Multipole Refinement Research Articles

Inter-layer charge disproportionation in the dual-layer organic metal (tTTF-I)2ClO4with unsymmetrical I⋯O halogen bond interactions

A mixed-valence salt of tTTF-I with ClO4(-), formulated as (tTTF-I)2ClO4, is characterized by the presence of two crystallographically independent donor molecules, segregated in different layers and linked together through I···O interactions with the ClO4(-) anion disordered at room temperature. The tTTF-I donor molecule was prepared by metallation of tTTF (trimethylene tetrathiafulvalene) followed by reaction with iodine to afford the mono and diiodo derivatives tTTF-I and tTTFI2, respectively. The crystal structure of the latter neutral tTTFI2 shows the occurrence of strong type II, II halogen bond interactions. Band structure calculations of the dual-layer structure of the 2 : 1 salt (tTTF-I)2ClO4 show co-existence of both 1D open and 2D closed Fermi surfaces. The salt undergoes a metal-insulator phase transition at T(MI) = 90 K, associated with an electronic dimensionality decrease, since already at 100 K, the 2D part of the Fermi surface transforms into 1D corrugated planes. High resolution X-ray investigations performed at 100 K, combined with multipolar refinements, indicate an approximately equivalent +0.5e charge in both donor molecules, as also deduced from the intramolecular bond distances. On the other hand, Raman spectroscopic investigations show that at ambient temperature the charge is actually distributed non-uniformly in conducting layers of tTTF-I molecules, with the identification of molecules with charges +1, +0.5, 0e, while at low temperature the charge distribution becomes essentially uniform (+0.5e), as confirmed from the X-ray high resolution data. These apparently contradictory behaviors are actually a consequence of a partial electron transfer between the two independent slabs to reach a common Fermi level in the metallic phase.

Experimental determination of core electron deformation in diamond

Synchrotron powder X-ray diffraction data are used to determine the core electron deformation of diamond. Core shell contraction inherently linked to covalent bond formation is observed in close correspondence with theoretical predictions. Accordingly, a precise and physically sound reconstruction of the electron density in diamond necessitates the use of an extended multipolar model, which abandons the assumption of an inert core. The present investigation is facilitated by negligible model bias in the extraction of structure factors, which is accomplished by simultaneous multipolar and Rietveld refinement accurately determining an atomic displacement parameter (ADP) of 0.00181 (1) Å(2). The deconvolution of thermal motion is a critical step in experimental core electron polarization studies, and for diamond it is imperative to exploit the monatomic crystal structure by implementing Wilson plots in determination of the ADP. This empowers the electron-density analysis to precisely administer both the deconvolution of thermal motion and the employment of the extended multipolar model on an experimental basis.

Molecular origins of nonlinear optical activity in zinc tris(thiourea)sulfate revealed by high-resolution x-ray diffraction data andab initiocalculations

Structure-property relationships are established in the nonlinear optical (NLO) material, zinc tris(thiourea)sulfate (ZTS), via an experimental charge-density study, x-ray constrained wave-function refinement, and quantum-mechanical calculations. The molecular charge-transfer characteristics of ZTS, that are important for NLO activity, are topologically analyzed via a multipolar refinement of high-resolution x-ray diffraction data, which is supported by neutron diffraction measurements. The extent to which each chemical bond is ionic or covalent in nature is categorized by Laplacian-based bonding classifiers of the electron density; these include bond ellipticities, energy densities, and the local source function. Correspondingly, the NLO origins of ZTS are judged to best resemble those of organic NLO materials. The molecular dipole moment, ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, and (hyper)polarizability coefficients, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$ and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, are calculated from the experimental diffraction data using the x-ray constrained wave-function method. Complementary gas-phase ab initio quantum-mechanical calculations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ offer a supporting comparison. When taken alone, the experimental charge-density analysis does not fare well in deriving ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, or ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, which is not entirely surprising given that the associated calculations are only generally valid for organic molecules. However, by refining the x-ray data within the constrained wave-function method, the evaluations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ are shown to agree very well with those from ab initio calculations and show remarkable normalization to experimental refractive index measurements. The small differences observed between ab initio and x-ray constrained wave-function refinement results can be related directly to gas- versus solid-state phase differences. ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$ is found to be 28.3 Debye (gas phase) and 29.7 Debye (solid state) while ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ coefficients are not only significant but are also markedly three dimensional in form. Accordingly, substantial octupolar as well as dipolar NLO contributions in ZTS are indicated, which challenges the traditional focus on dipolar NLO molecules. This evaluation of NLO properties and their relation to the molecular structure offers several ways by which ZTS may be more widely functionalized as a NLO material. More generally, this case study on ZTS demonstrates how experimental and computational techniques can be combined to understand NLO structure-property relationships, an important tool for the quantum-tailored molecular design of next-generation metalorganic NLO materials.

