The significance of ionic bonding in sulfur dioxide: bond orders from X-ray diffraction data

Synthesis and Structure of the Small Superelectrophile [C2(OH)2Me2]2

The acid-activation of 1,2-dicarbonyl compounds plays a key role in a variety of electrophilic reactions, some of which are only accessible in superacidic media when a superelectrophilic dication is formed. To obtain structural and electronic information about these elusive species, the vicinal dication [C2(OH)2Me2]2+ is synthesized and characterized by Raman spectroscopy and X-ray diffraction. Since this superelectrophile could not be stabilized in convenient superacids, the usage of liquid SO2 turned out to be crucial. The experimental data are discussed together with quantum-chemical calculations on the B3LYP/aug-cc-pVTZ level of theory. Natural Bond Orbital (NBO) analyses quantify the superelectrophilic interactions found in the solid state.

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

Synthesis and Structure of Protonated Sulfur Dioxide

Salts of protonated sulfur dioxide were synthesized by recrystallization of [FS(OX)2][SbF6] (X=H, D) in aprotic solvents at low temperatures. Hemiprotonated sulfur dioxide [(SO2)2H][Sb2F11] was obtained from the solvent SO2 and the monoprotonated sulfur dioxide [OSOD][Sb2F11], using 1,1,1,2-tetrafluoroethane as solvent. For both compounds, single crystals were obtained and an X-ray structure analysis was conducted. Furthermore, the salts were characterized by Raman spectroscopy and the results were discussed together with quantum chemical calculations on the M06-2X/aug-cc-pVTZ level of theory.

N,N'-Diaryl-Sulfurdiimides are Strongly Redox Tuned

The synthesis and extensive characterization of nine aryl sulfur diimides (SDIs, Ar-NSN-Ar) are presented with a robust computational and experimental investigation of the fundamental properties of these important members of the thiazyl family of compounds, with particular attention paid to their highly tunable electrochemical behaviour. This is the first work to undertake a systematic comparison of the electrochemical profiles of a coherent series of SDIs to demonstrate and quantify the response of their reduction potentials to substituent electron-donating and -withdrawing properties. This effect is found to be not only exceptionally strong, but also correlates very closely with computed orbital energies. Electron paramagnetic resonance spectroscopy is used to determine the nature, localization, and qualitative lifetimes of the radical anions of SDIs. This work also addresses significant misconceptions about physical properties of SDIs. Experimental data and modern computational methods are employed to provide a resolute answer to the long-standing contention of the solution-state conformations of SDIs, and to correct historical mistakes in the assignment of infrared spectroscopic data. High-quality crystal structures of all SDIs in this work showcase the utility of the recently introduced structural refinement software NoSpherA2, enabling full anisotropic refinement of H-atoms with accurate C-H bond lengths.

Dynamical refinement with multipolar electron scattering factors

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Hydrogen Bonds Stabilize Chloroselenite Anions: Crystal Structure of a New Salt and Donor-Acceptor Bonding to SeO2

The single-crystal X-ray diffraction structure characterizing a new 4-methylbenzamidinium salt of chloroselenite [C8H11N2][ClSeO2] is reported. This is only the second crystal structure report on a ClSeO2- salt. The structure contains an extended planar hydrogen bond net, including a double interaction with both O atoms of the anion (an R228 ring in Etter notation). The anion has the shortest Se-Cl distances on record for any chloroselenite ion, 2.3202(9) Å. However, the two Se-O distances are distinct at 1.629(2) and 1.645(2) Å, attributed to weak anion-anion bridging involving the oxygen with the longer bond. DFT computations at the RB3PW91-D3/aug-CC-pVTZ level of theory reproduce the short Se-Cl distance in a gas-phase optimized ion pair, but free optimization of ClSeO2- leads to an elongation of this bond. A good match to a known value for [Me4N][ClSeO2] is found, which fits to the Raman spectroscopic evidence for this long-known salt and to data measured on solutions of the anion in CH3CN. The assignment of the experimental Raman spectrum was corrected by means of the DFT-computed vibrational spectrum, confirming the strong mixing of the symmetry coordinate of the Se-Cl stretch with both ν2 and ν4 modes.

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.

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.

