Experimental Charge Density of α-Glycine at 23 K

Amino acids as stabilizers for lysozyme during the spray-drying process and storage

Amino acids (AAs) have been used as excipients in protein formulations both in solid and liquid state products due to their stabilizing effect. However, the mechanisms by which they can stabilize a protein have not been fully elucidated yet. The purpose of this study was to investigate the effect of AAs with distinct physicochemical properties on the stability of a model protein (lysozyme, LZM) during the spray-drying process and subsequent storage. Molecular descriptor based multivariate data analysis was used to select distinct AAs from the group of 20 natural AAs. Then, LZM and the five selected AAs (1:1 wt ratio) were spray-dried (SD). The solid form, residual moisture content (RMC), hygroscopicity, morphology, secondary/tertiary structure and enzymatic activity of LZM were evaluated before and after storage under 40 °C/75 % RH for 30 days. Arginine (Arg), leucine (Leu), glycine (Gly), tryptophan (Trp), aspartic acid (Asp) were selected because of their distinct properties by using principal component analysis (PCA). The SD LZM powders containing Arg, Trp, or Asp were amorphous, while SD LZM powders containing Leu or Gly were crystalline. Recrystallization of Arg, Trp, Asp and polymorph transition of Gly were observed after the storage under accelerated conditions. The morphologies of the SD particles vary upon the different AAs formulated with LZM, implying different drying kinetics of the five model systems. A tertiary structural change of LZM was observed in the SD powder containing Arg, while a decrease in the enzymatic activity of LZM was observed in the powders containing Arg or Asp after the storage. This can be attributed to the extremely basic and acidic conditions that Arg and Asp create, respectively. This study suggests that when AAs are used as stabilizers instead of traditional disaccharides, not only do classic vitrification theory and water replacement theory play a role, but the microenvironmental pH conditions created by basic or acidic AAs in the starting solution or during the storage of solid matter are also crucial for the stability of SD protein products.

Engineering of Pyroelectric Crystals Decoupled from Piezoelectricity as Illustrated by Doped α‐Glycine

Design of pyroelectric crystals decoupled from piezoelectricity is not only a topic of scientific curiosity but also demonstrates effects in principle that have the potential to be technologically advantageous. Here we report a new method for the design of such materials. Thus, the co-doping of centrosymmetric crystals with tailor-made guest molecules, as illustrated by the doping of α-glycine with different amino acids (Threonine, Alanine and Serine). The polarization of those crystals displays two distinct contributions, one arising from the difference in dipole moments between guest and host and the other from the displacement of host molecules from their symmetry-related positions. These contributions exhibit different temperature dependences and response to mechanical deformation. Thus, providing a proof of concept for the ability to design pyroelectric materials with reduced piezoelectric coefficient (d₂₂ ) to a minimal value, below the resolution limit of the method (<0.005 pm/V).

Tailoring multifunctional magnetic cationic metal-organic framework composite for synchronous enrichment of phosphopeptides/glycopeptides

Herein, for the first time, a multifunctional magnetic cationic MOF composite (Fe3O4@ILI-01@Ti4+) was successfully prepared for the synchronous enrichment of phosphopeptides/glycopeptides. The as-prepared Fe3O4@ILI-01@Ti4+ bears attractive properties like abundant surface...

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400-408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision-performance balance.

Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å-1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ-3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long-range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least-squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. III. Application to crystal structures via the Ewald and direct summation methods