Magnetization distribution and orbital moment in the nonsuperconducting chalcogenide compound K0.8Fe1.6Se2

We have used polarized and unpolarized neutron diffraction to determine the spatial distribution of the magnetization density induced by a magnetic field of 9 T in the tetragonal phase of K0.8Fe1.6Se2. The maximum entropy reconstruction shows clearly that most of the magnetization is confined to the region around the iron atoms whereas there is no significant magnetization associated with either Se or K atoms. The distribution of magnetization around the Fe atom is slightly nonspherical with a shape which is extended along the [0 0 1] direction in the projection. Multipolar refinement results show that the electrons which give rise to the paramagnetic susceptibility are confined to the Fe atoms and their distribution suggests that they occupy 3d t2g-type orbitals with around 66% in those of xz/yz symmetry. Detail modeling of the magnetic form factor indicates the presence of an orbital moment to the total paramagnetic moment of Fe2+

Erratum: Electronic Origin of the Structural Anomalies of Zinc and Cadmium

In the original publication, electron deformation maps based on experimental data have been presented that were derived from inconsistent multipole refinements. For this reason we withdraw Figures 3, 4 and 5, and all the discussions related. We shall provide consistent results, based on several independent data sets, in near future. All other results presented, as well as the respective conclusions drawn, remain unaffected by this corrigendum. We are grateful to Professor Wolfgang Scherer, University of Augsburg, for drawing our attention to the inconsistencies.

Modeling electron density distributions from X-ray diffraction to derive optical properties: Constrained wavefunction versus multipole refinement

The rational design of next-generation optical materials requires an understanding of the connection between molecular structure and the solid-state optical properties of a material. A fundamental challenge is to utilize the accurate structural information provided by X-ray diffraction to explain the properties of a crystal. For years, the multipole refinement has been the workhorse technique for transforming high-resolution X-ray diffraction datasets into the detailed electron density distribution of crystalline material. However, the electron density alone is not sufficient for a reliable calculation of the nonlinear optical properties of a material. Recently, the X-ray constrained wavefunction refinement has emerged as a viable alternative to the multipole refinement, offering several potential advantages, including the calculation of a wide range of physical properties and seeding the refinement process with a physically reasonable starting point. In this study, we apply both the multipole refinement and the X-ray constrained wavefunction technique to four molecules with promising nonlinear optical properties and diverse structural motifs. In general, both techniques obtain comparable figures of merit and generate largely similar electron densities, demonstrating the wide applicability of the X-ray constrained wavefunction method. However, there are some systematic differences between the electron densities generated by each technique. Importantly, we find that the electron density generated using the X-ray constrained wavefunction method is dependent on the exact location of the nuclei. The X-ray constrained wavefunction refinement makes smaller changes to the wavefunction when coordinates from the Hartree-Fock-based Hirshfeld atom refinement are employed rather than coordinates from the multipole refinement, suggesting that coordinates from the Hirshfeld atom refinement allow the X-ray constrained wavefunction method to produce more accurate wavefunctions. We then use the experimentally derived wavefunctions to calculate the molecular dipole moment, polarizability, hyperpolarizability, and refractive index and show that these are in good agreement with the values calculated using ab initio methods. Thus, this study shows that experimental wavefunctions can be reliably generated from X-ray diffraction datasets, and that optical properties can be reliably calculated from these wavefunctions. Such a concerted interplay of experiment and computation via the X-ray constrained wavefunction refinement stands to enable the molecular engineering of tailor-made next-generation optical materials.

