Charge density analysis for crystal engineering

Influence of N-protonation on electronic properties of acridine derivatives by quantum crystallography

Applications of 9-aminoacridine (9aa) and its derivatives span fields such as chemistry, biology, and medicine, including anticancer and antimicrobial activities. Protonation of such molecules can alter their bioavailability as weakly basic drugs like aminoacridines exhibit reduced solubility at high pH levels potentially limiting their effectiveness in patients with elevated gastric pH. In this study, we analyse the influence of protonation on the electronic characteristics of the molecular organic crystals of 9-aminoacridine. The application of quantum crystallography, including aspherical atom refinement, has enriched the depiction of electron density in the studied systems and non-covalent interactions, providing more details than previous studies. Our experimental results, combined with a topological analysis of the electron density and its Laplacian, provided detailed descriptions of how protonation changes the electron density distribution around the amine group and water molecule, concurrently decreasing the electron density at bond critical points of N/O-H bonds. Protonation also alters the molecular architecture of the systems under investigation. This is reflected in different proportions of the N⋯H and O⋯H intermolecular contacts for the neutral and protonated forms. Periodic DFT calculations of the cohesive energies of the crystal lattice, as well as computed interaction energies between molecules in the crystal, confirm that protonation stabilises the crystal structure due to a positive synergy between strong halogen and hydrogen bonds. Our findings highlight the potential of quantum crystallography in predicting crystal structure properties and point to its possible applications in developing new formulations for poorly soluble drugs.

Noncovalent bonding assessment by pair distribution function

Noncovalent interactions are essential in the formation and properties of a diverse range of materials. However, reliably identifying noncovalent interactions remains challenging using conventional methods such as X-ray diffraction, especially in nanocrystalline, poorly crystalline or amorphous materials which lack long-range lattice periodicity. Here, we demonstrate the accurate determination of deviations in the local structure and tilting of aromatic rings during the temperature-induced first order structural transition in the 1 : 1 adduct of 4,4'-bipyridinium squarate (BIPY:SQA) from the low temperature form HAZFAP01 to high temperature HAZFAP07 by X-ray pair distribution function. This work demonstrates how pair distribution function analyses can improve our understanding of local structural deviations resulting from noncovalent bonds and guide the development of novel functional materials.

The Relevance of Experimental Charge Density Analysis in Unraveling Noncovalent Interactions in Molecular Crystals

The work carried out by our research group over the last couple of decades in the context of quantitative crystal engineering involves the analysis of intermolecular interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding using experimental charge density methodology is reviewed. The focus is to extract electron density distribution in the intermolecular space and to obtain guidelines to evaluate the strength and directionality of such interactions towards the design of molecular crystals with desired properties. Following the early studies on halogen bonding interactions, several "sigma-hole" interaction types with similar electrostatic origins have been explored in recent times for their strength, origin, and structural consequences. These include interactions such as carbon (tetrel) bonding, pnicogen bonding, chalcogen bonding, and halogen bonding. Experimental X-ray charge density analysis has proved to be a powerful tool in unraveling the strength and electronic origin of such interactions, providing insights beyond the theoretical estimates from gas-phase molecular dimer calculations. In this mini-review, we outline some selected contributions from the X-ray charge density studies to the field of non-covalent interactions (NCIs) involving elements of the groups 14-17 of the periodic table. Quantitative insights into the nature of these interactions obtained from the experimental electron density distribution and subsequent topological analysis by the quantum theory of atoms in molecules (QTAIM) have been discussed. A few notable examples of weak interactions have been presented in terms of their experimental charge density features. These examples reveal not only the strength and beauty of X-ray charge density multipole modeling as an advanced structural chemistry tool but also its utility in providing experimental benchmarks for the theoretical studies of weak interactions in crystals.

Large scale dataset of real space electronic charge density of cubic inorganic materials from density functional theory (DFT) calculations

Driven by the big data science, material informatics has attracted enormous research interests recently along with many recognized achievements. To acquire knowledge of materials by previous experience, both feature descriptors and databases are essential for training machine learning (ML) models with high accuracy. In this regard, the electronic charge density ρ(r), which in principle determines the properties of materials at their ground state, can be considered as one of the most appropriate descriptors. However, the systematic electronic charge density ρ(r) database of inorganic materials is still in its infancy due to the difficulties in collecting raw data in experiment and the expensive first-principles based computational cost in theory. Herein, a real space electronic charge density ρ(r) database of 17,418 cubic inorganic materials is constructed by performing high-throughput density functional theory calculations. The displayed ρ(r) patterns show good agreements with those reported in previous studies, which validates our computations. Further statistical analysis reveals that it possesses abundant and diverse data, which could accelerate ρ(r) related machine learning studies. Moreover, the electronic charge density database will also assists chemical bonding identifications and promotes new crystal discovery in experiments.

