Charge densities in actinide compounds: strategies for data reduction and model building.

The data quality requirements for charge density studies on actinide compounds are extreme. Important steps in data collection and reduction required to obtain such data are summarized and evaluated. The steps involved in building an augmented Hansen-Coppens multipole model for an actinide pseudo-atom are provided. The number and choice of radial functions, in particular the definition of the core, valence and pseudo-valence terms are discussed. The conclusions in this paper are based on a re-examination and improvement of a previously reported study on [PPh4][UF6]. Topological analysis of the total electron density shows remarkable agreement between experiment and theory; however, there are significant differences in the Laplacian distribution close to the uranium atoms which may be due to the effective core potential employed for the theoretical calculations.

Direct air capture of CO-2 - topological analysis of the experimental electron density (QTAIM) of the highly insoluble carbonate salt of a 2,6-pyridine-bis(iminoguanidine), (PyBIGH2)(CO3)(H2O)4.

Chemical bonding and all intermolecular interactions in the highly insoluble carbonate salt of a 2,6-pyridine-bis(iminoguanidine), (PyBIGH2)(CO3)(H2O)4, recently employed in the direct air capture of CO2 via crystallization, have been analyzed within the framework of the quantum theory of atoms in molecules (QTAIM) based on the experimental electron density derived from X-ray diffraction data obtained at 20 K. Accurate hydrogen positions were included based on an analogous neutron diffraction study at 100 K. Topological features of the covalent bonds demonstrate the presence of multiple bonds of various orders within the PyBIGH2 2+ cation. Strong hydrogen bonds define ribbons comprising carbonate anions and water molecules. These ribbons are linked to stacks of essentially planar dications via hydrogen bonds from the guanidinium moieties and an additional one to the pyridine nitro-gen. The linking hydrogen bonds are approximately perpendicular to the anion-water ribbons. The observation of these putative interactions provided motivation to characterize them by topological analysis of the total electron density. Thus, all hydrogen bonds have been characterized by the properties of their (3,-1) bond critical points. Weaker interactions between the PyBIGH2 2+ cations have similarly been characterized. Integrated atomic charges are also reported. A small amount of cocrystallized hydroxide ion (∼2%) was also detected in both the X-ray and neutron data, and included in the multipole model for the electron-density refinement. The small amount of additional H+ required for charge balance was not detected in either the X-ray or the neutron data. The results are discussed in the context of the unusually low aqueous solubility of (PyBIGH2)(CO3)(H2O)4 and its ability to sequester atmospheric CO2.

QTAIM Assessment of the Intra- and Intermolecular Bonding in a Bis(nitramido-oxadiazolate) Energetic Ionic Salt at 20 K.

Accurate experimental determination of the electron density distribution for the energetic ionic salt bis(ammonium) 2,2'-dinitramido-5,5'-bis(1-oxa-3,4-diazolate) dihydrate (1) is obtained from multipole modeling of single-crystal X-ray diffraction data collected at 20 K. The intra- and intermolecular bonding is assessed in terms of the quantum theory of atoms in molecules (QTAIM) with a view to better understanding the physicochemical properties in relation to chemical bonding. Topological analysis reveals stronger bonding for the N-NO2 bond relative to energetic nitramines RDX and HMX and the indication of a trend between this and impact sensitivity of nitro-containing energetic materials is noted. The intermolecular bonding of 1 is dominated by classical H-bonds but includes multiple π-bonding interactions and interactions between H-bond donor and acceptor atoms where bond paths are deflected by H atoms. There also exists a weak O···O interaction between end-on nitro groups, as well as an intramolecular ring-forming 1,5-type interaction. An anharmonic description of thermal motion was required to obtain the best fitting model, despite the low temperature of the study. The experimental study was complemented by periodic boundary DFT calculations at the experimental geometry as well as gas phase calculations on the isolated dianion.

Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50.