Experimental evidence of orbital order inα-B12andγ-B28polymorphs of elemental boron

The electron density of the $\ensuremath{\alpha}$ form of boron has been obtained by multipole refinement against high-resolution, single-crystal x-ray diffraction data measured on a high-quality single crystal at a temperature of 100 K. Topological properties of this density have been used to show that all chemical bonds between B${}_{12}$ clusters in $\ensuremath{\alpha}$-B${}_{12}$ are formed due to one orbital on each boron atom that is oriented perpendicular to the surface of the cluster. It is shown that the same orbital order on B${}_{12}$ clusters persists in both $\ensuremath{\alpha}$-B${}_{12}$ and $\ensuremath{\gamma}$-B${}_{28}$ polymorphs and in several dodecaboranes, despite the fact that in every case the B${}_{12}$ clusters participate in entirely different kinds of exocluster bonds. It is likely that the same orbital order of B${}_{12}$ clusters can explain bonding in other boron polymorphs and boron-rich solids.

Charge Density Analysis of an Organic Ferroelectric. Croconic Acid: an Experimental and Theoretical Study

AbstractThe charge density in the high density (ρ = 1.912 g·cm–3) organic ferroelectric, croconic acid, was determined from low temperature (20 K) X‐ray diffraction data, and DFT theoretical calculations. The high density was associated with strong intermolecular interaction energies. The spontaneous polarization is correlated with the derived molecular dipole moment (9.3 Debye). Improvements in multipole refinement protocols are described. Limitations in the multipole model with respect to heteronuclear bond properties are discussed.

Charge density studies on 2,3,5,6-tetrafluoro- and pentafluoropyridine

Crystals of 2,3,5,6-tetrafluoropyridine and pentafluoropyridine have been grown by in situ methods in capillaries. The crystal structures of these compounds have been determined by X-ray diffraction up to high diffraction angles of 2θ = 100°. The charge density distributions of the crystals have been derived by multipole refinements. The charge densities of the title compounds as well as of pyridine have been calculated at the MP2(full)/cc-pVTZ level of theory. The structures are discussed with respect to differences to the non-substituted pyridine. The crystal structures are discussed with the focus on intermolecular interactions of the F⋯F, F⋯C and F⋯H type. The charge density topologies and parameters are discussed concerning atomic charges, bonding within the molecules and the nature of the intermolecular interactions. On the molecular level they are compared with those of pyridine.

Heteroaromaticity approached by charge density investigations and electronic structure calculations

In this paper we present the results of a high-resolution single crystal X-ray diffraction experiment at 15 K on a benzothiazol-substituted phosphane and a subsequent charge density study based on multipole refinement and a topological analysis according to Bader's quantum theory of atoms in molecules. Although two valence shell charge concentrations (VSCCs) in the non-bonding region of each phosphorus and sulfur atom were found, the integration of both heteroatomic basins emphasizes charge depletion. Nevertheless they are attractive for C-H···P and C-H···S hydrogen bonding in the solid state. The nature of the P-C bonds and the question of aromaticity in the heterocycles were subject to our investigations. The ellipticities along the bonds were analysed to approach delocalization. The source function is employed to visualise atomic contributions to aromaticity. Theoretical calculations have been carried out to compute nuclear chemical shifts, induced ring currents and a variety of delocalization indices. All applied measures for delocalization point in the same direction: while heteroaromaticity is present in the benzothiazolyl substituents, the bridging P-C bonds are only involved marginally, almost preventing total conjugation of the phosphane. The charge density distributions around the phosphorus and the sulfur atoms have very similar features but turn out to be chemically very different from each other. Commonly used simplifying concepts have difficulties in providing a comprehensive view on the electronic situation in the molecule. Our results raise doubts on the validity of the common interpretation of VSCCs as one-to-one representations of Lewis lone pairs.