Measurement(s)	electronic charge density
Technology Type(s)	computational methods
Factor Type(s)	inorganic material

Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.17694158

A quantum crystallographic approach to short hydrogen bonds

In this work we use high-resolution synchrotron X-ray diffraction for electron density mapping, in conjunction with ab initio modelling, to study short O-H⋯O and O+-H⋯O- hydrogen bonds whose behaviour is known to be tuneable by temperature. The short hydrogen bonds have donor-acceptor distances in the region of 2.45 Å and are formed in substituted urea and organic acid molecular complexes of N,N'-dimethylurea oxalic acid 2 : 1 (1), N,N-dimethylurea 2,4-dinitrobenzoate 1 : 1 (2) and N,N-dimethylurea 3,5-dinitrobenzoic acid 2 : 2 (3). From the combined analyses, these complexes are found to fall within the salt-cocrystal continuum and exhibit short hydrogen bonds that can be characterised as both strong and electrostatic (1, 3) or very strong with a significant covalent contribution (2). An additional charge assisted component is found to be important in distinguishing the relatively uncommon O-H⋯O pseudo-covalent interaction from a typical strong hydrogen bond. The electron density is found to be sensitive to the extent of static proton transfer, presenting it as a useful parameter in the study of the salt-cocrystal continuum. From complementary calculated hydrogen atom potentials, we attribute changes in proton position to the molecular environment. Calculated potentials also show zero barrier to proton migration, forming an 'energy slide' between the donor and acceptor atoms. The better fundamental understanding of the short hydrogen bond in the 'zone of fluctuation' presented in a salt-cocrystal continuum, enabled by studies like this, provide greater insight into their related properties and can have implications in the regulation of pharmaceutical materials.

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

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

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π⋅⋅⋅π and Reverse Electron Lone Pair⋅⋅⋅π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the crystal of a uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Partitioning of crystal space into atomic basins and atomic-like potential basins led us to the definite description of interatomic interaction and charge transfer. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of π-stacking and intricate C=O⋅⋅⋅π interactions and nonclassical hydrogen bonds present in the crystal. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with well-known functions, e. g., deformation electron density and electron localization function. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

Experimental and Computational Studies on Structure and Energetic Properties of Halogen Derivatives of 2-Deoxy-D-Glucose

The results of structural studies on a series of halogen-substituted derivatives of 2-deoxy-D-glucose (2-DG) are reported. 2-DG is an inhibitor of glycolysis, a metabolic pathway crucial for cancer cell proliferation and viral replication in host cells, and interferes with D-glucose and D-mannose metabolism. Thus, 2-DG and its derivatives are considered as potential anticancer and antiviral drugs. X-ray crystallography shows that a halogen atom present at the C2 position in the pyranose ring does not significantly affect its conformation. However, it has a noticeable effect on the crystal structure. Fluorine derivatives exist as a dense 3D framework isostructural with the parent compound, while Cl- and I-derivatives form layered structures. Analysis of the Hirshfeld surface shows formation of hydrogen bonds involving the halogen, yet no indication for the existence of halogen bonds. Density functional theory (DFT) periodic calculations of cohesive and interaction energies (at the B3LYP level of theory) have supported these findings. NMR studies in the solution show that most of the compounds do not display significant differences in their anomeric equilibria, and that pyranose ring puckering is similar to the crystalline state. For 2-deoxy-2-fluoro-D-glucose (2-FG), electrostatic interaction energies between the ligand and protein for several existing structures of pyranose 2-oxidase were also computed. These interactions mostly involve acidic residues of the protein; single amino-acid substitutions have only a minor impact on binding. These studies provide a better understanding of the structural chemistry of halogen-substituted carbohydrates as well as their intermolecular interactions with proteins determining their distinct biological activity.

Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions

Two pressure-induced phase transitions have been theoretically studied in the layered iron phosphorus triselenide (FePSe₃ ). Topological analysis of chemical bonding in FePSe₃ has been performed based on the results of first-principles calculations within the periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. The first transition at about 6 GPa is accompanied by the symmetry change from R 3 ¯ to C2/m, whereas the semiconductor-to-metal transition (SMT) occurs at about 13 GPa leading to the symmetry change from C2/m to P 3 ¯ 1 m . We found that the collapse of the band gap at about 13 GPa occurs due to changes in the electronic structure of FePSe₃ induced by relative displacements of phosphorus or selenium atoms along the c-axis direction under pressure. The results of the topological analysis of the electron density and its Laplacian demonstrate that the pressure changes not only the interatomic distances but also the bond nature between the intralayer and interlayer phosphorus atoms. The interlayer P-P interactions are absent in two non-metallic FePSe₃ phases while after SMT the intralayer P-P interactions weaken and the interlayer P-P interactions appear.

The Volumetric Source Function: Looking Inside van der Waals Interactions

The study of van der Waals interactions plays a central role in the understanding of bonding across a range of biological, chemical and physical phenomena. The presence of van der Waals interactions can be identified through analysis of the reduced density gradient, a fundamental parameter at the core of Density Functional Theory. An extension of Bader’s Quantum Theory of Atoms in Molecules is developed here through combination with the analysis of the reduced density gradient. Through this development, a new quantum chemical topological tool is presented: the volumetric source function. This technique allows insight into the atomic composition of van der Waals interactions, offering the first route towards applying the highly successful source function to these disperse interactions. A new algorithm has been implemented in the open-source code, CRITIC2, and tested on acetone, adipic and maleic acids molecular crystals, each stabilized by van der Waals interactions. This novel technique for studying van der Waals interactions at an atomic level offers unprecedented opportunities in the fundamental study of intermolecular interactions and molecular design for crystal engineering, drug design and bio-macromolecular processes.

