher affinity site, site I. The structure of the Zn2+/Mn2+ PhAH complex was solved at a resolution of 1.54 Å and the two catalytic metal binding sites, I and II, show only subtle displacement compared to that of the corresponding complex with the native Mg2+ ions. Low temperature echo-detected high field (W-band, 95 GHz) EPR (electron paramagnetic resonance) and 1H ENDOR (electron-nuclear double resonance) were carried out on a single crystal and rotation patterns were acquired in two perpendicular planes. Analysis of the rotation patterns resolved a total of six Mn2+sites; four symmetry related sites of one type and two out of the four of the other type. The observation of two chemically inequivalent Mn2+ sites shows that Mn2+ ions populates both site I and II and the zero-field splitting ( ZFS) tensors of the Mn2+ in the two sites were determined. The Mn2+site with the larger D-value was assigned to site I based on the 1H ENDOR spectra, which identified the relevant water ligands. This assignment is consistent with the seemingly larger deviation of site I from octahedral symmetry, compared to site II. The ENDOR results gave the coordinates of the protons of two water ligands and adding them to the crystal structure revealed their involvement in a network of H-bonds stabilizing the binding of the metal ions and PhAH. Although specific hyperfine interactions with the inhibitor were not determined, the spectroscopic properties of the Mn2+ in the two sites were consistent with the crystal structure. Density functional theory (DFT) calculations carried out on a cluster representing the catalytic site, with Mn2+ in site I and Zn2+ in site II, and vice versa, gave overestimated D values on the order of the experimental ones, although the larger D value was found for Mn2+ in site II rather than in site I. This was attributed to the high sensitivity of the ZFS parameters to the Mn-O bond lengths and orientations, such that small, but significant differences between the optimized and crystal structure alter the ZFS considerably, well above the difference between the two sites.
PMCID: PMC2538446  PMID: 17367133
18.  Simulations of a protein crystal: Explicit treatment of crystallization conditions links theory and experiment in the streptavidin-biotin complex 
Biochemistry  2008;47(46):12065-12077.
A 250ns molecular dynamics simulation of the biotin-liganded streptavidin crystal lattice, including cryo-protectant molecules and crystallization salts, is compared to a 250ns simulation of the lattice solvated with pure water. The simulation using detailed crystallization conditions preserves the initial X-ray structure better than the simulation using pure water, even though the protein molecules display comparable mobility in either simulation. Atomic fluctuations computed from the simulation with crystallization conditions closely reproduce fluctuations derived from experimental temperature factors (correlation coefficient 0.88, omitting two N-terminal residues with very high experimental B-factors). In contrast, fluctuations calculated from the simulation with pure water were less accurate, particularly for two of the streptavidin loops exposed to solvent in the crystal lattice. Finally, we obtain good agreement between the water and cryo-protectant densities obtained from the simulated crystallization conditions and the electron density due to solvent molecules in the X-ray structure. Our results suggest that detailed lattice simulations with realistic crystallization conditions can be used to assess potential function parameters, validate simulation protocols, and obtain valuable insights that solution-phase simulations do not easily provide. We anticipate that this will prove to be a powerful strategy for molecular dynamics simulations of biomolecules.
PMCID: PMC2765329  PMID: 18950193
Protein crystal; simulation; streptavidin; lattice; molecular mechanics; water; glycerol; atomic fluctuations
19.  Crystal structure of di­chlorido­(2,2′:6′,2′′-terpyridine-κ3 N,N′,N′′)zinc: a redeter­min­ation 
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.
PMCID: PMC4257341  PMID: 25484786
crystal structure; redetermination; 2,2′:6′,2′′-terpyridine; zinc complex; π–π inter­actions
20.  Rigidity analysis of protein biological assemblies and periodic crystal structures 
BMC Bioinformatics  2013;14(Suppl 18):S2.
We initiate in silico rigidity-theoretical studies of biological assemblies and small crystals for protein structures. The goal is to determine if, and how, the interactions among neighboring cells and subchains affect the flexibility of a molecule in its crystallized state. We use experimental X-ray crystallography data from the Protein Data Bank (PDB). The analysis relies on an effcient graph-based algorithm. Computational experiments were performed using new protein rigidity analysis tools available in the new release of our KINARI-Web server
We provide two types of results: on biological assemblies and on crystals. We found that when only isolated subchains are considered, structural and functional information may be missed. Indeed, the rigidity of biological assemblies is sometimes dependent on the count and placement of hydrogen bonds and other interactions among the individual subchains of the biological unit. Similarly, the rigidity of small crystals may be affected by the interactions between atoms belonging to different unit cells.