A comparison of electron density from Hirshfeld-atom refinement, X-ray wavefunction refinement and multipole refinement on three urea derivatives

Electron density distributions of three urea derivatives N-methylurea, N-phenylurea and N,N′-diphenylurea were determined by single-crystal X-ray diffraction. High-resolution data were measured with synchrotron radiation. Data were subjected to a multipole refinement using the Hansen–Coppens multipole model, to Hirshfeld-atom refinement with and without a surrounding cluster of point charges/dipoles and to X-ray wavefunction refinement. Electron density distributions were evaluated in terms of deformation and residual electron density plots as well as bond critical points, atomic volumes and charges as defined in Bader's Theory of Atoms In Molecules. Given a sufficiently extended basis-set Hirshfeld-atom refinement yields results superior to multipole model refinements; best figures of merit were achieved by X-ray wavefunction refinement. Results indicate how conventional crystallographic studies can be systematically improved.

ChemInform Abstract: Polyimido Sulfur Anions and Ylides

AbstractReview: 127 refs.

Resolution-dependent scaling – a solution for problems in a multipole refinement?

Resolution-dependent scaling – a solution for problems in a multipole refinement?

Multipolar refinement of amino acids with anisotropic H-atom treatment

Multipolar refinement of amino acids with anisotropic H-atom treatment

Differences in Charge Density Distribution and Stability of Two Polymorphs of Benzidine Dihydrochloride

Charge density distribution analysis supplemented by energy studies of two known (previously reported) polymorphic forms of benzidine dihydrochloride — triclinic P1̅ (TP) and orthorhombic Pbcn (OP) — is presented. High resolution X-ray diffraction measurement results were additionally related to the theoretically evaluated charge density distribution on the basis of periodic ab initio computations. In the case of TP, collected neutron diffraction structural data were included in the high resolution X-ray multipole refinement procedure. Although TP and OP form generally similar layered crystal architectures, the two structures differ significantly in details, due to slightly different conformations of the benzidinium cation, different packing, and thus intermolecular interactions. This is reflected in charge density distribution, crystal morphology, and growth. For TP, the integrated charge for the chloride anions is equal to ca. −0.90e, while for OP it is −1.07e. In consequence, charges for the benzidinium cation are equal to +1.85e for TP and +2.12e for OP. Different charge distributions for both polymorphs cause significant differences in the electrostatic potential. In the case of OP, the electrostatic potential for the −NH3+ group is substantially higher than for TP. Lower values of charge density at aromatic rings of the benzidinium cation for TP can be associated with significant contribution of stacking type of interactions. TP is slightly (ca. 10–15 kJ·mol–1) more thermodynamically advantageous than OP, however, the difference constitutes just a small percentage of the total cohesive energy derived (ca. −1500 kJ·mol–1). Therefore, both polymorphic forms can be obtained simultaneously from one solution under the same conditions. On the other hand, TP is characterized by a more homogeneous distribution of ionic fragments in its crystal lattice than OP. The straightforward comparison of the crucial interlayer interaction energies and the surface free energy values between both polymorphs shows that in the case of TP crystal faces should more preferably grow, being slightly less stable than in OP. Lower surface free energy in OP, and especially low interlayer interaction energy of (100) slabs, presumably hampers further growth of the initially formed crystals, explaining the difficulties in obtaining OP crystals of the size suitable for neutron diffraction experiments. Naturally, kinetic and solvent effects should not be neglected. Nevertheless, the energy results show that despite the resemblance of the cohesive energy values of polymorphs, the character and features of their crystal architectures may cause significant differences in crystallization mechanisms and crystal quality. It appears that there is little correlation between geometrical parameters of hydrogen bonds and their energies.