Polarization of Electron Density Databases of Transferable Multipolar Atoms

Polarizability is a key molecular property involved in either macroscopic (i.e., dielectric constant) and microscopic properties (i.e., interaction energies). In rigid molecules, this property only depends on the ability of the electron density (ED) to acquire electrostatic moments in response to applied electric fields. Databases of transferable electron density fragments are a cheap and efficient way to access molecular EDs. This approach is rooted in the relative conservation of the atomic ED between different molecules, termed transferability principle. The present work discusses the application of this transferability principle to the polarizability, an electron density-derived property, partitioned in atomic contributions using the Quantum Theory of Atoms In Molecules topology. The energetic consequences of accounting for in situ deformation (polarization) of database multipolar atoms are investigated in detail by using a high-quality quantum chemical benchmark.

Pharmaceutical Cocrystals: New Solid Phase Modification Approaches for the Formulation of APIs

Cocrystals can be used as an alternative approach based on crystal engineering to enhance specific physicochemical and biopharmaceutical properties of active pharmaceutical ingredients (APIs) when the approaches to salt or polymorph formation do not meet the expected targets. In this article, an overview of pharmaceutical cocrystals will be presented, with an emphasis on the intermolecular interactions in cocrystals and the methods for their preparation. Furthermore, cocrystals of direct pharmaceutical interest, along with their in vitro properties and available in vivo data and characterization techniques are discussed, highlighting the potential of cocrystals as an attractive route for drug development.

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.

Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg₃Al₂Si₃O₁₂), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ_EXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ_EXP are in substantial agreement with those of ρ_THEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ_EXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

Characterization of fluorine-centred `F...O' σ-hole interactions in the solid state

In the current study, the crystal structure of 1-(3-nitrophenyl)-2,2,2-trifluoroethanone (A1) and (E)-4-((4-fluorophenyl) diazenyl)phenol (A2) has been analyzed for the characterization of the presence of a `unique' and `rare' intermolecular C(sp3/sp2)—F...O contact, which has been observed to play a significant role in the crystal packing. Theoretical charge-density calculations have been performed to study the nature and strength associated with the existence of this intermolecular F...O contact, wherein the F atom is attached to ansp3-hybridized C atom in the case of A1 and to ansp2hybridized carbon in the case of A2. The crystal packing of the former contains two `electronically different' Csp3—F...O contacts which are present across and in between the layers of molecules. In the latter case, it is characterized by the presence of a very `short' (2.708 Å) and `highly directional' (168° at ∠C4—F1...O1 and 174° at ∠C10—O1...F1) Csp2—F...O contact. According to the Cambridge Structural Database (CSD) study, it is a rare example in molecular crystals. Topological features of F...O contacts in the solid state were compared with the gas-phase models. The two-dimensional and three-dimensional static deformation density obtained from theoretical multipole modeling confirm the presence of a charge depleted region on the F atoms. Minimization of the electrostatic repulsion between like charges are observed through subtle arrangements in the electronic environment in two of the short intermolecular F...O contacts. These contacts were investigated using inputs from pair energy decomposition analysis, Bader's quantum theory of atoms in molecules (QTAIM), Hirshfeld surface analysis, delocalization index, reduced density gradient (RDG) plot, electrostatic potential surface and distributed atomic polarizability. The intermolecular energy decomposition (PIXEL) and RDG–NCI (non-covalent interaction) analysis of the F...O contacts establish the interaction to be dispersive in nature. The mutual polarization of an O atom by fluorine andviceversaprovides real physical insights into the role of atomic polarizability in interacting atoms in molecules in crystals.

Charge density and optical properties of multicomponent crystals containing active pharmaceutical ingredients or their analogues

Active pharmaceutical ingredients (APIs), through their favourable donor/acceptor spatial distribution and synthon formation flexibility, are attractive building blocks in modern materials crystallography. The optical properties of a crystal strongly depend on two factors,i.e.the spatial distribution of molecules in the crystal structure and the electronic properties of molecular building blocks (dipole moments, polarizabilities, hyperpolarizabilities). Although the latter are easy to predict throughab initiocalculations, the former are not. Only a combination of experimental and theoretical charge density studies together with prediction and measurement of optical properties enable full analysis of the obtained functional material in terms of its usefulness in practical applications. This article presents design strategies of optical materials based on selected pharmaceutical molecules. Factors that contribute to molecular recognition in the four selected polar/chiral crystal phases (derived through charge density and Hirshfeld surfaces analysis) have been determined. Theoretically predicted optical properties of the molecular/ionic building blocks as well as bulk effects have been confirmed experimentally. This research is a first step in the design of novel optical materials based on push–pull molecules and APIs.