We have analyzed a dataset of approximately 300 proteins, from which we generated 982 crystals (some of which are biological assemblies). We identified two types of behaviors. (a) Some crystals and/or biological assemblies will aggregate into rigid bodies that span multiple unit cells/asymmetric units. Some of them create substantially larger rigid cluster in the crystal/biological assembly form, while in other cases, the aggregation has a smaller effect just at the interface between the units. (b) In other cases, the rigidity properties of the asymmetric units are retained, because the rigid bodies did not combine.
We also identified two interesting cases where rigidity analysis may be correlated with the functional behavior of the protein. This type of information, identified here for the first time, depends critically on the ability to create crystals and biological assemblies, and would not have been observed only from the asymmetric unit.
For the Ribonuclease A protein (PDB file 5RSA), which is functionally active in the crystallized form, we found that the individual protein and its crystal form retain the flexibility parameters between the two states. In contrast, a derivative of Ribonuclease A (PDB file 9RSA), has no functional activity, and the protein in both the asymmetric and crystalline forms, is very rigid.
For the vaccinia virus D13 scaffolding protein (PDB file 3SAQ), which has two biological assemblies, we observed a striking asymmetry in the rigidity cluster decomposition of one of them, which seems implausible, given its symmetry. Upon careful investigation, we tracked the cause to a placement decision by the Reduce software concerning the hydrogen atoms, thus affecting the distribution of certain hydrogen bonds. The surprising result is that the presence or lack of a very few, but critical, hydrogen bonds, can drastically affect the rigid cluster decomposition of the biological assembly.
The rigidity analysis of a single asymmetric unit may not accurately reflect the protein's behavior in the tightly packed crystal environment. Using our KINARI software, we demonstrated that additional functional and rigidity information can be gained by analyzing a protein's biological assembly and/or crystal structure. However, performing a larger scale study would be computationally expensive (due to the size of the molecules involved). Overcoming this limitation will require novel mathematical and computational extensions to our software.
PMCID: PMC3817814  PMID: 24564201
21.  The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’ 
ChemistryOpen  2014;3(5):177-189.
Reliable thermochemical measurements and theoretical predictions for reactions involving large transition metal complexes in which long-range intramolecular London dispersion interactions contribute significantly to their stabilization are still a challenge, particularly for reactions in solution. As an illustrative and chemically important example, two reactions are investigated where a large dipalladium complex is quenched by bulky phosphane ligands (triphenylphosphane and tricyclohexylphosphane). Reaction enthalpies and Gibbs free energies were measured by isotherm titration calorimetry (ITC) and theoretically ‘back-corrected’ to yield 0 K gas-phase reaction energies (ΔE). It is shown that the Gibbs free solvation energy calculated with continuum models represents the largest source of error in theoretical thermochemistry protocols. The (‘back-corrected’) experimental reaction energies were used to benchmark (dispersion-corrected) density functional and wave function theory methods. Particularly, we investigated whether the atom-pairwise D3 dispersion correction is also accurate for transition metal chemistry, and how accurately recently developed local coupled-cluster methods describe the important long-range electron correlation contributions. Both, modern dispersion-corrected density functions (e.g., PW6B95-D3(BJ) or B3LYP-NL), as well as the now possible DLPNO-CCSD(T) calculations, are within the ‘experimental’ gas phase reference value. The remaining uncertainties of 2–3 kcal mol−1 can be essentially attributed to the solvation models. Hence, the future for accurate theoretical thermochemistry of large transition metal reactions in solution is very promising.
PMCID: PMC4234214  PMID: 25478313
density functional theory; isothermal titration calorimetry; local coupled cluster; London dispersion interactions; transition metal reactions
22.  Molecular replacement then and now 
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.
PMCID: PMC3817701  PMID: 24189239
molecular replacement; models; accuracy; quality
23.  Exploiting the Synergy of Powder X-ray Diffraction and Solid-State NMR Spectroscopy in Structure Determination of Organic Molecular Solids 
We report a strategy for structure determination of organic materials in which complete solid-state nuclear magnetic resonance (NMR) spectral data is utilized within the context of structure determination from powder X-ray diffraction (XRD) data. Following determination of the crystal structure from powder XRD data, first-principles density functional theory-based techniques within the GIPAW approach are exploited to calculate the solid-state NMR data for the structure, followed by careful scrutiny of the agreement with experimental solid-state NMR data. The successful application of this approach is demonstrated by structure determination of the 1:1 cocrystal of indomethacin and nicotinamide. The 1H and 13C chemical shifts calculated for the crystal structure determined from the powder XRD data are in excellent agreement with those measured experimentally, notably including the two-dimensional correlation of 1H and 13C chemical shifts for directly bonded 13C–1H moieties. The key feature of this combined approach is that the quality of the structure determined is assessed both against experimental powder XRD data and against experimental solid-state NMR data, thus providing a very robust validation of the veracity of the structure.