The intra- and intermolecular bonding in the known phase of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate, TKX-50, has been analyzed on the basis of the experimentally determined charge density distribution from high-resolution X-ray diffraction data obtained at 20 K. This was compared to the charge density obtained from DFT calculations with periodic boundary conditions using both direct calculations and derived structure factors. Results of topological analysis of the electron density corroborate that TKX-50 is best described as a layered structure linked primarily by a number of hydrogen bonds as well as by a variety of other interactions. Additional bonding interactions were identified, including a pair of equivalent 1,5-type intramolecular closed-shell interactions in the dianion. Refinement of anharmonic motion was shown to be essential for obtaining an adequate model, despite the low temperature of the study. Although generally unusual, the implementation of anharmonic refinement provided a significant improvement compared to harmonic refinement of both traditional and split-core multipole models.

Revisiting the charge density analysis of 2,5-dichloro-1,4-benzoquinone at 20†K.

A high-resolution X-ray diffraction measurement of 2,5-dichloro-1,4-benzoquinone (DCBQ) at 20 K was carried out. The experimental charge density was modeled using the Hansen-Coppens multipolar expansion and the topology of the electron density was analyzed in terms of the quantum theory of atoms in molecules (QTAIM). Two different multipole models, predominantly differentiated by the treatment of the chlorine atom, were obtained. The experimental results have been compared to theoretical results in the form of a multipolar refinement against theoretical structure factors and through direct topological analysis of the electron density obtained from the optimized periodic wavefunction. The similarity of the properties of the total electron density in all cases demonstrates the robustness of the Hansen-Coppens formalism. All intra- and intermolecular interactions have been characterized.

Bonding in Uranium(V) Hexafluoride Based on the Experimental Electron Density Distribution Measured at 20 K.

The electron density distribution of [PPh4][UF6] was obtained from high-resolution X-ray diffraction data measured at 20 K. The electron density was modeled with an augmented Hansen-Coppens multipolar formalism. Topological analysis reveals that the U-F bond is of incipient covalent nature. Theoretical calculations add further support to the bonding description gleaned from the experimental model. The impact of the uranium anomalous dispersion terms on the refinement is also discussed.

Charge Density and Electrostatic Potential Study of 16α,17ß-Estriol and the Binding of Estrogen Molecules to the Estrogen Receptors ERα and ERß.

An accurate X-ray diffraction study at 20 K combined with DFT theoretical calculations has been performed for the estriol crystal with two conformationally different molecules in the asymmetric unit. The electron density has been modeled via a multipole expansion, using both experimental and theoretical structure factors, and a topological analysis has been performed. The experimental molecular geometry, hydrogen bonding, atomic charges, dipole moments, and other topological characteristics are compared with those calculated theoretically. In particular, the molecular electrostatic potential has been extracted and compared with those reported for other estrogen molecules exhibiting different binding affinities to the estrogen receptors (ERα and ERß).

Experimental and Theoretical Electron Density Determination for Two Norbornene Derivatives: Topological Analysis Provides Insights on Reactivity.

The electron density distribution of two substituted norbornene derivatives (cis-5-norbornene-endo-2,3-dicarboxylic anhydride (1) and 7-oxabicylo[2.2.1]hept-5-ene-exo-2,3-dicarboxylic anhydride (2) has been determined from low-temperature (20 K) X-ray diffraction data and from DFT calculations with periodic boundary conditions. Topological analysis of the electron density is discussed with respect to exo-selective additions, the partial retro-Diels-Alder (rDA) character of the ground state, and intermolecular interaction energies.

Inter- and Intramolecular Interactions in Crystalline 2-Nitrobenzoic Acid - An Experimental and Theoretical QTAIM Analysis.

We have quantified the inter- and intramolecular interactions in crystalline 2-nitrobenzoic acid from QTAIM analysis of the topology of the electron density distribution obtained from both a low temperature (20 K) X-ray diffraction experiment and from theoretical calculations. The covalent bonds have been characterized by the properties at their (3,-1) bond critical points; in particular the nature of the aromatic/nitro group C-N bond is discussed. All noncovalent bonds of the type O···H (both strong and weak), C···C, O···O, and O···C have also been characterized. Intermolecular interactions may be roughly divided into three types, the formation of a classical carboxylic acid hydrogen bonded dimer, an unusual ribbon of O···O interactions parallel to a, and a number of predominantly O···H interactions perpendicular to a. Integrated atomic charges (in particular for the acidic hydrogen, ∼+0.6) and the derived molecular dipole moment are reported.

