A transferable quantum mechanical energy model for intermolecular interactions using a single empirical parameter.

The calculation of intermolecular interactions in molecular crystals using model energies provides a unified route to understanding the complex interplay of driving forces in crystallization, elastic properties and more. Presented here is a new single-parameter interaction energy model (CE-1p), extending the previous CrystalExplorer energy model and calibrated using density functional theory (DFT) calculations at the ωB97M-V/def2-QZVP level over 1157 intermolecular interactions from 147 crystal structures. The new model incorporates an improved treatment of dispersion interactions and polarizabilities using the exchange-hole dipole model (XDM), along with the use of effective core potentials (ECPs), facilitating application to molecules containing elements across the periodic table (from H to Rn). This new model is validated against high-level reference data with outstanding performance, comparable to state-of-the-art DFT methods for molecular crystal lattice energies over the X23 set (mean absolute deviation 3.6 kJ mol-1) and for intermolecular interactions in the S66x8 benchmark set (root mean-square deviation 3.3 kJ mol-1). The performance of this model is further examined compared to the GFN2-xTB tight-binding model, providing recommendations for the evaluation of intermolecular interactions in molecular crystal systems.

Tandem High-Pressure Crystallography-Optical Spectroscopy Unpacks Noncovalent Interactions of Piezochromic Fluorescent Molecular Rotors.

To develop luminescent molecular materials with predictable and stimuli-responsive emission, it is necessary to correlate changes in their geometries, packing structures, and noncovalent interactions with the associated changes in their optical properties. Here, we demonstrate that high-pressure single-crystal X-ray diffraction can be combined with high-pressure UV-visible absorption and fluorescence emission spectroscopies to elucidate how subtle changes in structure influence optical outputs. A piezochromic aggregation-induced emitter, sym-heptaphenylcycloheptatriene (Ph7C7H), displays bathochromic shifts in its absorption and emission spectra at high pressure. Parallel X-ray measurements identify the pressure-induced changes in specific phenyl-phenyl interactions responsible for the piezochromism. Pairs of phenyl rings from neighboring molecules approach the geometry of a stable benzene dimer, while conformational changes alter intramolecular phenyl-phenyl interactions correlated with a relaxed excited state. This tandem crystallographic and spectroscopic analysis provides insights into how subtle structural changes relate to the photophysical properties of Ph7C7H and could be applied to a library of similar compounds to provide general structure-property relationships in fluorescent organic molecules with rotor-like geometries.

Solution-phase decomposition of ferrocene into wüstite-iron oxide core-shell nanoparticles.

We report an improved method for the controlled solvent-phase decomposition of ferrocene into highly crystalline monodisperse iron oxide nanoparticles at relatively low temperatures. Solution-phase decomposition of ferrocene into nanoparticles has received little attention in the literature, due to the percieved stability of ferrocene. However, we synthesised wüstite FeO-iron oxide core-shell nanoparticles by thermally decomposing ferrocene in 1-octadecene solvent and in the presence of oleic acid and oleylamine, as surfactants. We report procedures that provide cubic and spherical core-shell iron oxide nanoparticles whose size (29.3 ± 2.3 nm for spheres, 38.6 ± 6.9 nm for distorted cubes and 23.5 ± 2.4 nm for distorted cubes with concave faces) and shape can be controlled through simple adjustments to reaction parameters. Transmission electron microscopy, scanning transmission electron microscopy, energy dispersive X-ray spectroscopy, electron energy-loss spectroscopy and powder X-ray diffraction analysis methods were used to characterise the nanoparticles.

Global Analysis of the Mechanical Properties of Organic Crystals.

Organic crystals, although widely studied, have not been considered nascent candidate materials in engineering design. Here we summarize the mechanical properties of organic crystals that have been reported over the past three decades, and we establish a global mechanical property profile that can be used to predict and identify mechanically robust organic crystals. Being composed of light elements, organic crystals populate a narrow region in the mechanical property-density space between soft, disordered organic materials and stiff, ordered materials. Two subsets of extraordinarily stiff and hard organic crystalline materials were identified and rationalized by the normalized number density, strength, and directionality of their intermolecular interactions. We conclude that future lightweight, soft, all-organic components in devices should capitalize on the greatest asset of organic single crystals-namely, the combination of long-range structural order and softness.

Quantifying Mechanical Properties of Molecular Crystals: A Critical Overview of Experimental Elastic Tensors.

This review presents a critical and comprehensive overview of current experimental measurements of complete elastic constant tensors for molecular crystals. For a large fraction of these molecular crystals, detailed comparisons are made with elastic tensors obtained using the corrected small basis set Hartree-Fock method S-HF-3c, and these are shown to be competitive with many of those obtained from more sophisticated density functional theory plus dispersion (DFT-D) approaches. These detailed comparisons between S-HF-3c, experimental and DFT-D computed tensors make use of a novel rotation-invariant spherical harmonic description of the Young's modulus, and identify outliers among sets of independent experimental results. The result is a curated database of experimental elastic tensors for molecular crystals, which we hope will stimulate more extensive use of elastic tensor information-experimental and computational-in studies aimed at correlating mechanical properties of molecular crystals with their underlying crystal structure.

