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 the engineering design. Here we summarize the reported mechanical properties of organic crystals 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 the future light-weight, soft, all-organic components in devices should capitalize on the combination of long-range structural order and softness as the greatest asset of organic single crystals.

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.

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.

Intermolecular interactions in crystals of small unsubstituted cyclic ethers and substituted epoxides

CE-B3LYP model energies are used to investigate intermolecular interactions in crystals of the relatively weakly bound cyclic ethers, as well as a number of substituted epoxides that have been the focus of high-quality experimental electron density studies. This approach readily provides a complete picture of all intermolecular interactions in these molecular crystals, and CE-B3LYP lattice energies for the unsubstituted cyclic ethers are in excellent agreement with available thermodynamic data. When compared with the outcomes of multipole modelling of X-ray diffraction data, these results suggest that experimental interaction energies are typically underestimated and, contrarily, experimental lattice energies are typically overestimated. These observations deserve careful investigation.

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.

Tetraiodoallene, I2C=C=CI2 – the missing link between I2C=CI2 and I2C=C=C=CI2 – and the oxidation product, 2,2-diiodoacrylicacid, I2C=CH(CO2H)

The X-ray structure of tetraiodoallene is reported. On standing, atmospheric hydrolysis converts this compound into 2,2-diiodoacrylic acid, for which a structure has also been determined. Energy framework diagrams have been constructed for the two compounds.

The Polymorphs of ROY: A Computational Study of Lattice Energies and Conformational Energy Differences

The remarkable structural diversity observed in polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (commonly known as ROY) challenges computational attempts to predict or rationalize their relative stability. This modest study explores the applicability of CE-B3LYP model energy calculation of lattice energies (using experimental crystal structures), supplemented by a systematic approach to account for conformational energy differences. The CE-B3LYP model provides sensible estimates of absolute and relative lattice energies for the polymorphs, provided care is taken to achieve convergence in the summation of pairwise terms. Conformational energy differences based on density functional theory (DFT) energies are shown to be unreliable, but MP2 energies based on DFT-optimized structures show considerable promise.

Towards the use of experimental electron densities to estimate reliable lattice energies

Lattice energies derived from experimental charge densities are critically assessed, with a view to encouraging further research of this nature.

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.

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

Magnetically recoverable and recyclable Fe₃O₄@Au nanocatalysts for A³-coupling reactions.

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.

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′ form “equi-energetic” crystal structures and exhibit “quasi-isostructurality”.

Energy frameworks: insights into interaction anisotropy and the mechanical properties of molecular crystals

We present an approach to understanding crystal packing via 'energy frameworks', that combines efficient calculation of accurate intermolecular interaction energies with a novel graphical representation of their magnitude. In this manner intriguing questions, such as why some crystals bend with an applied force while others break, and why one polymorph of a drug exhibits exceptional tabletability compared to others, can be addressed in terms of the anisotropy of the topology of pairwise intermolecular interaction energies. This approach is applied to a sample of organic molecular crystals with known bending, shearing and brittle behaviour, to illustrate its use in rationalising their mechanical behaviour at a molecular level.

Electrostatic complementarity in pseudoreceptor modeling based on drug molecule crystal structures: the case of loxistatin acid (E64c)

A combination of pseudoreceptor modeling and electrostatic complementarity maps properties of a native pocket for an enzyme ligand.

Accurate and Efficient Model Energies for Exploring Intermolecular Interactions in Molecular Crystals

The energy of interaction between molecules is commonly expressed in terms of four key components: electrostatic, polarization, dispersion, and exchange-repulsion. Using monomer wave functions to obtain accurate estimates of electrostatic, polarization, and repulsion energies along with Grimme's dispersion corrections, a series of energy models are derived by fitting to dispersion-corrected DFT energies for a large number of molecular pairs extracted from organic and inorganic molecular crystals. The best performing model reproduces B3LYP-D2/6-31G(d,p) counterpoise-corrected energies with a mean absolute deviation (MAD) of just over 1 kJ mol(-1) but in considerably less computation time. It also performs surprisingly well against benchmark CCSD(T)/CBS energies, with a MAD of 2.5 kJ mol(-1) for a combined data set including Hobza's X40, S22, A24, and S66 dimers. Two of these energy models, the most accurate and the fastest, are expected to find widespread application in investigations of molecular crystals.