Room-temperature ultrahigh-resolution time-of-flight neutron and X-ray diffraction studies of H/D-exchanged crambin.

The room-temperature (RT) X-ray structure of H/D-exchanged crambin is reported at 0.85 Å resolution. As one of the very few proteins refined with anisotropic atomic displacement parameters at two temperatures, the dynamics of atoms in the RT and 100 K structures are compared. Neutron diffraction data from an H/D-exchanged crambin crystal collected at the Protein Crystallography Station (PCS) showed diffraction beyond 1.1 Å resolution. This is the highest resolution neutron diffraction reported to date for a protein crystal and will reveal important details of the anisotropic motions of H and D atoms in protein structures.

Charge transfer vibronic transitions in uranyl tetrachloride compounds.

The electronic and vibronic interactions of uranyl (UO(2))(2+) in three tetrachloride crystals have been investigated with spectroscopic experiments and theoretical modeling. Analysis and simulation of the absorption and photoluminescence spectra have resulted in a quantitative understanding of the charge transfer vibronic transitions of uranyl in the crystals. The spectra obtained at liquid helium temperature consist of extremely narrow zero-phonon lines (ZPL) and vibronic bands. The observed ZPLs are assigned to the first group of the excited states formed by electronic excitation from the 3σ ground state into the f(δ,ϕ) orbitals of uranyl. The Huang-Rhys theory of vibronic coupling is modified successfully for simulating both the absorption and luminescence spectra. It is shown that only vibronic coupling to the axially symmetric stretching mode is Franck-Condon allowed, whereas other modes are involved through coupling with the symmetric stretching mode. The energies of electronic transitions, vibration frequencies of various local modes, and changes in the O═U═O bond length of uranyl in different electronic states and in different coordination geometries are evaluated in empirical simulations of the optical spectra. Multiple uranyl sites derived from the resolution of a superlattice at low temperature are resolved by crystallographic characterization and time- and energy-resolved spectroscopic studies. The present empirical simulation provides insights into fundamental understanding of uranyl electronic interactions and is useful for quantitative characterization of uranyl coordination.

Characterization of bonding in cesium uranyl chloride: topological analysis of the experimental charge density.

The topological analysis of the charge density distribution in Cs(2)UO(2)Cl(4) obtained from an accurate X-ray diffraction experiment at 20K is reported. Details of the techniques applied during data collection and data refinement are discussed. A split Hansen-Coppens multipole model for uranium and cesium atoms has been used to describe the charge density features associated with valence electrons and core deformations. The analysis of the deformation density distribution, QTAIM space partitioning, the Laplacian of the electron density, and electron localization function are discussed. Local QTAIM descriptors for bonds to uranium and cesium are reported, as well as integrated properties of each individual atom. U(5f), U(6s), U(6p), U(6d), and U(7s) shells were required to describe the aspherical charge density of the uranium pseudoatom. Observed deformation of the cesium atom core was described by applying the multipole model to Cs(5s) and Cs(5p) shells.

Chemical bonding in cesium uranyl chloride based on the experimental electron density distribution.

Details of the electron density distribution in Cs(2)UO(2)Cl(4) have been obtained from an accurate X-ray diffraction experiment at 20 K. The electron density was described with the Hansen-Coppens multipole model. Topological analysis of the electron density confirms that the U-O bond is probably a triple bond, the U-Cl bonds are incipient covalent interactions, and the Cs-Cl and Cs-O interactions are of the closed-shell type. The results obtained serve as a proof of principle that electron density features related to chemical bonding may be obtained from X-ray data for even the heaviest elements.

