A solid solution to computational challenges presented by crystal structures exhibiting disorder.

Crystal structues exhibiting disorder still present a barrier for many computational methods. Dittrich et al. [(2024). IUCrJ, 11, 347-358] showcase a unified approach, tackling solid solutions, near symmetry and more.

Functionalised organometallic photoswitches containing dihydropyrene units.

Functionalising organic molecular photoswitches with metal complexes has been shown to alter and enhance their switching states. These organometallic photoswitches provide a promising basis for novel smart molecular materials and molecular electronic devices. We have detailed the synthesis and characterisation of mono- and bimetallic half-sandwich ruthenium and iron complexes functionalised with alkynyl dihydropyrenes (DHP). Their electronic and photophysical properties were determined by the use of chemical, electrochemical and spectroelectrochemical techniques. The introduction of the metal alkynyl moiety allows access to additional redox and protonation states not accessible by the DHP alone. An additional metal alkynyl moiety inhibits observable photochromic switching. Analysis of the NIR and IR bands in the mixed valence complexes suggests there is a high degree of charge delocalisation across the DHP.

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.

Multistate Switching of Some Ruthenium Alkynyl and Vinyl Spiropyran Complexes.

To study the switching properties of photochromes, we undertook the synthesis and characterization of several ruthenium organometallic complexes of the type [Ru(Cp*)(dppe)(C≡C-SP)] or [Ru(CO)(dppe)(PPh3)Cl(CH═CH-SP)], where SP = spiropyran. The spectroscopic and electrochemical properties of the complexes were determined by careful cyclic voltammetric and spectroelectrochemical experiments. Whereas the mononuclear alkynyl ruthenium complexes undergo one-electron oxidations localized over the metal alkynyl moiety, the oxidation of the mononuclear vinyl ruthenium complexes is centered on the indoline moiety of the spiropyran. Through these studies, we demonstrate access to several stable redox states, in addition to switching states attained via acidochromism and/or photoisomerization.

CrystalClear: an open, modular protocol for predicting molecular crystal growth from solution.

We present a new protocol for the prediction of free energies that determine the growth of sites in molecular crystals for subsequent use in Monte Carlo simulations using tools such as CrystalGrower [Hill et al., Chemical Science, 2021, 12, 1126-1146]. Key features of the proposed approach are that it requires minimal input, namely the crystal structure and solvent only, and provides automated, rapid generation of the interaction energies. The constituent components of this protocol, namely interactions between molecules (growth units) in the crystal, solvation contributions and treatment of long-range interactions are described in detail. The power of this method is shown via prediction of crystal shapes for ibuprofen grown from ethanol, ethyl acetate, toluene and acetonitrile, adipic acid grown from water, and five polymorphs (ON, OP, Y, YT04 and R) of ROY (5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile), with promising results. The predicted energies may be used directly or subsequently refined against experimental data, facilitating insight into the interactions governing crystal growth, while also providing a prediction of the solubility of the material. The protocol has been implemented in standalone, open-source software made available alongside this publication.

Targeted design of porous materials without strong, directional interactions.

A porous molecular crystal (TSCl) was found to crystallise from dichloromethane and water during the synthesis of tetrakis(4-sulfophenylmethane). Crystal structure prediction (CSP) rationalises the driving force behind the formation of this porous TSCl phase and the intermolecular interactions that direct its formation. Gas sorption analysis showed that TSCl is permanently porous with selective adsorption of CO2 over N2, H2 and CH4 and a maximum CO2 uptake of 74 cm3 g-1 at 195 K. Calculations revealed that TSCl assembles via a combination of weak hydrogen bonds and strong dispersion interactions. This illustrates that CSP can underpin approaches to crystal engineering that do not involve more intuitive directional interactions, such as hydrogen bonding.

2,7- and 4,9-Dialkynyldihydropyrene Molecular Switches: Syntheses, Properties, and Charge Transport in Single-Molecule Junctions.

This paper describes the syntheses of several functionalized dihydropyrene (DHP) molecular switches with different substitution patterns. Regioselective nucleophilic alkylation of a 5-substituted dimethyl isophthalate allowed the development of a workable synthetic protocol for the preparation of 2,7-alkyne-functionalized DHPs. Synthesis of DHPs with surface-anchoring groups in the 2,7- and 4,9-positions is described. The molecular structures of several intermediates and DHPs were elucidated by X-ray single-crystal diffraction. Molecular properties and switching capabilities of both types of DHPs were assessed by light irradiation experiments, spectroelectrochemistry, and cyclic voltammetry. Spectroelectrochemistry, in combination with density functional theory (DFT) calculations, shows reversible electrochemical switching from the DHP forms to the cyclophanediene (CPD) forms. Charge-transport behavior was assessed in single-molecule scanning tunneling microscope (STM) break junctions, combined with density functional theory-based quantum transport calculations. All DHPs with surface-contacting groups form stable molecular junctions. Experiments show that the molecular conductance depends on the substitution pattern of the DHP motif. The conductance was found to decrease with increasing applied bias.

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.

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.

A Universal Force Field for Materials, Periodic GFN-FF: Implementation and Examination.

In this study, the adaption of the recently published molecular GFN-FF for periodic boundary conditions (pGFN-FF) is described through the use of neighbor lists combined with appropriate charge sums to handle any dimensionality from 1D polymers to 2D surfaces and 3D solids. Numerical integration over the Brillouin zone for the calculation of π bond orders of periodic fragments is also included. Aside from adapting the GFN-FF method to handle periodicity, improvements to the method are proposed in regard to the calculation of topological charges through the inclusion of a screened Coulomb term that leads to more physical charges and avoids a number of pathological cases. Short-range damping of three-body dispersion is also included to avoid collapse of some structures. Analytic second derivatives are also formulated with respect to both Cartesian and strain variables, including prescreening of terms to accelerate the dispersion/coordination number contribution to the Hessian. The modified pGFN-FF scheme is then applied to a wide range of different materials in order to examine how well this universal model performs.