Hybrid G/BN@2H-MoS2 Nanomaterial Composites: Structural, Electronic and Molecular Adsorption Properties

Hybrid structures often possess superior properties to those of their component materials. This arises from changes in the structural or physical properties of the new materials. Here, we investigate the structural, electronic, and gas-adsorption properties of hybrid structures made from graphene/hexagonal boron nitride and 2H-molybdenum disulfide (G/BN@MoS₂) monolayers. We consider hybrid systems in which the G/BN patch is at the Mo plane (model I) and the S plane (model II). We find that the implanted hexagon of G or BN in MoS₂ alters its electronic properties: G@MoS₂ (I,II) are metallic, while BN@MoS₂ (I) is an n-type conducting and BN@MoS₂ (II) is semiconducting. We study the molecular adsorption of some diatomic gases (H₂, OH, N₂, NO, CO), triatomic gases (CO₂, NO₂, H₂S, SO₂), and polyatomic gases (COOH, CH₄, and NH₃) on our hybrid structures while considering multiple initial adsorption sites. Our results suggest that the hybrid systems may be suitable materials for some applications: G@MOS₂ (I) for oxygen reduction reactions, BN@MoS₂ (I,II) for NH₃-based hydrogen production, and G@MoS₂ (I) and BN@MoS₂ (I,II) for filtration of No, Co, SO₂, H₂S, and NO₂.

Electron density of the 1:2 complex of valinomycin with calcium triflate observed in crystals of the composition (valinomycin)Ca2(OTf)4(THF)5(H2O)4

The electron density of a 1:2 complex of valinomycin with calcium triflate consisting of 10 substructures and a total of 279 atoms was examined using the invariom formalism. In addition to geometric properties, sites and strengths of hydrogen bonds were identified from bond topological properties and from electron density concentrations mapped onto Hirshfeld surfaces. In contrast to free valinomycin and corresponding complexes with potassium the hydrogen bonds are all intermolecular and evenly distributed over the complex. A series of electrostatic potential (ESP) surfaces show the mutual influence in the ensemble of this high Z′ structure.

Hybrid MXene-Graphene/Hexagonal Boron Nitride Structures: Electronic and Molecular Adsorption Properties

Recent advances in experimental techniques allow for the fabrication of hybrid structures. Here, we study the electronic and molecular adsorption properties of the graphene (G)/hexagonal boron nitride (h-BN)-MXenes (Mo2C) hybrid nanosheets. We use first-principles calculations to explore the structure and electronic properties of the hybrid structures of G-2H-Mo2C and h-BN-2H-Mo2C with two different oxygen terminations of the Mo2C surface. The embedding of G or h-BN patches creates structural defects at the patch-Mo2C border and adds new states in the vicinity of the Fermi energy. Since this can be utilized for molecular adsorption and/or sensing, we investigate the ability of the G-M-O1 and BN-M-O1 hybrid structures to adsorb twelve molecules. Generally, the adsorption on the hybrid systems is significantly higher than on the pristine systems, except for N2 and H2, which are weakly adsorbed on all systems. We find that OH, NO, NO2, and SO2 are chemisorbed on the hybrid systems. COOH may be chemisorbed, or it may dissociate depending on its location at the edge between the G/h-BN and the MXene. NH3 is chemisorbed/physisorbed on the BN/G-M-O1 systems. CO, H2S, CO2, and CH4 are physisorbed on the hybrid systems. Our results indicate that the studied hybrid systems can be used for molecular filtration/sensing and catalysis.

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.

Synthesis, X-ray Structure Determination, and Comprehensive Photochemical Characterization of (Trifluoromethyl)diazirine-Containing TRPML1 Ligands

Potential (trifluoromethyl)diazirine-based TRPML1 ion channel ligands were designed and synthesized, and their structures were determined by single-crystal X-ray diffraction analysis. Photoactivation studies via ¹⁹F NMR spectroscopy and HPLC-MS analysis revealed distinct kinetical characteristics in selected solvents and favorable photochemical properties in an aqueous buffer. These photoactivatable TRPML activators represent useful and valuable tools for TRPML photoaffinity labeling combined with mass spectrometry.