The previously reported exact potential and multipole moment (EP/MM) method for fast and accurate evaluation of the intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density [Volkov, Koritsanszky & Coppens (2004). Chem. Phys. Lett. 391, 170-175; Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524-536; Nguyen & Volkov (2019). Acta Cryst. A75, 448-464] is extended to the calculation of electrostatic interaction energies in molecular crystals using two newly developed implementations: (i) the Ewald summation (ES), which includes interactions up to the hexadecapolar level and the EP correction to account for short-range electron-density penetration effects, and (ii) the enhanced EP/MM-based direct summation (DS), which at sufficiently large intermolecular separations replaces the atomic multipole moment approximation to the electrostatic energy with that based on the molecular multipole moments. As in the previous study [Nguyen, Kisiel & Volkov (2018). Acta Cryst. A74, 524-536], the EP electron repulsion integral is evaluated analytically using the Löwdin α-function approach. The resulting techniques, incorporated in the XDPROP module of the software package XD2016, have been tested on several small-molecule crystal systems (benzene, L-dopa, paracetamol, amino acids etc.) and the crystal structure of a 181-atom decapeptide molecule (Z = 4) using electron densities constructed via the University at Buffalo Aspherical Pseudoatom Databank [Volkov, Li, Koritsanszky & Coppens (2004). J. Phys. Chem. A, 108, 4283-4300]. Using a 2015 2.8 GHz Intel Xeon E3-1505M v5 computer processor, a 64-bit implementation of the Löwdin α-function and one of the higher optimization levels in the GNU Fortran compiler, the ES method evaluates the electrostatic interaction energy with a numerical precision of at least 10^-5 kJ mol^-1 in under 6 s for any of the tested small-molecule crystal structures, and in 48.5 s for the decapeptide structure. The DS approach is competitive in terms of precision and speed with the ES technique only for crystal structures of small molecules that do not carry a large molecular dipole moment. The electron-density penetration effects, correctly accounted for by the two described methods, contribute 28-64% to the total electrostatic interaction energy in the examined systems, and thus cannot be neglected.

TAAM: a reliable and user friendly tool for hydrogen-atom location using routine X-ray diffraction data

Hydrogen is present in almost all of the molecules in living things. It is very reactive and forms bonds with most of the elements, terminating their valences and enhancing their chemistry. X-ray diffraction is the most common method for structure determination. It depends on scattering of X-rays from electron density, which means the single electron of hydrogen is difficult to detect. Generally, neutron diffraction data are used to determine the accurate position of hydrogen atoms. However, the requirement for good quality single crystals, costly maintenance and the limited number of neutron diffraction facilities means that these kind of results are rarely available. Here it is shown that the use of Transferable Aspherical Atom Model (TAAM) instead of Independent Atom Model (IAM) in routine structure refinement with X-ray data is another possible solution which largely improves the precision and accuracy of X-H bond lengths and makes them comparable to averaged neutron bond lengths. TAAM, built from a pseudoatom databank, was used to determine the X-H bond lengths on 75 data sets for organic molecule crystals. TAAM parametrizations available in the modified University of Buffalo Databank (UBDB) of pseudoatoms applied through the DiSCaMB software library were used. The averaged bond lengths determined by TAAM refinements with X-ray diffraction data of atomic resolution (d_min ≤ 0.83 Å) showed very good agreement with neutron data, mostly within one single sample standard deviation, much like Hirshfeld atom refinement (HAR). Atomic displacements for both hydrogen and non-hydrogen atoms obtained from the refinements systematically differed from IAM results. Overall TAAM gave better fits to experimental data of standard resolution compared to IAM. The research was accompanied with development of software aimed at providing user-friendly tools to use aspherical atom models in refinement of organic molecules at speeds comparable to routine refinements based on spherical atom model.

On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two-centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.

Continuous Generation of Millimeter-Sized Glycine Crystals in Non-Seeded Millifluidic Slug Flow

Millimeter-sized α-glycine crystals were generated from continuous non-seeded cooling crystallization in slug flow. The crystallization process is composed of three steps in sequence: slug formation, crash-cooling nucleation, and growth. Stable uniform slugs of three different aspect ratios (slug length/tubing inner diameter) were formed, by adjusting the flow rates of both the solution and air streams. Besides supersaturation, the slug aspect ratio can also affect primary nucleation outcome. Stable slug flow can accommodate a relative supersaturation (C/C*) of up to 1.5 without secondary nucleation. Large glycine crystals can grow to millimeter size within 10 min, inside millimeter-sized slugs without reducing the slug quality.

Perceptible isotopic effect in 3D-framework of α-glycine at low temperatures

Glycine, the most fundamental amino acid, albeit studied for many decades, has kept researchers captivated with interesting structural variations relevant to important biological, astrophysical and technological applications. We report here a noticeable effect of deuteration on the three dimensional hydrogen bonding network of α-glycine using low temperature infrared absorption studies in a wide spectral range, corroborated with Raman scattering studies. These systematic studies in the range 300-4.2 K have demonstrated a relatively compact assembly of glycine molecules in the three dimensional bilayered structure of hydrogenated glycine (gly-h) at low temperatures. This is inferred from a remarkable temperature effect in the weak intra-bilayer hydrogen bond ~ along the b-axis, which strengthens upon cooling. A pronounced increase in the intensity of NH₃ torsional and NH stretching modes has been observed. This is accompanied with a large rate of stiffening and softening respectively of these modes upon cooling and a change in slope across 210 K and 80 K. In contrast, the D---O hydrogen bond lengths in fully deuterated isotope (gly-d), as estimated using empirical correlation, show that the weak intra-bilayer hydrogen bond is not strengthened upon cooling down to 180 K, whereas the stronger intra-layer hydrogen bonds in the ac-plane become further strong. The ND₃ torsional vibrations show no temperature effect. This implies a relatively stable two dimensional layered structure formed by strongly hydrogen bonded glycine sheets in the ac-plane. Below 180 K, similar qualitative trends have been obtained for the hydrogen bond lengths in the two isotopes. In addition, temperature induced variation of the characteristic "indicator" band of zwitterionic gly-h and gly-d has also been reported.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. I. The Löwdin α-function method

