Validation of X-ray Wavefunction Refinement

Probing the Isolobal Relation between Cp'''NiP3 and White Phosphorus by Experimental Charge Density Analysis

An in-depth analysis of the description of bonding within Cp'''Ni-cyclo-P3 (Cp'''=1,2,4-tri-tert-butylcyclopentadienyl, [Ni]P3) employing X-ray diffraction based multipolar modeling, density functional theory (DFT) as well as an "experimental wavefunction" obtained from X-ray restrained wavefunction (XRW) fitting is presented. The results are compared to DFT calculations on white phosphorus - an isolobal analogue to [Ni]P3. A complementary bonding analysis shows insights into the reactivity of [Ni]P3. The isolobal principle is reflected in every aspect of our analysis and the employed methods seamlessly predict the differences in reactivity of [Ni]P3 and P4. Crystallographic modeling, solid-state NMR, and DFT calculations describe the dynamic behavior of the cyclo-P3 unit in the title molecule.

Dynamic Covalent Bonds in the Ebselen Class of Antioxidants Probed by X-ray Quantum Crystallography

Dynamic bonds are essential structural ingredients of dynamic covalent chemistry that involve reversible cleavage and formation of bonds. Herein, we explore the electronic characteristics of Se-N bonds in the organo-selenium antioxidant ebselen and its derivatives for their propensity to function as dynamic covalent bonds by employing high-resolution X-ray quantum crystallography and complementary computational studies. An analysis of the experimentally reconstructed X-ray wavefunctions reveals the salient electronic features of the Se-N bonds with very low electron density localized at the bonding region and a positive Laplacian value at the bond critical point. Bond orders and percentage covalency and ionicity estimated from the X-ray wavefunctions, along with localized orbital locator (LOL) and electron localization function (ELF) analyses show that the Se-N bond is unique in its closed shell-like features, despite being a covalent bond. Time-dependent DFT calculations simulate the cleavage of Se-N bonds in ebselen in the excited state, further substantiating their nature as dynamic bonds.

Development of Stable Carbanionic Substituents

During the past decade, carbon (C-H) acids depicted as 'Tf2 CHR' (Tf=CF3 SO2 ) have attracted considerable attention as a new class of superacidic molecules, which show stronger acidity than sulfuric acid molecules. In recent years, the author has developed a synthetic methodology for such strong acids and has opened the door to chemistry of highly stabilised carbanions [Tf2 CR]- , which are the conjugate bases of the carbon acids. These carbanion-containing salts are stable and easy-to-handle species. Our efforts have revealed that the ionic but lipophilic characters of this type of carbanion can be used as a unique 'substituent' for increasing both the water solubility and the lipophilicity of organic compounds. This Personal Account provides an overview of our [Tf2 CR]- chemistry, including its synthesis, structure, reactivity, and applications.

Elucidating the nature of chemical bonds in a coordination compound through quantum crystallographic techniques

Investigations simultaneously involving multiple techniques of quantum crystallography could be very useful to prove the consistency of obtained results or to highlight different facets of the same scientific phenomenon or problem. Pinto et al. [Acta Cryst. (2023), B79, 282-296] exploit three different quantum crystallographic techniques (Hansen & Coppens multipole model refinement, QTAIM analysis of the electron density, and Hirshfeld atom refinement) to characterize the nature of chemical bonds and of intra/intermolecular interactions in an organometallic compound.

Reversing the Bond Length Alternation Order in Conjugated Polyenes by Substituent Effects

We have synthesised several push-pull substituted conjugated polyenes and determined their accurate C-C bond lengths and charge-density distributions by utilising quantum crystallographic techniques. In a series of alkene, dienes, and triene bearing two (trifluoromethyl)sulfonyl (triflyl) groups on the terminal carbon atom, unique reversal of the bond-length alternation (BLA) order has been observed. This is a pronounced aberration from the molecular structure predicted by the Lewis-structure-based neutral resonance structure. Such reversal of BLA order has not been observed in push-pull compounds bearing conventional electron-withdrawing groups such as carbonyl and cyano groups instead of triflyl groups. Bonding behaviour of both normal and reversed bond length alternating systems has been revealed by complementary bonding analysis using several bond descriptors based on the experimentally fitted wavefunctions.

Introduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbacks

In a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136-146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λ_J for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.

Remarks on X-ray constrained/restrained wavefunction fitting

X-ray constrained/restrained wavefunctions (XCWs/XRWs) result from a combination of theory and experiment and are therefore affected by experimental errors and model uncertainties. The present XCW/XRW procedure does not take this into account, thus limiting the meaning and significance of the obtained wavefunctions.

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

π-Hole bonding in a new co-crystal hydrate of gallic acid and pyrazine: static and dynamic charge density analysis

A new cocrystal hydrate of gallic acid with pyrazine (4GA, Py, 4H₂O; GA₄PyW₄) was obtained and characterized by single crystal X-ray diffraction. In addition to structure determination, experimental charge density analysis was carried out in terms of Multipole Modelling (MP), X-ray wavefunction refinement (XWR) and maximum entropy method (MEM). As a part of XWR, the structural refinement via Hirshfeld atom refinement was carried out and resulted in O-H bond lengths close to values from neutron diffraction. A systematic comparison of molecular conformations and aromatic interactions in this new cocrystal hydrate was performed with other existing polymorphs of gallic acid. In GA₄PyW₄, the two symmetry-independent gallic acid molecules have a syn COOH orientation and form the common (COOH)₂ dimeric synthon. The carboxyl C atom displays the characteristics of π-holes with electropositive regions above and below the molecular plane and engages in acceptor-donor interactions with oxygen atoms of acidic O-H groups and phenol groups of neighbouring gallic acid molecules. The signature of the π-hole was identified from experimental charge density analysis, both in static density maps in MP and XWR as well as dynamic density in MEM, but it cannot be pinned down to a specific atom-atom interaction. This study presents the first comparison between an XWR and a MEM experimental electron-density determination.

New venues in electron density analysis

We provide a comprehensive overview of the chemical information within the electron density: how to extract information, but also how to obtain and how to assess the quality of the...

H-Atom Assignment and Sb-O Bonding of [Mes3SbOH][O3SPh] Confirmed by Neutron Diffraction, Multipole Modeling, and Hirshfeld Atom Refinement

Neutron wavelength-resolved Laue diffraction experiments permit accurate refinement of the H-atom positions and anisotropic displacement parameters of [Mes₃SbOH][O₃SPh]. A multipole-based charge density refinement and a topological analysis of the refined electron density were also performed. Hirshfeld atom refinement (HAR) recovers the neutron-determined H-atom parameters, and the quantum-mechanical electron density used in HAR recovers the electron density topology from the refined multipole model. These results confirm that [Mes₃SbOH][O₃SPh] does indeed feature a hydroxystibonium cation with a nominal Sb-O single bond and not a stibine oxide with an Sb=O/Sb⁺-O^- bond.

Vanishing of the atomic form factor derivatives in non-spherical structural refinement - a key approximation scrutinized in the case of Hirshfeld atom refinement

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR₂ factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

Relativistic Hirshfeld atom refinement of an organo-gold(I) compound

The main goal of this study is the validation of relativistic Hirshfeld atom refinement (HAR) as implemented in Tonto for high-resolution X-ray diffraction datasets of an organo-gold(I) compound. The influence of the relativistic effects on statistical parameters, geometries and electron density properties was analyzed and compared with the influence of electron correlation and anharmonic atomic motions. Recent work in this field has indicated the importance of relativistic effects in the static electron density distribution of organo-mercury compounds. This study confirms that differences in electron density due to relativistic effects are also of significant magnitude for organo-gold compounds. Relativistic effects dominate not only the core region of the gold atom, but also influence the electron density in the valence and bonding region, which has measurable consequences for the HAR refinement model parameters. To study the effects of anharmonic motion on the electron density distribution, dynamic electron density difference maps were constructed. Unlike relativistic and electron correlation effects, the effects of anharmonic nuclear motion are mostly observed in the core area of the gold atom.