Experimental and Theoretical Charge Density Studies of 8-Hydroxyquinoline Cocrystallized with Salicylic Acid

The experimental electron density distribution (EDD) in 8-hydroxyquinoline cocrystallized with salicylic acid, 1, has been determined from a multipole refinement of high-resolution X-ray diffraction data collected at 100 K. The experimental EDD is compared with theoretical densities resulting from high-level ab initio and BHandH calculations using Atoms in Molecules theory. 1 crystallizes in the triclinic crystal system, and the asymmetric unit consists of a neutral salicylic acid molecule, a salicylate anion, and an 8-hydroxyquinolinium cation exhibiting a number of inter- and intramolecular hydrogen bonds and π-π interactions. Topological analysis reveals that π-π interactions are of the "closed-shell" type, characterized by rather low and flat charge density. In general, the agreement of the topological values (ρ(bcp) and ∇(2)ρ(bcp)) between experiment and theory is good, with mean differences of 0.010 e Å(-3) and 0.036 e Å(-5), respectively. The energetics of the π-π interactions have been estimated, and excellent agreement is observed between the relative energy and the strength of π-stacking derived from the Espinosa approach, with an average difference of only 4.4 kJ mol(-1).

Can a Formally Zwitterionic Rhodium(I) Complex Emulate the Charge Density of a Cationic Rhodium(I) Complex? A Combined Synchrotron X-ray and Theoretical Charge-Density Study

The molecular electron densities of structurally related cationic ([(κ(2)-3-P(i)Pr(2)-2-NMe(2)-indene)Rh(COD)](CF(3)SO(3)), [1c](CF(3)SO(3))) and formally zwitterionic ([(κ(2)-3-P(i)Pr(2)-2-NMe(2)-indenide)Rh(COD)], 1z) complexes were accurately determined using synchrotron bright-source X-ray radiation at 30 K followed by multipolar refinement (COD = η(4)-1,5-cyclooctadiene). The densities were also obtained from density functional theory calculations with a large, locally dense basis set. A 28-electron ([Ar]3d(10)) core of the Rh atom was modeled by an effective core potential to obtain a density that was then augmented with relativistic cores according to the Keith-Frisch approximation. Calculations were performed at the experimental geometry and after vacuum-phase geometry optimization starting from the experimental geometry. Experimental and calculated geometries and electron-density distributions show that the electron density and electronic structure in the region of the Rh center are not significantly altered by protonation of the aromatic ring and that formal removal of CF(3)SO(3)H from [1c](CF(3)SO(3)) affords a complex 1z possessing substantial zwitterionic character (with a charge separation of ca. 0.9 electronic charge) featuring a negatively charged aromatic indenide framework. Further, the molecular electrostatic potentials of 1c and 1z exhibit similar topography around the metal, despite being drastically different in the vicinity of the indene or indenide portion of the cation (1c) and zwitterion (1z), respectively. Collectively, these observations obtained from high-level experimental and theoretical electron-density analysis confirm, for the first time, that appropriately designed zwitterionic complexes can effectively emulate the charge distribution found within ubiquitous cationic platinum-group metal catalyst complexes, in keeping with recent catalytic investigations.

Bonding situation and N–O-bond strengths in amine-N-oxides—a combined experimental and theoretical study

The bonding situation and energetics of the N-O bond in a series of amine-N-oxides, Ph(x)(CH(3))(3-x)N-O, where x = 0-3, were analyzed experimentally and theoretically. There is a notable nearly linear decrease of the N-O bond dissociation energies (BDEs) for this series with an increasing number of phenyl groups x. This was investigated experimentally by X-ray high angle multipole refinement techniques in combination with subsequent topological analysis of the electron density for the representative (CH(3))(2)PhN-O, 2, and complementary theoretical calculations at the DFT and multireference CASSCF and MR-perturbation theory (MCQDPT2) levels. Both the theoretical and experimental results unambiguously revealed a polar covalent σ-bond for the N-O bond with an essentially identical bonding situation for all amine-N-oxides studied. This apparent disparity between the bonding situation and the trend of BDEs is attributed to the large differences of the relaxation energies of the corresponding amines Ph(x)(CH(3))(3-x)N, (x = 0-3), respectively, the required preparation energies (ΔE(prep)) for the reverse N-O bond forming process. The detailed theoretical analysis of the amines allowed us to trace the trend of larger values of ΔE(prep) for a higher number of phenyl groups x to an increase of n(N) → π*(C-C) delocalization interactions.