Evaluation of density functional theory for a large and diverse set of organic and inorganic equilibrium structures.

Density functional theory (DFT) has been extensively benchmarked for energetic properties; however, less attention has been given to equilibrium structures and the effect of using a certain DFT geometry on subsequent energetic properties. We evaluate the performance of 52 contemporary DFT methods for obtaining the structures of 122 species in the W4-11-GEOM database. This dataset includes a total of 246 unique bonds: 117 H─X, 65 X─Y, 49 X═Y, and 15 XY bonds (where X and Y are first- and second-row atoms) and 133 key bond angles: 96 X-Y-H, 22 X-Y-Z, and 15 H-X-H angles. The reference geometries are optimized at the CCSD(T)/jul-cc-pV(n+d)Z level of theory (n = 5, 6). The performance of DFT is evaluated in conjunction with the Def2-nZVPP (n = T, Q), cc-pV(T+d)Z, and jul-cc-pV(T+d)Z basis sets. The root-mean-square deviations (RMSDs) over the bond distances of the best performing functionals from each rung of Jacob's Ladder are 0.0086 (SOGGA11), 0.0088 (τ-HCTH), 0.0059 (B3LYP), 0.0054 (TPSSh), and 0.0032 (DSD-PBEP86) Å. We evaluate the effect of the choice of the DFT geometry on subsequent molecular energies calculated with W1-F12 theory. Geometries obtained with GGA and MGGA methods result in large RMSDs in the subsequent W1-F12 energies; however, six hybrid GGA functionals (B3LYP, B3P86, mPW3PBE, B3PW91, mPW1LYP, and X3LYP) result in an excellent performance with RMSDs between 0.25 and 0.30 kJ mol-1 relative to the CCSD(T)/CBS reference geometries. The B2GP-PLYP and mPW2-PLYP DHDFT methods result in near-CCSD(T) accuracy with RMSDs of 0.11 and 0.10 kJ mol-1 , respectively.

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.

An Expandable Hydrogen-Bonded Organic Framework Characterized by Three-Dimensional Electron Diffraction.

A molecular crystal of a 2-D hydrogen-bonded organic framework (HOF) undergoes an unusual structural transformation after solvent removal from the crystal pores during activation. The conformationally flexible host molecule, ABTPA, adapts its molecular conformation during activation to initiate a framework expansion. The microcrystalline activated phase was characterized by three-dimensional electron diffraction (3D ED), which revealed that ABTPA uses out-of-plane anthracene units as adaptive structural anchors. These units change orientation to generate an expanded, lower density framework material in the activated structure. The porous HOF, ABTPA-2, has robust dynamic porosity (SABET = 1183 m2 g-1) and exhibits negative area thermal expansion. We use crystal structure prediction (CSP) to understand the underlying energetics behind the structural transformation and discuss the challenges facing CSP for such flexible molecules.

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.

Mining predicted crystal structure landscapes with high throughput crystallisation: old molecules, new insights.

Organic molecules tend to close pack to form dense structures when they are crystallised from organic solvents. Porous molecular crystals defy this rule: they contain open space, which is typically stabilised by inclusion of solvent in the interconnected pores during crystallisation. The design and discovery of such structures is often challenging and time consuming, in part because it is difficult to predict solvent effects on crystal form stability. Here, we combine crystal structure prediction (CSP) with a robotic crystallisation screen to accelerate the discovery of stable hydrogen-bonded frameworks. We exemplify this strategy by finding new phases of two well-studied molecules in a computationally targeted way. Specifically, we find a new 'hidden' porous polymorph of trimesic acid, δ-TMA, that has a guest-free hexagonal pore structure, as well as three new solvent-stabilized diamondoid frameworks of adamantane-1,3,5,7-tetracarboxylic acid (ADTA). Beyond porous solids, this hybrid computational-experimental approach could be applied to a wide range of materials problems, such as organic electronics and drug formulation.

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.

Basis set convergence of CCSD(T) equilibrium geometries using a large and diverse set of molecular structures.

We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D) and 0.0006 (T) Å. Overall, the CCSD(T)-F12/cc-pVDZ-F12 level of theory offers a stellar price-performance ratio and we recommend using it when highly accurate reference geometries are needed (e.g., in composite ab initio theories such as W4 and HEAT).

High Throughput Profiling of Molecular Shapes in Crystals.

Molecular shape is important in both crystallisation and supramolecular assembly, yet its role is not completely understood. We present a computationally efficient scheme to describe and classify the molecular shapes in crystals. The method involves rotation invariant description of Hirshfeld surfaces in terms of of spherical harmonic functions. Hirshfeld surfaces represent the boundaries of a molecule in the crystalline environment, and are widely used to visualise and interpret crystalline interactions. The spherical harmonic description of molecular shapes are compared and classified by means of principal component analysis and cluster analysis. When applied to a series of metals, the method results in a clear classification based on their lattice type. When applied to around 300 crystal structures comprising of series of substituted benzenes, naphthalenes and phenylbenzamide it shows the capacity to classify structures based on chemical scaffolds, chemical isosterism, and conformational similarity. The computational efficiency of the method is demonstrated with an application to over 14 thousand crystal structures. High throughput screening of molecular shapes and interaction surfaces in the Cambridge Structural Database (CSD) using this method has direct applications in drug discovery, supramolecular chemistry and materials design.