CrystalExplorer: a program for Hirshfeld surface analysis, visualization and quantitative analysis of molecular crystals.

CrystalExplorer is a native cross-platform program supported on Windows, MacOS and Linux with the primary function of visualization and investigation of molecular crystal structures, especially through the decorated Hirshfeld surface and its corresponding two-dimensional fingerprint, and through the visualization of void spaces in the crystal via isosurfaces of the promolecule electron density. Over the past decade, significant changes and enhancements have been incorporated into the program, such as the capacity to accurately and quickly calculate and visualize quantitative intermolecular interactions and, perhaps most importantly, the ability to interface with the Gaussian and NWChem programs to calculate quantum-mechanical properties of molecules. The current version, CrystalExplorer21, incorporates these and other changes, and the software can be downloaded and used free of charge for academic research.

Bridging Crystal Engineering and Drug Discovery by Utilizing Intermolecular Interactions and Molecular Shapes in Crystals.

Most structure-based drug discovery methods utilize crystal structures of receptor proteins. Crystal engineering, on the other hand, utilizes the wealth of chemical information inherent in small-molecule crystal structures in the Cambridge Structural Database (CSD). We show that the interaction surfaces and shapes of molecules in experimentally determined small-molecule crystal structures can serve as effective tools in drug discovery. Our description of the shape and interaction propensities of molecules in their crystal structures can be used to screen them for specific binding compatibility with protein targets, as demonstrated through the high-throughput profiling of around 138 000 small-molecule structures in the CSD and a series of drug-protein crystal structures. Electron-density-based intermolecular boundary surfaces in small-molecule crystal structures and in target-protein pockets are utilized to identify potential ligand molecules from the CSD based on 3D shape and intermolecular interaction matching.

Investigation of an Unusual Crystal Habit of Hydrochlorothiazide Reveals Large Polar Enantiopure Domains and a Possible Crystal Nucleation Mechanism.

The observation of an unusual crystal habit in the common diuretic drug hydrochlorothiazide (HCT), and identification of its subtle conformational chirality, has stimulated a detailed investigation of its crystalline forms. Enantiomeric conformers of HCT resolve into an unusual structure of conjoined enantiomorphic twin crystals comprising enantiopure domains of opposite chirality. The purity of the domains and the chiral molecular conformation are confirmed by spatially revolved synchrotron micro-XRD experiments and neutron diffraction, respectively. Macroscopic inversion twin symmetry observed between the crystal wings suggests a pseudoracemic structure that is not a solid solution or a layered crystal structure, but an unusual structural variant of conglomerates and racemic twins. Computed interaction energies for molecular pairs in the racemic and enantiopure polymorphs of HCT, and the observation of large opposing unit-cell dipole moments for the enantiopure domains in these twin crystals, suggest a plausible crystal nucleation mechanism for this unusual crystal habit.

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.

Measurement of Electric Fields Experienced by Urea Guest Molecules in the 18-Crown-6/Urea (1:5) Host-Guest Complex: An Experimental Reference Point for Electric-Field-Assisted Catalysis.

High-resolution synchrotron and neutron single-crystal diffraction data of 18-crown-6/(pentakis)urea measured at 30 K are combined, with the aim of better appreciating the electrostatics associated with intermolecular interactions in condensed matter. With two 18-crown-6 molecules and five different urea molecules in the crystal, this represents the most ambitious combined X-ray/synchrotron and neutron experimental charge density analysis to date on a cocrystal or host-guest system incorporating such a large number of unique molecules. The dipole moments of the five urea guest molecules in the crystal are enhanced considerably compared to values determined for isolated molecules, and 2D maps of the electrostatic potential and electric field show clearly how the urea molecules are oriented with dipole moments aligned along the electric field exerted by their molecular neighbors. Experimental electric fields in the range of 10-19 GV m-1, obtained for the five different urea environments, corroborate independent measurements of electric fields in the active sites of enzymes and provide an important experimental reference point for recent discussions focused on electric-field-assisted catalysis.

Accurate Lattice Energies for Molecular Crystals from Experimental Crystal Structures.

Using four different benchmark sets of molecular crystals, we establish the level of confidence for lattice energies estimated using CE-B3LYP model energies and experimental crystal structures. [ IUCrJ 2017 , 4 , 575 - 587 10.1107/S205225251700848X .] We conclude that they compare very well with available benchmark estimates derived from sublimation enthalpies, and in many cases they are comparable with, and sometimes better than, more computationally demanding approaches, such as those based on periodic DFT plus dispersion methodologies. The performance over the complete set of 110 crystals indicates a mean absolute deviation from benchmark energies of only 6.6 kJ mol-1. Applications to polymorphic crystals and larger molecules are also presented and critically discussed. The results highlight the importance of recognizing the consequences of different sets of crystal/molecule geometries when different methodologies are compared, as well as the need for more extensive benchmark sets of crystal structures and associated lattice energies.