PMCID: PMC3876745  PMID: 24386493
24.  On the use of logarithmic scales for analysis of diffraction data 
Conventional and free R factors and their difference, as well as the ratio of the number of measured reflections to the number of atoms in the crystal, were studied as functions of the resolution at which the structures were reported. When the resolution was taken uniformly on a logarithmic scale, the most frequent values of these functions were quasi-linear over a large resolution range.
Predictions of the possible model parameterization and of the values of model characteristics such as R factors are important for macromolecular refinement and validation protocols. One of the key parameters defining these and other values is the resolution of the experimentally measured diffraction data. The higher the resolution, the larger the number of diffraction data N ref, the larger its ratio to the number N at of non-H atoms, the more parameters per atom can be used for modelling and the more precise and detailed a model can be obtained. The ratio N ref/N at was calculated for models deposited in the Protein Data Bank as a function of the resolution at which the structures were reported. The most frequent values for this distribution depend essentially linearly on resolution when the latter is expressed on a uniform logarithmic scale. This defines simple analytic formulae for the typical Matthews coefficient and for the typically allowed number of parameters per atom for crystals diffracting to a given resolution. This simple dependence makes it possible in many cases to estimate the expected resolution of the experimental data for a crystal with a given Matthews coefficient. When expressed using the same logarithmic scale, the most frequent values for R and R free factors and for their difference are also essentially linear across a large resolution range. The minimal R-factor values are practically constant at resolutions better than 3 Å, below which they begin to grow sharply. This simple dependence on the resolution allows the prediction of expected R-factor values for unknown structures and may be used to guide model refinement and validation.
PMCID: PMC2789003  PMID: 19966414
resolution; logarithmic scale; R factor; data-to-parameter ratio
25.  PHOENIX: A Scoring Function for Affinity Prediction Derived Using High-Resolution Crystal Structures and Calorimetry Measurements 
Binding affinity prediction is one of the most critical components to computer-aided structure-based drug design. Despite advances in first-principle methods for predicting binding affinity, empirical scoring functions that are fast and only relatively accurate are still widely used in structure-based drug design. With the increasing availability of X-ray crystallographic structures in the Protein Data Bank and continuing application of biophysical methods such as isothermal titration calorimetry to measure thermodynamic parameters contributing to binding free energy, sufficient experimental data exists that scoring functions can now be derived by separating enthalpic (ΔH) and entropic (TΔS) contributions to binding free energy (ΔG). PHOENIX, a scoring function to predict binding affinities of protein-ligand complexes, utilizes the increasing availability of experimental data to improve binding affinity predictions by the following: model training and testing using high-resolution crystallographic data to minimize structural noise, independent models of enthalpic and entropic contributions fitted to thermodynamic parameters assumed to be thermodynamically biased to calculate binding free energy, use of shape and volume descriptors to better capture entropic contributions. A set of 42 descriptors and 112 protein-ligand complexes were used to derive functions using partial least squares for change of enthalpy (ΔH) and change of entropy (TΔS) to calculate change of binding free energy (ΔG), resulting in a predictive r2 (r2pred) of 0.55 and a standard error (SE) of 1.34 kcal/mol. External validation using the 2009 version of the PDBbind “refined set” (n = 1612) resulted in a Pearson correlation coefficient (Rp) of 0.575 and a mean error (ME) of 1.41 pKd. Enthalpy and entropy predictions were of limited accuracy individually. However, their difference resulted in a relatively accurate binding free energy. While the development of an accurate and applicable scoring function was an objective of this study, the main focus was evaluation of the use of high-resolution X-ray crystal structures with high-quality thermodynamic parameters from isothermal titration calorimetry for scoring function development. With the increasing application of structure-based methods in molecular design, this study suggests that using high-resolution crystal structures, separating enthalpy and entropy contributions to binding free energy, and including descriptors to better capture entropic contributions may prove to be effective strategies towards rapid and accurate calculation of binding affinity.
PMCID: PMC3046228  PMID: 21214225

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