Ionization Energies and Dyson Orbitals of the Iso-electronic SO2, O3, and S3 Molecules from Electron Propagator Calculations

Adiabatic and vertical ionization energies corresponding to the X̃ A12, à B22, and B̃ A22 final states of SO₂⁺, O₃⁺, and S₃⁺ have been calculated with a variety of electron-propagator and coupled-cluster methods. The BD-T1 electron-propagator method for vertical ionization energies and coupled-cluster adiabatic and zero-point corrections yield agreement with experiment to within 0.1 eV in all cases but one. The remaining discrepancies for the à B22 state of SO₂⁺ indicate a need for higher levels of theory in determining cationic minima and their accompanying vibrational frequencies. Predictions for the still unobserved à B22 and B̃ A22 final states of S₃⁺ are included. To account for increased biradical character in O₃ and S₃, highly correlated reference states are required to produce the correct order of final states. Electron correlation plays a subtle role in determining the contours of the Dyson orbitals obtained with BD-T1 and NR2 electron-propagator calculations.

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.

Reactions of Molybdenum and Tungsten Oxide Tetrafluoride with Sulfur(IV) Lewis Bases: Structure and Bonding in [WOF4]4, MOF4(OSO), and [SF3][M2O2F9] (M = Mo, W)

The structure of [WOF₄]₄ has been reinvestigated by low-temperature X-ray crystallography and DFT (MN15/def2-SVPD) studies. Whereas the W₄F₄ ring of the tetramer is planar and disordered in the solid state, the optimized gas-phase geometry prefers a disphenoidally puckered W₄F₄ ring and demonstrates asymmetric fluorine bridging. Dissolution of MOF₄ (M = Mo, W) in SO₂ and SF₄ results in the formation of MOF₄(OSO) and [SF₃][M₂O₂F₉], respectively. Both SO₂ adducts and [SF₃][Mo₂O₂F₉] have been characterized by X-ray crystallography. The crystal structure of [SF₃][Mo₂O₂F₉] reveals dimerization of the ion pair that results in a rare heptacoordinate sulfur center. Optimization of the {[SF₃][M₂O₂F₉]}₂ dimers in the gas phase, however, results in the elongation of one contact such that the sulfur centers are effectively hexacoordinate. Meanwhile, the crystal structure of [SF₃][W₂O₂F₉]·HF instead demonstrates hexacoordinate sulfur centers and a highly unusual coordination to [SF₃]⁺ from [W₂O₂F₉]^- through an oxido ligand. While [SF₃][W₂O₂F₉] does not decompose at ambient temperature, MOF₄(OSO) and [SF₃][Mo₂O₂F₉] are unstable toward evolution of SO₂ or SF₄. Computational studies reveal that the monomerization of [WOF₄]₄ in the gas phase at 25 °C is thermodynamically unfavorable using SO₂, but favorable using SF₄, consistent with the relative thermal stabilities of WOF₄(OSO) and [SF₃][W₂O₂F₉].

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.

X-ray constrained spin-coupled technique: theoretical details and further assessment of the method

One of the well-established methods of modern quantum crystallography is undoubtedly the X-ray constrained wavefunction (XCW) approach, a technique that enables the determination of wavefunctions which not only minimize the energy of the system under examination, but also reproduce experimental X-ray diffraction data within the limit of the experimental errors. Initially proposed in the framework of the Hartree–Fock method, the strategy has been gradually extended to other techniques of quantum chemistry, but always remaining limited to a single-determinant ansatz for the wavefunction to extract. This limitation has been recently overcome through the development of the novel X-ray constrained spin-coupled (XCSC) approach [Genoni et al. (2018). Chem. Eur. J. 24, 15507–15511] which merges the XCW philosophy with the traditional spin-coupled strategy of valence bond theory. The main advantage of this new technique is the possibility of extracting traditional chemical descriptors (e.g. resonance structure weights) compatible with the experimental diffraction measurements, without the need to introduce information a priori or perform analyses a posteriori. This paper provides a detailed theoretical derivation of the fundamental equations at the basis of the XCSC method and also introduces a further advancement of its original version, mainly consisting in the use of molecular orbitals resulting from XCW calculations at the Hartree–Fock level to describe the inactive electrons in the XCSC computations. Furthermore, extensive test calculations, which have been performed by exploiting high-resolution X-ray diffraction data for salicylic acid and by adopting different basis sets, are presented and discussed. The computational tests have shown that the new technique does not suffer from particular convergence problems. Moreover, all the XCSC calculations provided resonance structure weights, spin-coupled orbitals and global electron densities slightly different from those resulting from the corresponding unconstrained computations. These discrepancies can be ascribed to the capability of the novel strategy to capture the information intrinsically contained in the experimental data used as external constraints.