Importance of the consideration of anharmonic motion in charge-density studies: a comparison of variable-temperature studies on two explosives, RDX and HMX.

Extremely accurate X-ray data were obtained for the explosive RDX (hexahydro-1,3,5-trinitro-1,3,5-triazine) at three different temperatures (20, 120 and 298 K). Collected reflections were integrated using the latest version of the program VIIPP which uses separate Kα(1)/Kα(2) contributions to the profile fitting during integration. For each temperature both anharmonic and harmonic descriptions of the atomic thermal motion were utilized in the model refinements along with the multipole expansion of the electron density. H atoms were refined anisotropically and agree well with a previous neutron study. Topological analysis [Bader (1990). Atoms in Molecules: A Quantum Theory. The International Series of Monographs of Chemistry, edited by J. Halpern & M. L. H. Green. Oxford: Clarendon Press] of the attained electron density followed. For 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), old data collected at 20 and 120 K were re-integrated with the new version of VIIPP and refined in the same manner as for RDX. In both cases theoretical structure factors were also calculated based on the 20 K structures, and employed in comparison multipole refinements for the atoms at rest. Limiting the refinement to a harmonic model of the atomic displacements may result in a biased and erroneous electron density, especially when atomic vibrations are significant (as in RDX) and at temperatures higher than obtained by using liquid helium. Given the similarity of the two compounds the effects of anharmonic motion are strikingly more severe in the case of RDX. Our study reinforces the conclusion of Meindl et al. [Acta Cryst. (2010), A66, 362-371] that in certain cases it is necessary to include anharmonic term(s) of the probability density function (or temperature factor) in order to obtain a meaningful electron density suitable for topological analysis, even for compact (high-density) light-atom structures. For RDX it was observed that the oxygen lone-pair concentrations of electrons are located close to perpendicular to the N-O bond vectors, which is typical for explosive materials. Conjugation of the electron density in the -N-NO(2) fragment has been established based on the topological bond orders. Nine moderately strong hydrogen bonds and nine N-N, O-N and O-O bonding interactions were found and described. The RDX molecular electronic energy per mole is 4.02-4.04 a.u., very close to the reported value for HMX.

17Alpha-estradiol x 1/2 H2O: super-structural ordering, electronic properties, chemical bonding, and biological activity in comparison with other estrogens.

The biological function of steroidal estrogens is related to their electronic properties. An experimental charge density study has been carried out on 17alpha-estradiol and compared to similar studies on more potent estrogens. High accuracy X-ray data were measured with a Rigaku rotating anode diffractometer equipped with an R-Axis Rapid curved image plate detector at 20 K. The total electron density in the 17alpha-estradiol x 1/2 H(2)O crystal was modeled using the Hansen-Coppens multipole model. Topological analysis of the electron density based on Bader's QTAIM theory was performed. The crystal structure, chemical bonding, and molecular properties, including the electrostatic potential (ESP), are reported and discussed. Observed disordering of hydroxyl and water hydrogen atom positions are interpreted as a superstructural ordering in a lower symmetry space group. The ESP's for the resulting four conformers are compared with each other and with that of 17beta-estradiol. The relative binding affinities are discussed in terms of the observed potentials.

Chemical bonding and structure-reactivity correlation in Meldrum's acid: a combined experimental and theoretical electron density study.

Chemical bonding in Meldrum's acid (MA) based on the experimental electron density obtained from high-resolution X-ray diffraction data at 20 K and from solid state theoretical calculations at the experimental molecular geometry have been analyzed by using the Quantum Theory of Atoms in Molecules. The total electron density was modeled with use of the Hansen-Coppens multipole formalism, and features associated with both intra- and intermolecular bond critical points, topological bond orders, atomic charges, and the electrostatic potential have been characterized and used to understand structure-reactivity relationships. The acidic methylene hydrogen atoms carry modest positive charges. A notable feature is the presence of an intramolecular H...H interaction that imparts stability to the boat conformation. A correlation between the topological bond order and the nature of the chemical bonds in MA illustrates the fact that elimination of carbon dioxide/acetone is an important feature of the chemistry of MA. The surface electrostatic potential and the charge distribution rationalize the sites of nucleophilic/electrophilic attack.