The previously reported [Volkov et al. (2004). Chem. Phys. Lett. 391, 170-175] exact potential and multipole moment (EP/MM) method for evaluation of intermolecular electrostatic interaction energies using the nuclei-centered pseudoatom representation of electron densities is significantly improved in terms of both speed and accuracy by replacing the numerical quadrature integration of the exact potential with a fully analytical technique. The resulting approach, incorporated in the XDPROP module of the software package XD, has been tested on several molecular systems ranging in size from water-water to dodecapeptide-dodecapeptide dimers using electron densities constructed via the University at Buffalo Aspherical Atom Databank. The improved hybrid method provides electrostatic interaction energies within the uncertainty of ≤0.2 kJ mol^-1 for all benchmark systems. The running time for a dimer of a sizable, 225-atom dodecapeptide is under 4 s on a 2012 central processing unit (2.8 GHz AMD Opteron 6348) and under 3 s on a relatively modern processor (2.8 GHz Intel Xeon E3-1505M v5).

Polar Imperfections in Amino Acid Crystals: Design, Structure, and Emerging Functionalities

Crystals are physical arrays delineated by polar surfaces and often contain imperfections of a polar nature. Understanding the structure of such defects on the molecular level is of topical importance since they strongly affect the macroscopic properties of materials. Moreover, polar imperfections in crystals can be created intentionally and specifically designed by doping nonpolar crystals with "tailor-made" additives as dopants, since their incorporation generally takes place in a polar mode. Insertion of dopants also induces a polar deformation of neighboring host molecules, resulting in the creation of polar domains within the crystals. The contribution of the distorted host molecules to the polarity of such domains should be substantial, particularly in crystals composed of molecules with large dipole moments, such as the zwitterionic amino acids, which possess dipole moments as high as ∼14 D. Polar materials are pyroelectric, i.e., they generate surface charge as a result of temperature change. With the application of recent very sensitive instruments for measuring electric currents, coupled with theoretical computations, it has become possible to determine the structure of polar imperfections, including surfaces, at a molecular level. The detection of pyroelectricity requires attachment of electrodes, which might induce various artifacts and modify the surface of the crystal. Therefore, a new method for contactless pyroelectric measurement using X-ray photoelectron spectroscopy was developed and compared to the traditional periodic temperature change technique. Here we describe the molecular-level determination of the structure of imperfections of different natures in molecular crystals and how they affect the macroscopic properties of the crystals, with the following specific examples: (i) Experimental support for the nonclassical crystal growth mechanism as provided by the detection of pyroelectricity from near-surface solvated polar layers present at different faces of nonpolar amino acid crystals. (ii) Enantiomeric disorder in dl-alanine crystals disclosed by detection of anomalously strong pyroelectricity along their nonpolar directions. The presence of such disorder, which is not revealed by accurate diffraction techniques, explains the riddle of their needlelike morphology. (iii) The design of mixed polar crystals of l-asparagine·H₂O/l-aspartic acid with controlled degrees of polarity, as determined by pyroelectricity and X-ray diffraction, and their use in mechanistic studies of electrofreezing of supercooled water. (iv) Pyroelectricity coupled with dispersion-corrected density functional theory calculations and molecular dynamics simulations as an analytical method for the molecular-level determination of the structure of polar domains created by doping of α-glycine crystals with different l-amino acids at concentrations below 0.5%. (v) Selective insertion of minute amounts of alcohols within the bulk of α-glycine crystals, elucidating their role as inducers of the metastable β-glycine polymorph. In conclusion, the various examples demonstrate that although these imperfections are present in minute amounts, they can be detected by the sensitive pyroelectric measurement, and by combining them with theoretical computations one can elucidate their diverse emerging functionalities.