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.

Na+[Me3NB12Cl11]-·SO2: a rare example of a sodium-SO2 complex

In the title compound, Na+[Me3NB12Cl11]-·SO2 [systematic name: sodium 1-(trimethylammonio)-undeca-chloro-closo-dodeca-borate sulfur dioxide], the SO2 mol-ecule is η 1-O-coordinated to the Na+ cation. Surprisingly, the SO2 mol-ecule is more weakly bound to sodium than is found in other sodium-SO2 complexes and the SO2 mol-ecule is essentially undistorted compared to the structure of free SO2. The Na+ cation has a coordination number of eight in a distorted twofold-capped trigonal prism and makes contacts to three individual boron cluster anions, resulting in an overall three-dimensional network. Although the number of known η 1-O-coordinated SO2 complexes is growing, sodium-SO2 complexes are still rare.

DORI Reveals the Influence of Noncovalent Interactions on Covalent Bonding Patterns in Molecular Crystals Under Pressure

The study of organic molecular crystals under high pressure provides fundamental insight into crystal packing distortions and reveals mechanisms of phase transitions and the crystallization of polymorphs. These solid-state transformations can be monitored directly by analyzing electron charge densities that are experimentally obtained at high pressure. However, restricting the analysis to the featureless electron density does not reveal the chemical bonding nature and the existence of intermolecular interactions. This shortcoming can be resolved by the use of the DORI (density overlap region indicator) descriptor, which is capable of simultaneously detecting both covalent patterns and noncovalent interactions from electron density and its derivatives. Using the biscarbonyl[14]annulene crystal under pressure as an example, we demonstrate how DORI can be exploited on experimental electron densities to reveal and monitor changes in electronic structure patterns resulting from molecular compression. A novel approach based on a flood-fill-type algorithm is proposed for analyzing the topology of the DORI isosurface. This approach avoids the arbitrary selection of DORI isovalues and provides an intuitive way to assess how compression packing affects covalent bonding in organic solids.

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.

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Reversible uptake of sulfur-containing gases by single crystals of a 8 metallacrown

The exposure of green crystals of the [CrF(O₂C^tBu)₂]₈Cr₈ metallacrown to SO₂ and H₂S gases results in the binding of the gas molecules in the internal molecular cavity, despite the absence of any pores or channels in the structure.

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.

Aspherical scattering factors for SHELXL - model, implementation and application

A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.

Bond orders for intermolecular interactions in crystals: charge transfer, ionicity and the effect on intramolecular bonds

The question of whether intermolecular interactions in crystals originate from localized atom⋯atom interactions or as a result of holistic molecule⋯molecule close packing is a matter of continuing debate. In this context, the newly introduced Roby-Gould bond indices are reported for intermolecular 'σ-hole' interactions, such as halogen bonding and chalcogen bonding, and compared with those for hydrogen bonds. A series of 97 crystal systems exhibiting these interaction motifs obtained from the Cambridge Structural Database (CSD) has been analysed. In contrast with conventional bond-order estimations, the new method separately estimates the ionic and covalent bond indices for atom⋯atom and molecule⋯molecule bond orders, which shed light on the nature of these interactions. A consistent trend in charge transfer from halogen/chalcogen bond-acceptor to bond-donor groups has been found in these intermolecular interaction regions via Hirshfeld atomic partitioning of the electron populations. These results, along with the 'conservation of bond orders' tested in the interaction regions, establish the significant role of localized atom⋯atom interactions in the formation of these intermolecular binding motifs.