Further Validation of Quantum Crystallography Approaches

Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.

lamaGOET: an interface for quantum crystallography

In quantum crystallography, theoretical calculations and crystallographic refinements are closely intertwined. This means that the employed software must be able to perform both quantum-mechanical calculations and crystallographic least-squares refinements. So far, the program Tonto is the only one able to do that. The lamaGOET interface described herein deals with this issue since it interfaces dedicated quantum-chemical software (the widely used Gaussian package and the specialized ELMOdb program) with the refinement capabilities of Tonto. Three different flavours of quantum-crystallographic refinements of the dipetide glycyl-l-threonine dihydrate are presented to showcase the capabilities of lamaGOET: Hirshfeld atom refinement (HAR), HAR-ELMO, namely HAR coupled with extremely localized molecular orbitals, and X-ray constrained wavefunction fitting.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Measuring Density Functional Parameters from Electron Diffraction Patterns

We integrate density functional theory (DFT) into quantitative convergent-beam electron diffraction (QCBED) to create a synergy between experiment and theory called QCBED-DFT. This synergy resides entirely in the electron density which, in real materials, gives rise to the experimental CBED patterns used by QCBED-DFT to refine DFT model parameters. We use it to measure the Hubbard energy U for two strongly correlated electron systems, NiO and CeB_{6} (U=7.4±0.6  eV for d orbitals in NiO and U=3.0±0.6  eV for f orbitals in CeB_{6}), and the boron position parameter x for CeB_{6} (x=0.1992±0.0003). In verifying our measurements, we demonstrate an accuracy test for any modeled electron density.

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.

HgH2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH₂ molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.

Accurate crystal structures and chemical properties from NoSpherA2

The relationship between the structure and the properties of a drug or material is a key concept of chemistry. Knowledge of the three-dimensional structure is considered to be of such importance that almost every report of a new chemical compound is accompanied by an X-ray crystal structure – at least since the 1970s when diffraction equipment became widely available. Crystallographic software of that time was restricted to very limited computing power, and therefore drastic simplifications had to be made. It is these simplifications that make the determination of the correct structure, especially when it comes to hydrogen atoms, virtually impossible. We have devised a robust and fast system where modern chemical structure models replace the old assumptions, leading to correct structures from the model refinement against standard in-house diffraction data using no more than widely available software and desktop computing power. We call this system NoSpherA2 (Non-Spherical Atoms in Olex2). We explain the theoretical background of this technique and demonstrate the far-reaching effects that the improved structure quality that is now routinely available can have on the interpretation of chemical problems exemplified by five selected examples.

NoSpherA2 brings quantum crystallography to routine structure determination and to the analysis of chemical properties for any class of materials.

Hirshfeld atom like refinement with alternative electron density partitions

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

Sila-Ibuprofen

The synthesis, characterization, biological activity, and toxicology of sila-ibuprofen, a silicon derivative of the most common nonsteroidal anti-inflammatory drug, is reported. The key improvements compared with ibuprofen are a four times higher solubility in physiological media and a lower melting enthalpy, which are attributed to the carbon-silicon switch. The improved solubility is of interest for postsurgical intravenous administration. A potential for pain relief is rationalized via inhibition experiments of cyclooxygenases I and II (COX-I and COX-II) as well as via a set of newly developed methods that combine molecular dynamics, quantum chemistry, and quantum crystallography. The binding affinity of sila-ibuprofen to COX-I and COX-II is quantified in terms of London dispersion and electrostatic interactions in the active receptor site. This study not only shows the potential of sila-ibuprofen for medicinal application but also improves our understanding of the mechanism of action of the inhibition process.

The X-ray constrained wavefunction of the [Mn(CO)4{(C6H5)2P-S-C(Br2)-P(C6H5)2}]Br complex: a theoretical and experimental study of dihalogen bonds and other noncovalent interactions

The synthesis and X-ray structure determination of the [Mn(CO)₄{(C₆H₅)₂P-S-C(Br₂)-P(C₆H₅)₂}]Br complex (1) are described. The C-Br...Br dihalogen bond present in 1 has been characterized by means of topological studies of the electron density. Both the quantum theory of atoms in molecules and the electron localization function approaches have been applied to several theoretically calculated wavefunctions as well as to an X-ray constrained wavefunction. In addition, a number of theoretical techniques, such as the source function, the reduced density gradient method and the interacting quantum atoms approach, among others, have been used to analyse the dihalogen bond as well as several intramolecular interactions of the type C-H...Br-C which have also been detected in 1. The results show clearly that while bonding in the latter interactions are dominated by electrostatic components, the former has a high degree of covalency.