Towards the use of experimental electron densities to estimate reliable lattice energies

Lattice energies derived from experimental charge densities are critically assessed, with a view to encouraging further research of this nature.

CrystalExplorer model energies and energy frameworks: extension to metal coordination compounds, organic salts, solvates and open-shell systems

The application domain of accurate and efficient CE-B3LYP and CE-HF model energies for intermolecular interactions in molecular crystals is extended by calibration against density functional results for 1794 molecule/ion pairs extracted from 171 crystal structures. The mean absolute deviation of CE-B3LYP model energies from DFT values is a modest 2.4 kJ mol-1 for pairwise energies that span a range of 3.75 MJ mol-1. The new sets of scale factors determined by fitting to counterpoise-corrected DFT calculations result in minimal changes from previous energy values. Coupled with the use of separate polarizabilities for interactions involving monatomic ions, these model energies can now be applied with confidence to a vast number of molecular crystals. Energy frameworks have been enhanced to represent the destabilizing interactions that are important for molecules with large dipole moments and organic salts. Applications to a variety of molecular crystals are presented in detail to highlight the utility and promise of these tools.

ζ-Glycine: insight into the mechanism of a polymorphic phase transition

Glycine is the simplest and most polymorphic amino acid, with five phases having been structurally characterized at atmospheric or high pressure. A sixth form, the elusive ζ phase, was discovered over a decade ago as a short-lived intermediate which formed as the high-pressure ∊ phase transformed to the γ form on decompression. However, its structure has remained unsolved. We now report the structure of the ζ phase, which was trapped at 100 K enabling neutron powder diffraction data to be obtained. The structure was solved using the results of a crystal structure prediction procedure based on fully ab initio energy calculations combined with a genetic algorithm for searching phase space. We show that the fate of ζ-glycine depends on its thermal history: although at room temperature it transforms back to the γ phase, warming the sample from 100 K to room temperature yielded β-glycine, the least stable of the known ambient-pressure polymorphs.

A theoretical-electron-density databank using a model of real and virtual spherical atoms

A database describing the electron density of common chemical groups using combinations of real and virtual spherical atoms is proposed, as an alternative to the multipolar atom modelling of the molecular charge density. Theoretical structure factors were computed from periodic density functional theory calculations on 38 crystal structures of small molecules and the charge density was subsequently refined using a density model based on real spherical atoms and additional dummy charges on the covalent bonds and on electron lone-pair sites. The electron-density parameters of real and dummy atoms present in a similar chemical environment were averaged on all the molecules studied to build a database of transferable spherical atoms. Compared with the now-popular databases of transferable multipolar parameters, the spherical charge modelling needs fewer parameters to describe the molecular electron density and can be more easily incorporated in molecular modelling software for the computation of electrostatic properties. The construction method of the database is described. In order to analyse to what extent this modelling method can be used to derive meaningful molecular properties, it has been applied to the urea molecule and to biotin/streptavidin, a protein/ligand complex.

Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg₃Al₂Si₃O₁₂), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ_EXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ_EXP are in substantial agreement with those of ρ_THEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ_EXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

Origin and structure of polar domains in doped molecular crystals

Doping is a primary tool for the modification of the properties of materials. Occlusion of guest molecules in crystals generally reduces their symmetry by the creation of polar domains, which engender polarization and pyroelectricity in the doped crystals. Here we describe a molecular-level determination of the structure of such polar domains, as created by low dopant concentrations (<0.5%). The approach comprises crystal engineering and pyroelectric measurements, together with dispersion-corrected density functional theory and classical molecular dynamics calculations of the doped crystals, using neutron diffraction data of the host at different temperatures. This approach is illustrated using centrosymmetric α-glycine crystals doped with minute amounts of different L-amino acids. The experimentally determined pyroelectric coefficients are explained by the structure and polarization calculations, thus providing strong support for the local and global understanding of how different dopants influence the properties of molecular crystals.