Binding of genistein to the estrogen receptor based on an experimental electron density study.

In a continuing effort to determine a relationship between the biological function and the electronic properties of steroidal and nonsteroidal estrogens by analysis of the submolecular properties, an experimental charge density study has been pursued on the nonsteroidal phytoestrogen, genistein. X-ray diffraction data were obtained using a Rigaku R-Axis Rapid high-power rotating anode diffractometer with a curved image plate detector at 20(1) K. The total electron density was modeled using the Hansen-Coppens multipole model. Genistein packs in puckered sheets characterized by intra- and intermolecular hydrogen bonds while weaker intermolecular hydrogen bonds (O...H-C) exist between the sheets. A topological analysis of the electron density of genistein was then completed to characterize all covalent bonds, three O...H-O and four O...H-C intermolecular hydrogen bonds. Two O...H-O hydrogen bonds are incipient (partially covalent) type bonds, while the other O...H-O hydrogen bond and O...H-C hydrogen bonds are of the pure closed-shell interaction type. In addition, two intermolecular H...H interactions have also been characterized from the topology of the electron density. The binding of genistein to the estrogen receptor is discussed in terms of the electrostatic potential derived from the electron density distribution.

Structure and bonding in beta-HMX-characterization of a trans-annular N...N interaction.

Chemical bonding in the beta-phase of the 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) crystal based on the experimental electron density obtained from X-ray diffraction data at 20 K, and solid state theoretical calculations, has been analyzed in terms of the quantum theory of atoms in molecules. Features of the intra- and intermolecular bond critical points and the oxygen atom lone-pair locations are discussed. An unusual N...N bonding interaction across the 8-membered ring has been discovered and characterized. Hydrogen bonding, O...O and O...C intermolecular interactions are reported. Atomic charges and features of the electrostatic potential are discussed.

Atoms-in-molecules study of intra- and intermolecular bonding in the pentaerythritol tetranitrate crystal.

Chemical bonding in the pentaerythritol tetranitrate crystal based on the experimental electron density obtained from X-ray diffraction data at 100 K and theoretical calculations at the experimental molecular geometry have been analyzed in terms of the Quantum Theory of Atoms in Molecules. Features of the intra- and intermolecular bond critical points and the oxygen atom lone-pair locations are discussed. Numerous intermolecular bonding interactions, including O...H and O...O, have been found and characterized. Atomic charges and atomic energies were integrated and compared with those for similar compounds. The N-O topological bond orders have been calculated for the first time, and the PETN atomic valences have been estimated.

Experimental and theoretical electron density study of estrone.

The electron density and the electrostatic potential (ESP) distributions of estrone have been determined using X-ray diffraction analysis and compared with theoretical calculations in the solid and gas phases. X-ray diffraction measurements are performed with a Rigaku Rapid rotating anode diffractometer at 20 K. The electron density in the estrone crystal has been described with the multipole model, which allowed extensive topological analysis and calculation of the ESP. From DFT calculations in the solid state a theoretical X-ray diffraction data set has been produced and treated in the same way as the experimental data. Two sets of single molecule DFT calculations were performed: (a) An electron density distribution was obtained via a single-point calculation with a large basis set at the experimental geometry and subsequently analyzed according to the quantum theory of atoms in molecules (AIM) to obtain the bond and most atomic properties, and (b) another electron density distribution was obtained with a smaller basis set, but at a geometry optimized using the same basis set for the analysis of atomic energies. An interesting locally stabilizing hydrogen-hydrogen bond path linking H(1) and H(11B) is found which represents the first characterization of such bonding in a steroid molecule. AIM delocalization indices were shown to be well correlated to the experimental electron density at the bond critical points through an exponential relationship. The aromaticity of ring A, chemical bonding, the O(1)...O(2) distance necessary for estrogenic activity, and the electrostatic potential features are also discussed.