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

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

Intermolecular interactions in molecular crystals: what's in a name?

Structure-property relationships are the key to modern crystal engineering, and for molecular crystals this requires both a thorough understanding of intermolecular interactions, and the subsequent use of this to create solids with desired properties. There has been a rapid increase in publications aimed at furthering this understanding, especially the importance of non-canonical interactions such as halogen, chalcogen, pnicogen, and tetrel bonds. Here we show how all of these interactions - and hydrogen bonds - can be readily understood through their common origin in the redistribution of electron density that results from chemical bonding. This redistribution is directly linked to the molecular electrostatic potential, to qualitative concepts such as electrostatic complementarity, and to the calculation of quantitative intermolecular interaction energies. Visualization of these energies, along with their electrostatic and dispersion components, sheds light on the architecture of molecular crystals, in turn providing a link to actual crystal properties.

The Elusive Structural Origin of Plastic Bending in Dimethyl Sulfone Crystals with Quasi-isotropic Crystal Packing.

Bending in molecular crystals is typically associated with the anisotropy of intermolecular interactions. The intriguing observation is reported of plastic bending in dimethyl sulfone, which exhibits nearly isotropic crystal packing and interaction topology, defying the known structural models of bending crystals. The origin of the bending phenomenon has been explored in terms of intermolecular interaction energies, experimental X-ray charge density analysis, and variable temperature neutron diffraction studies. H⋅⋅⋅H dihydrogen interactions and differences in electrostatic complementarity between molecular layers are found to facilitate the bending behavior.

Magnetically recoverable Fe3O4@Au-coated nanoscale catalysts for the A3-coupling reaction.

The utility of novel Fe3O4@Au nanoparticles as magnetically separable and recyclable heterogeneous catalysts for the A3-coupling reaction of aldehydes, amines and terminal alkynes to yield the corresponding propargylamines is demonstrated. Herein we present a comprehensive analysis of the experimentally observed trends in the conversions with computational analysis using LUMO density on molecular isosurfaces and the electrostatic potential (ESP) effects estimated using DFT calculations.

Energy frameworks and a topological analysis of the supramolecular features in in situ cryocrystallized liquids: tuning the weak interaction landscape via fluorination.

Weak intermolecular interactions observed in crystalline materials are often influenced or forced by stronger interactions such as classical hydrogen bonds. Room temperature liquids offer a scenario where such strong interactions are absent so that the role and nature of the weak interactions can be studied more reliably. In this context, we have analyzed the common organic reagent benzoyl chloride (BC) and a series of its fluorinated derivatives using in situ cryocrystallography. The intermolecular interaction energies have been estimated and their topologies explored using energy framework analysis in a series of ten benzoyl chloride analogues, which reveal that the ππ stacking interactions serve as the primary building blocks in these crystal structures. The crystal packing is also stabilized by a variety of interaction motifs involving weak C-HO/F/Cl hydrogen bonds and FF, FCl, and ClCl interactions. It is found that fluorination alters the electrostatic nature of the benzoyl chlorides, with subsequent changes in the formation of different weak interaction motifs. The effects of fluorination on these weak intermolecular interactions have been systematically analyzed further via detailed inputs from a topological analysis of the electron density and Hirshfeld surface analysis.

Structural Collapse of the Hydroquinone-Formic Acid Clathrate: A Pressure-Medium-Dependent Phase Transition.

The energy landscape governing a new pressure-induced phase transition in the hydroquinone-formic acid clathrate is reported in which the host structure collapses, opening up the cavity channels within which the guest molecules migrate and order. The reversible isosymmetric phase transition causes significant changes in the morphology and the birefringence of the crystal. The subtle intermolecular interaction energies in the clathrate are quantified at varying pressures using novel model energies and energy frameworks. These calculations show that the high-pressure phase forms a more stable host network at the expense of less-stable host-guest interactions. The phase transition can be kinetically hindered using a nonhydrostatic pressure-transmitting medium, enabling the comparison of intermolecular energies in two polymorphic structures in the same pressure range. Overall this study illustrates a need for accurate intermolecular energies when analyzing self-assembly structures and supramolecular aggregates.

'Quasi-isostructural polymorphism' in molecular crystals: inputs from interaction hierarchy and energy frameworks.

The polymorphs of (Z)-2-fluoro-N'-phenyl benzamidamide with multiple Z' produce quasi-isostructural supramolecular architectures, wherein C-H···F interaction plays a significant role. The energy framework analysis indicates 2D structural similarities in the interaction topologies of these crystalline forms. The results point to a unique class of 'quasi-isostructural polymorphs' which are nearly equi-energetic crystal structures exhibiting high degrees of similarity in physical properties.