Electron density, disorder and polymorphism: high-resolution diffraction studies of the highly polymorphic neuralgic drug carbamazepine

Analysis of neutron and high-resolution X-ray diffraction data on form (III) of carbamazepine at 100 K using the atoms in molecules (AIM) topological approach afforded excellent agreement between the experimental results and theoretical densities from the optimized gas-phase structure and from multipole modelling of static theoretical structure factors. The charge density analysis provides experimental confirmation of the partially localized π-bonding suggested by the conventional structural formula, but the evidence for any significant C-N π bonding is not strong. Hirshfeld atom refinement (HAR) gives H atom positional and anisotropic displacement parameters that agree very well with the neutron parameters. X-ray and neutron diffraction data on the dihydrate of carbemazepine strongly indicate a disordered orthorhombic crystal structure in the space group Cmca, rather than a monoclinic crystal structure in space group P2(1)/c. This disorder in the dihydrate structure has implications for both experimental and theoretical studies of polymorphism.

SHADE3server: a streamlined approach to estimate H-atom anisotropic displacement parameters using periodicab initiocalculations or experimental information

A major update of theSHADEserver (http://shade.ki.ku.dk) is presented. In addition to all of the previous options for estimating H-atom anisotropic displacement parameters (ADPs) that were offered bySHADE2, the newest version offers two new methods. The first method combines the original translation–libration–screw analysis with input from periodicab initiocalculations. The second method allows the user to input experimental information from spectroscopic measurements or from neutron diffraction experiments on related structures and utilize this information to evaluate ADPs of H atoms. Tools are provided to set up theab initiocalculations and to derive the internal motion from the calculations. The new server was tested on a range of compounds where neutron diffraction data were available. In most cases, the results are significantly better than previous estimates, and for strong hydrogen bonds in proton sponges, theab initiocalculations become crucial.

Dielectric properties of liquid phase molecular clusters using the external field method: molecular dynamics study

We analyzed the dielectric properties of molecular liquids using the external field method with reaction field approximations. The applicability of this method to determine the dielectric properties of molecules with zero (1,4-dioxane) and non-zero (water and bio-molecular aqueous solutions) permanent dipole moment was studied. The relative static dielectric constant obtained using the external field method for polar and non-polar molecular liquids, including molecules with zero permanent dipole moment, agreed well with the experimental values presented in the literature. Our results indicate that the Debye relaxation time constants estimated from the non-equilibrium simulations using the external field method were accurate for molecules whose permanent dipole moments were less than 12 D.

The active site of hen egg-white lysozyme: flexibility and chemical bonding

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.

Experimental Electron Density and Neutron Diffraction Studies on the Polymorphs of Sulfathiazole

High resolution X-ray diffraction data on forms I-IV of sulfathiazole and neutron diffraction data on forms II-IV have been collected at 100 K and analyzed using the Atoms in Molecules topological approach. The molecular thermal motion as judged by the anisotropic displacement parameters (adp's) is very similar in all four forms. The adp of the thiazole sulfur atom had the greatest amplitude perpendicular to the five-membered ring, and analysis of the temperature dependence of the adps indicates that this is due to genuine thermal motion rather than a concealed disorder. A minor disorder (∼1-2%) is evident for forms I and II, but a statistical analysis reveals no deleterious effect on the derived multipole populations. The topological analysis reveals an intramolecular S-O···S interaction, which is consistently present in all experimental topologies. Analysis of the gas-phase conformation of the molecule indicates two low-energy theoretical conformers, one of which possesses the same intramolecular S-O···S interaction observed in the experimental studies and the other an S-O···H-N intermolecular interaction. These two interactions appear responsible for "locking" the molecular conformation. The lattice energies of the various polymorphs computed from the experimental multipole populations are highly dependent on the exact refinement model. They are similar in magnitude to theoretically derived lattice energies, but the relatively high estimated errors mean that this method is insufficiently accurate to allow a definitive stability order for the sulfathiazole polymorphs at 0 K to be determined.

Topological Properties of Chemical Bonds from Static and Dynamic Electron Densities

Dynamic and static electron densities (EDs) based on the independent spherical atom model (IAM) and multipole (MP) models of crambin were successfully computed, holding no series-termination effects. The densities are compared to EDs of small biological molecules at diverse temperatures. It is outlined that proteins exhibit an intrinsic flexibility, present as frozen disorder at 100 K, in contrast to small molecules. The flexibility of the proteins is reflected by atomic displacement parameters (B-factors), which are considerably larger than for small molecules at 298 K. Thus, an optimal deconvolution of deformation density and thermal motion is not guaranteed, which prevents a free refinement of MP parameters but allows an application of transferable, fixed MP parameters. The analysis of the topological properties, such as the density at bond critical points (BCPs) and the Laplacian, reveals systematic differences between static and dynamic EDs. Zero-point-vibrations, yet present in dynamic EDs at low temperature, affect but marginally the EDs of small molecules. The zero-point-vibrations cause a smearing of the ED, which becomes more pronounced with increasing temperature. Topological properties, primarily the Laplacian, of covalent bonds appear to be more sensitive to effects by temperature and the polarity of the bonds. However, dynamic EDs at ca. 20 K based on MP models provide a good characterization of chemical bonding. Both the density at BCPs and the Laplacian of hydrogen bonds constitute similar values from static and dynamic EDs for all studied temperatures. Deformation densities demonstrate the necessity of the employment of MP parameters in order to comprise the nature of covalent bonds. The character of hydrogen bonds can be roughly pictured by IAM, whereas MP parameters are recommended for a classification of hydrogen bonds beyond a solely interpretation of topological properties.