Polyimido sulfur anions and ylides

Isovalent electronic replacement of the oxygen atoms in the classic SO(n)(m-) molecules and ions by NR imido groups yields the polyimido sulfur species S(NR)(n)(m-), n = 2, 3, 4 and m = 0, 2. The crucial cornerstone to the richness of SN chemistry is the access to sulfur diimides S(NR)(2) and triimides S(NR)(3). While the syntheses of the first are well established the preparations of the second were hazardous and of poor yields. A new facile, safe and elaborated route to give quantitative yields is presented. It involves the synthesis of triimido sulfites S(NR)(3)(2-), which are versatile ligands in their own right. With a trigonal pyramidal shape, containing three basal negatively charged nitrogen atoms, they are rare examples of dianionic tripodal ligands. Various (mixed) metal complexes are presented. Lithium coordination at the N-S-N bisections converts the dianion into the inverse tripod ligand Li(3)(NR)(3)S(+), capable of anion solvation. Among others, this motif stabilizes unprecedented monomeric methyllithium and lithium enolate. In the reaction of sulfur diimides S(NR)(2) and triimides S(NR)(3) with organometallics the diimidosulfinates RS(NR)(2)(-) and triimidosulfonates RS(NR)(3)(-) are synthesised. Both display a rich coordination chemistry to various metals, which is discussed in the review. Furthermore, the S-organo substituent can be modified in various ways. It can be a linker between two SN moieties or can be shaped to a R(2)N- or R(2)P-donating side arm of any form or length to give hemilabile scorpionates. Their ample application in metal coordination and anion solvation is presented. These monoanions can be converted to the related ylides by deprotonation of the S-alkyl group. The diimidosulfur(IV) ylides (R(2)C)S(NR)(2)(2-) and triimidosulfur(VI) ylides (R(2)C)S(NR)(3)(2-) contain the CR(2) methylene group, isoelectronic to the NR imido group. Their coordination behaviour and reactivity are discussed. In addition to the rich SN chemistry the S-N and S-C bonding is elucidated by means of theoretical and experimental charge density investigations and topological analyses on the basis of multipole refinement. As the most important result hypervalency at sulfur and S=N(C) double bonding are ruled out as superfluous concepts.

Topological features and electronic structure of 4-chloro-1H-pyrrolo[2,3-b]pyridine: experimental charge density analysis and DFT studies

The experimental charge density distribution in 4-chloro-1H-pyrrolo[2,3-b]pyridine has been carried out using high resolution X-ray diffraction data collected at 100(2) K. Multipole refinement based on the Hansen–Coppens formalism coupled with an estimation of anisotropic displacement parameters (ADPs) of hydrogen atoms converged to R(F) = 0.0353 for 5700 reflections with I > 3σ(I) and sin θ/λ ≤ 1.08 A−1. The topology of the bonding scheme within the molecule as well as of the intermolecular N–H⋯N and C–H⋯Cl hydrogen bonds has been investigated. The covalent nature of N–C and C–C bonds in the pyrrolopyridine skeleton of the molecule has been established by (3, −1) bond critical points associated with relatively large electron densities [2.07(2)–2.74(3) e A−3] and highly negative Laplacian values [−11.37(4) to −19.20(10) e A−5]. The topological parameters corresponding to H⋯N and H⋯Cl critical points indicate a moderately strong intermolecular N–H⋯N hydrogen bond and a weak C–H⋯Cl closed-shell interaction. The electronic structure of the title compound has been calculated by density functional theory (DFT) at the BLYP level. A large HOMO–LUMO energy gap (3.59 eV; HOMO is the highest occupied molecular orbital and LUMO is the lowest unoccupied molecular orbital) implies a high kinetic stability of the title compound.