Quantum Crystallography in the Last Decade: Developments and Outlooks

In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.

Refinement of organic crystal structures with multipolar electron scattering factors

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near-atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyse these high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atom model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis. In this study a comparison is presented of IAM and TAAM (transferable aspherical atom model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. Structure refinements were performed on a carbamazepine crystal using electron structure-factor amplitudes determined experimentally [Jones et al. (2018). ACS Cent. Sci. 4, 1587-1592] or modelled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared with IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer-resolution diffraction data.

Energetics of interactions in the solid state of 2-hydroxy-8-X-quinoline derivatives (X = Cl, Br, I, S-Ph): comparison of Hirshfeld atom, X-ray wavefunction and multipole refinements

In this work, two methods of high-resolution X-ray data refinement: multipole refinement (MM) and Hirshfeld atom refinement (HAR) - together with X-ray wavefunction refinement (XWR) - are applied to investigate the refinement of positions and anisotropic thermal motion of hydrogen atoms, experiment-based reconstruction of electron density, refinement of anharmonic thermal vibrations, as well as the effects of excluding the weakest reflections in the refinement. The study is based on X-ray data sets of varying quality collected for the crystals of four quinoline derivatives with Cl, Br, I atoms and the -S-Ph group as substituents. Energetic investigations are performed, comprising the calculation of the energy of intermolecular interactions, cohesive and geometrical relaxation energy. The results obtained for experimentally derived structures are verified against the values calculated for structures optimized using dispersion-corrected periodic density functional theory. For the high-quality data sets (the Cl and -S-Ph compounds), both MM and XWR could be successfully used to refine the atomic displacement parameters and the positions of hydrogen atoms; however, the bond lengths obtained with XWR were more precise and closer to the theoretical values. In the application to the more challenging data sets (the Br and I compounds), only XWR enabled free refinement of hydrogen atom geometrical parameters, nevertheless, the results clearly showed poor data quality. For both refinement methods, the energy values (intermolecular interactions, cohesive and relaxation) calculated for the experimental structures were in similar agreement with the values associated with the optimized structures - the most significant divergences were observed when experimental geometries were biased by poor data quality. XWR was found to be more robust in avoiding incorrect distortions of the reconstructed electron density as a result of data quality issues. Based on the problem of anharmonic thermal motion refinement, this study reveals that for the most correct interpretation of the obtained results, it is necessary to use the complete data set, including the weak reflections in order to draw conclusions.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

The upcoming subatomic resolution revolution

Subatomic resolution macromolecular crystallography has been revealing the most fascinating details of macromolecular structures for many years. This most extreme form of macromolecular crystallography is going through rapid changes. A new generation of superbrilliant X-ray sources and detectors is facilitating the rapid acquisition of high-quality datasets. Equally important, a new breed of methods and highly integrated advanced computational tools for structure refinement and analysis is poised to change the way we use subatomic resolution data and reposition high-resolution macromolecular crystallography in medicinal chemistry studies. Subatomic resolution macromolecular crystallography may soon be a routine source of detailed molecular information besides precise geometries, including binding energies and other chemical descriptors, opening new possibilities of application.

Revisiting a Historical Concept by Using Quantum Crystallography: Are Phosphate, Sulfate and Perchlorate Anions Hypervalent?