Disulfuryl Dichloride ClSO2 OSO2 Cl: A Conformation and Polymorphism Chameleon

Disulfuryl dichloride ClSO₂ OSO₂ Cl was characterized by vibrational spectroscopy in the gaseous and liquid phase as well as in the Ar-matrix. By varying the temperature, certain bands could be assigned to several conformers. Gas-phase electron diffraction revealed a dominance of the anti-conformer at ambient temperature. The same conformation was found in the solid state. Via the in situ technique for crystallization, not less than four different modifications were identified. Among these different modifications, the structural parameters of the molecules remain relatively constant, but the aggregation pattern changes. Although the molecules aggregate by chlorine⋅⋅⋅oxygen contacts in each modification, the geometrical parameters of these interaction show significant differences and were evaluated and are in part inconsistent with the halogen bonding concept.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

X-ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework

Molecular orbitals were obtained by X-ray molecular orbital analysis (XMO). The initial molecular orbitals (MOs) of the refinement were calculated by the ab initio self-consistent field (SCF) MO method. Well tempered basis functions were selected since they do not produce cusps at the atomic positions on the residual density maps. X-ray structure factors calculated from the MOs were fitted to observed structure factors by the least-squares method, keeping the orthonormal relationship between MOs. However, the MO coefficients correlate severely with each other, since basis functions are composed of similar Gaussian-type orbitals. Therefore, a method of selecting variables which do not correlate severely with each other in the least-squares refinement was devised. MOs were refined together with the other crystallographic parameters, although the refinement with the atomic positional parameters requires a lot of calculation time. The XMO method was applied to diformohydrazide, (NHCHO)₂, without using polarization functions, and the electron-density distributions, including the maxima on the covalent bonds, were represented well. Therefore, from the viewpoint of X-ray diffraction, it is concluded that the MOs averaged by thermal vibrations of the atoms were obtained successfully by XMO analysis. The method of XMO analysis, combined with X-ray atomic orbital (AO) analysis, in principle enables one to obtain MOs or AOs without phase factors from X-ray diffraction experiments on most compounds from organic to rare earth compounds.

Computational investigations of 18-electron triatomic sulfur–nitrogen anions

MRCI-SD/def2-QZVP and PBE0/def2-QZVP calculations have been employed for the analysis of geometries, stabilities, and bonding of isomers of the 18-electron anions N2S2−, NS2−, and NSO−. Isomers of the isoelectronic neutral molecules SO2, S2O, S3, and O3 are included for comparison. The sulfur-centered acyclic NSN2−, NSS−, and NSO− anions are the most stable isomers of their respective molecular compositions. However, the nitrogen-centered isomers SNS− and SNO− lie close enough in energy to their more stable counterparts to allow their occurrence. The experimental structural information, where available, is in good agreement with the optimized bond parameters. The bonding in all investigated species is qualitatively similar, though electron density analyses reveal important quantitative differences that arise from bond polarization. Most of the investigated systems can be described with a single configuration wave function, the two notable exceptions being isomers SSS and OOO that show some diradical character. The computed MRCI-SD/def2-QZVP absorption maxima for SNS− and NSS− are 342 and 327 nm, respectively. The corresponding PBE0/def2-QZVP values in acetonitrile are 353 and 333 nm. These data support the proposed initial formation of SNS− from electrochemical or chemical reduction of SSNS− based on experimental UV–vis spectra. The interconversion of SNS− and NSS− is calculated to be facile and reversible, leading to an equilibrium mixture that also includes the remarkably stable dianion SNSNSS2−. Thus, salts of either SNS− or NSS− with bulky organic cations represent feasible synthetic targets.

Synthesis and Characterization of Stable Phosphorus Carbabetaines

Phosphorus 1,3- and 1,4-carbabetaines with 'P(+)-C-C(-)' and 'P(+)-C-C-C(-)' structures, respectively, in which the carbanion moiety was significantly stabilized by two trifluoromethylsulfonyl groups, have been synthesized and characterized. Analysis of their X-ray crystal structures revealed that any attractive interactions between the anionic and cationic moieties were negligibly weak. This result was corroborated by using natural bond orbital (NBO) and Bader's quantum theory of atoms in molecules (QTAIM) models. In contrast, performing the same analysis of a known 1,3-carbabetaine equivalent, which can be drawn as a 'P(+)-C-C=C-O(-)' resonance structure, revealed pronounced charge-transfer interactions between the anionic and cationic moieties.