An improved experimental databank of transferable multipolar atom models--ELMAM2. Construction details and applications

ELMAM2 is a generalized and improved library of experimentally derived multipolar atom types. The previously published ELMAM database is restricted mostly to protein atoms. The current database is extended to common functional groups encountered in organic molecules and is based on optimized local axes systems taking into account the local pseudosymmetry of the molecular fragment. In this approach, the symmetry-restricted multipoles have zero populations, while others take generally significant values. The various applications of the database are described. The deformation electron densities, electrostatic potentials and interaction energies calculated for several tripeptides and aromatic molecules are calculated using ELMAM2 electron-density parameters and compared with the former ELMAM database and density functional theory calculations.

The conformers of 3-fluoroalanine. A theoretical study

Quantum chemical calculations (DFT, SCS-MP2) show that the relative energies of the four principal alanine conformations are only marginally altered by the introduction of a single fluorine substituent into the methyl group. The fluorine gauche effect and attractive interactions of fluorine to the O-H or N-H moieties (formation of hydrogen bridges) do stabilize particular conformers of 3-fluoroalanine. This is true for the neutral molecule both in the gas phase and in aqueous solution (CPCM-model), but also for the zwitterionic forms and the conformers of the related carboxylate ions and also for the respective ammonium ions in aqueous solution. In water (CPCM calculations), the zwitterion is almost equal in energy to the most stable conformer of the neutral 3-fluoroalanine. Compared to alanine the atomic charges of the amino group and the carboxyl function of 3-fluoroalanine are not significantly influenced by the fluorine at C3, which relates to the fact that both experimental pK(a) values are almost equal for alanine and 3-fluoroalanine.

Experimental and theoretical charge density studies at subatomic resolution

Analysis of accurate experimental and theoretical structure factors of diamond and silicon reveals that the contraction of the core shell due to covalent bond formation causes significant perturbations of the total charge density that cannot be ignored in precise charge density studies. We outline that the nature and origin of core contraction/expansion and core polarization phenomena can be analyzed by experimental studies employing an extended Hansen-Coppens multipolar model. Omission or insufficient treatment of these subatomic charge density phenomena might yield erroneous thermal displacement parameters and high residual densities in multipolar refinements. Our detailed studies therefore suggest that the refinement of contraction/expansion and population parameters of all atomic shells is essential to the precise reconstruction of electron density distributions by a multipolar model. Furthermore, our results imply that also the polarization of the inner shells needs to be adopted, especially in cases where second row or even heavier elements are involved in covalent bonding. These theoretical studies are supported by direct multipolar refinements of X-ray powder diffraction data of diamond obtained from a third-generation synchrotron-radiation source (SPring-8, BL02B2).

Experimental charge density of an L-phenylalanine formic acid complex with a short hydrogen bond determined at 25 K

The experimental charge density and related atomic and bond topological properties of an L-phenylalanine formic acid complex were derived from a high resolution X-ray data set (sin θ/λ = 1.18 Å–1/d = 0.42 Å) measured at 25 K. The complex consists of a zwitterionic and a cationic phenylalanine molecule with formate as counterion. Special focus was directed on the density distribution in the region of a strong O—H ·· O hydrogen bond (O ·· O = 2.491(1) Å) which is formed between the two phenylalanine units. The obtained results are compared with the 15 previously derived experimental amino acid charge density data, with various theoretical calculations at experimental geometries and with the complete set of topological descriptors based on ab initio calculations of the neutral forms of all 20 amino acids published recently in the literature. A comparison of all available data in this biologically important class of compounds gives an impression about the significance of the quantitative results from experimental and theoretical charge density determinations.