Hirshfeld atom refinement for modelling strong hydrogen bonds

High-resolution low-temperature synchrotron X-ray diffraction data of the salt L-phenylalaninium hydrogen maleate are used to test the new automated iterative Hirshfeld atom refinement (HAR) procedure for the modelling of strong hydrogen bonds. The HAR models used present the first examples of Z' > 1 treatments in the framework of wavefunction-based refinement methods. L-Phenylalaninium hydrogen maleate exhibits several hydrogen bonds in its crystal structure, of which the shortest and the most challenging to model is the O-H...O intramolecular hydrogen bond present in the hydrogen maleate anion (O...O distance is about 2.41 Å). In particular, the reconstruction of the electron density in the hydrogen maleate moiety and the determination of hydrogen-atom properties [positions, bond distances and anisotropic displacement parameters (ADPs)] are the focus of the study. For comparison to the HAR results, different spherical (independent atom model, IAM) and aspherical (free multipole model, MM; transferable aspherical atom model, TAAM) X-ray refinement techniques as well as results from a low-temperature neutron-diffraction experiment are employed. Hydrogen-atom ADPs are furthermore compared to those derived from a TLS/rigid-body (SHADE) treatment of the X-ray structures. The reference neutron-diffraction experiment reveals a truly symmetric hydrogen bond in the hydrogen maleate anion. Only with HAR is it possible to freely refine hydrogen-atom positions and ADPs from the X-ray data, which leads to the best electron-density model and the closest agreement with the structural parameters derived from the neutron-diffraction experiment, e.g. the symmetric hydrogen position can be reproduced. The multipole-based refinement techniques (MM and TAAM) yield slightly asymmetric positions, whereas the IAM yields a significantly asymmetric position.

Host perturbation in a β-hydroquinone clathrate studied by combined X-ray/neutron charge-density analysis: implications for molecular inclusion in supramolecular entities

X-ray/neutron (X/N) diffraction data measured at very low temperature (15 K) in conjunction with ab initio theoretical calculations were used to model the crystal charge density (CD) of the host-guest complex of hydroquinone (HQ) and acetonitrile. Due to pseudosymmetry, information about the ordering of the acetonitrile molecules within the HQ cavities is present only in almost extinct, very weak diffraction data, which cannot be measured with sufficient accuracy even by using the brightest X-ray and neutron sources available, and the CD model of the guest molecule was ultimately based on theoretical calculations. On the other hand, the CD of the HQ host structure is well determined by the experimental data. The neutron diffraction data provide hydrogen anisotropic thermal parameters and positions, which are important to obtain a reliable CD for this light-atom-only crystal. Atomic displacement parameters obtained independently from the X-ray and neutron diffraction data show excellent agreement with a |ΔU| value of 0.00058 Å(2) indicating outstanding data quality. The CD and especially the derived electrostatic properties clearly reveal increased polarization of the HQ molecules in the host-guest complex compared with the HQ molecules in the empty HQ apohost crystal structure. It was found that the origin of the increased polarization is inclusion of the acetonitrile molecule, whereas the change in geometry of the HQ host structure following inclusion of the guest has very little effect on the electrostatic potential. The fact that guest inclusion has a profound effect on the electrostatic potential suggests that nonpolarizable force fields may be unsuitable for molecular dynamics simulations of host-guest interaction (e.g., in protein-drug complexes), at least for polar molecules.

Simulations of guest transport in clathrates of Dianin's compound and hydroquinone

Clathrates have been proposed for use in a variety of applications including gas storage, mixture separation and catalysis due to the potential for controlled guest diffusion through their porous lattices. Here molecular dynamics simulations are employed to study guest transport in clathrates of hydroquinone (HQ) and Dianin's compound (DC). Systems investigated were HQ with methanol and acetonitrile, and DC with methanol and ethanol. Simulations were set up with one guest in the pore, two guests in the pore and one vacancy in the pore and a filled pore, and free-energy barriers for movement between cavities of the pore were estimated for all cases. Comparison between these simulations indicates that guest transport most likely proceeds by molecules moving from full to empty cavities consecutively, one by one, rather than in a concerted manner. Thus, the presence of empty cavities is very important for guest transport, which becomes more energetically demanding in fully loaded systems. Flexibility of the host can assist guest transport. In the studied DC clathrates transport occurs via an intermediate conformation in which the hydroxyl group of the alcohol guest molecule participates in the hydrogen-bonded ring of the host. We also address the issue of the number of methanol guest molecules that DC accommodates, for which conflicting information exists. We found that this is likely to be temperature dependent and suggest that under some conditions the system is most likely non-stoichiometric.