There are many examples of atoms in molecules that violate Lewis' octet rule, because they have more than four electron pairs assigned to their valence. These atoms are referred to as hypervalent. However, hypervalency may be regarded as an artifact arising from Lewis' description of molecules, which is based on the assumption that electrons are localized in two-center two-electron bonds and lone pairs. In the present paper, the isoelectronic phosphate (PO₄ ^3- ), sulfate (SO₄ ^2- ) and perchlorate (ClO₄ ^- ) anions were examined with respect to the concept of hypervalency. Lewis formulas containing a hypervalent central atom exist for all three anions. Based on X-ray wavefunction refinements of high-resolution X-ray diffraction data of representative crystal structures (MgNH₄ PO₄ ⋅6 H₂ O, Li₂ SO₄ ⋅H₂ O, and KClO₄ ), complementary bonding analyses were performed. In this way, experimental information from the new field of quantum crystallography validate long-known facts, or refute long-standing misunderstandings. It is shown that the P-O and S-O bonds are highly polarized covalent bonds and, thus, the increase in the valence population following three-center four-electron bonding is not sufficient to yield hypervalent phosphorus or sulfur atoms, respectively. However, for the highly covalent Cl-O bond, most bonding indicators imply a hypervalent chlorine atom.

Complementary bonding analysis of the N–Si interaction in pentacoordinated silicon compounds using quantum crystallography

The unique combination of quantum crystallography and complementary bonding analysis is used to investigate the bonding of pentacoordinated silicon atoms.

Electron density: historical remarks with a focus on the Berlin school

The history of electron density (ED) research is surveyed and its historical highlights in the 20th century are summarized. The progress, reached at the beginnig of the 21st century, is described including contributions from the Berlin school. Key experimental advances concern X-ray sources and synchrotron radiation, measuring reflection data at very low temperatures (down to ~10 K), as well as the introduction of area detectors. Methodological progress was reached by new software systems for the refinement and analysis of ED data sets. This allowed to obtain quantitative ED properties, making use of Bader’s Quantum Theory of Atoms in Molecules (QTAIM). More recently methods, which combine experimental X-ray data and quantum-chemically derived wave functions, established the rapidly developing new field of “Quantum Crystallography.”

Ground-State Charge-Density Distribution in a Crystal of the Luminescent ortho-Phenylenediboronic Acid Complex with 8-Hydroxyquinoline

This contribution is devoted to the first electron density studies of a luminescent oxyquinolinato boron complex in the solid state. ortho-Phenylenediboronic acid mixed with 8-hydroxyquinoline in dioxane forms high-quality single crystals via slow solvent evaporation, which allows successful high resolution data collection (sin θ/λ = 1.2 Å^-1) and charge density distribution modeling. Particular attention has been paid to the boron-oxygen fragment connecting the two parts of the complex, and to the solvent species exhibiting anharmonic thermal motion. The experiment and theory compared rather well in terms of atomic charges and volumes, except for the boron centers. Boron atoms, as expected, constitute the most electron-deficient species in the complex molecule, whereas the neighboring oxygen and carbon atoms are the most significantly negatively charged ones. This part of the molecule appears to be very much involved in the charge transfer occurring between the acid fragment and oxyquinoline moiety leading to the observed fluorescence, as supported by the time-dependent density functional theory (TDDFT) results and the generated transition density maps. TDDFT calculations indicated that p-type atomic orbitals contributing to the HOMO-1, HOMO, and LUMO play the major role in the lowest energy transitions, and enabled further comparison with the charge density features, which is discussed in details. Furthermore, the results confirmed the known fact the Q ligand character is most important for the spectroscopic properties of this class of complexes.

Investigating the Resonance in Nitric Acid and the Nitrate Anion Based on a Modern Bonding Analysis

The nitrate anion, NO3−, is often regarded as a textbook example for the very fundamental concept of resonance. Usually, three equivalent resonance structures with one N–O double bond and two N–O single bonds are considered. Consequently, each of the three N–O bonds should have a partial double bond character. In this study, we analyse the resonance in NO3− in comparison with the related species HNO3 and FNO3 by applying a combination of the Quantum Theory of Atoms in Molecules (QTAIM), a natural bond orbital (NBO) analysis, the electron localizability indicator (ELI), and valence bond (VB) calculations. Despite the fundamental importance of nitrate salts and nitric acid for the environment, chemistry, and industry, a bonding analysis is absent from the literature so far. The classical resonance structures are clearly reflected by the bond analysis tools, but are not the only contributions to the bonding situation. The resonance in HNO3 and FNO3 is greatly perturbed by the hydrogen and fluorine atoms. In addition to theoretical calculations, experimental electron density and wave function refinements were carried out on a KNO3 crystal.