Joshua J. McKinnon

Fingerprinting intermolecular interactions in molecular crystals

We have recently described a remarkable new way of exploring packing modes and intermolecular interactions in molecular crystals using a novel partitioning of crystal space. These molecular Hirshfeld surfaces reflect intermolecular interactions in a novel visual manner, offering a hitherto unseen picture of molecular shape in a crystalline environment. The surfaces encode information about all intermolecular interactions simultaneously, but sophisticated interactive graphics are required in order to extract the information most efficiently. To overcome this we have devised a two-dimensional mapping which summarizes quantitatively the nature and type of intermolecular interaction experienced by a molecule in the bulk, and presents it in a convenient graphical format. The mapping takes advantage of the triangulation of the Hirshfeld surfaces, and plots the fraction of points on the surface as a function of the closest distances from the point to nuclei inside and outside the surface. In this manner all interaction types (for example, hydrogen bonding, close and distant van der Waals contacts, C–H⋯π interactions, π–π stacking) are readily identifiable, and it becomes a straightforward matter to classify molecular crystals by the nature of interactions, and to rapidly identify similarities and differences which can become obscured when examining crystal packing diagrams. These plots are a novel visual representation of all the intermolecular interactions simultaneously, and are unique for a given crystal structure and polymorph. Applications to a wide variety of molecular crystals and intermolecular interactions are presented, including polymorphic systems, as well as crystals where Z′ > 1.

Novel tools for visualizing and exploring intermolecular interactions in molecular crystals

A new way of exploring packing modes and intermolecular interactions in molecular crystals is described, using Hirshfeld surfaces to partition crystal space. These molecular Hirshfeld surfaces, so named because they derive from Hirshfelds stockholder partitioning, divide the crystal into regions where the electron distribution of a sum of spherical atoms for the molecule (the promolecule) dominates the corresponding sum over the crystal (the procrystal). These surfaces reflect intermolecular interactions in a novel visual manner, offering a previously unseen picture of molecular shape in a crystalline environment. Surface features characteristic of different types of intermolecular interactions can be identified, and such features can be revealed by colour coding distances from the surface to the nearest atom exterior or interior to the surface, or by functions of the principal surface curvatures. These simple devices provide a striking and immediate picture of the types of interactions present, and even reflect their relative strengths from molecule to molecule. A complementary two-dimensional mapping is also presented, which summarizes quantitatively the types of intermolecular contacts experienced by molecules in the bulk and presents this information in a convenient colour plot. This paper describes the use of these tools in the compilation of a pictorial glossary of intermolecular interactions, using identifiable patterns of interaction between small molecules to rationalize the often complex mix of interactions displayed by large molecules.

Hirshfeld Surfaces: A New Tool for Visualising and Exploring Molecular Crystals

Striking new images of molecular crystals are afforded by isosurface rendering of smooth, nonoverlapping molecular surfaces arising from a novel partitioning of crystal space. Surface features characteristic of different types of intermolecular interactions are identified, for example for the edge-to-face C−H⋅⋅⋅π interaction in the packing diagram of benzene shown here.

Electrostatic potentials mapped on Hirshfeld surfaces provide direct insight into intermolecular interactions in crystals

Ab initio electrostatic potentials for molecules can readily be mapped onto their Hirshfeld surfaces and displayed within a crystal packing diagram. In this manner the close molecular contacts in the crystal can be rationalized and discussed in terms of the electrostatic complementarity of touching surface patches in adjacent molecules. By way of example a detailed discussion is given of molecular electrostatic potentials for a large number of small, symmetric, cyclic molecules that crystallize in space groupsP41212 or P43212, with a focus on the qualitative insight that can be obtained and the ways in which this complements the intermolecular electrostatic energies recently reported for some of these materials.

Towards quantitative analysis of intermolecular interactions with Hirshfeld surfaces

Enhancements to the properties based on Hirshfeld surfaces enable quantitative comparisons between contributions to crystal packing from various types of intermolecular contacts.

Visualisation and characterisation of voids in crystalline materials

We present a simple and more realistic alternative to the conventional approach of mapping void space by rolling a probe sphere of variable radius over a fused-sphere representation of a molecular crystal. Based on isosurfaces of the procrystal electron density, this approach can be used to locate and visualise the void space in crystalline materials, as well as readily compute surface areas and volumes of the voids. The method is quite general, computationally rapid, and capable of locating and characterising all “empty” space, and not just the larger cavities and channels, in molecular crystals, organic, metal–organic and inorganic polymers. Examples elaborate on its application to a variety of crystalline systems where voids have been the subject of recent discussion, including porous dipeptides, metal–organic and covalent organic frameworks. Comparison is made with existing computational methods, as well as with the results from experimental techniques that provide estimates of volumes and surface areas of void space and porosity.

Solvent inclusion in the structural voids of form II carbamazepine: single-crystal X-ray diffraction, NMR spectroscopy and Hirshfeld surface analysis

Single-crystal X-ray diffraction and solution 1H NMR spectroscopy, in conjunction with Hirshfeld surface analysis, give evidence of solvent inclusion in the trigonal polymorph of carbamazepine, which in the unsolvated form is characterised by the presence of large structural voids.

Polymorphism in 3-methyl-4-methoxy-4′-nitrostilbene (MMONS), a highly active NLO material

During crystallization experiments two new polymorphs of the highly-active organic nonlinear optical (NLO) material 3-methyl-4-methoxy-4′-nitrostilbene (MMONS) have been discovered. Crystallization conditions of all three polymorphs and their characterization via crystal structure determination from single crystal X-ray diffraction data at 100 K have been discussed in detail. Two of the polymorphs exhibit different conformations, while a third polymorph incorporates both conformers as well as disorder. Comparisons between various types of intermolecular contacts in these three polymorphic forms have been quantified via Hirshfeld surface analysis.

Improvement of anisotropic displacement parameters from invariom-model refinements for three L-hydroxylysine structures

Three L-hydroxylysine structures have been determined at 100 K by single-crystal X-ray diffraction. High-resolution data using either a laboratory or synchrotron source were collected and subjected to invariom- and independent atom-model (IAM) refinements. Anisotropic displacement parameters (ADPs) obtained from invariom refinement were compared (i) with results from a full multipole and (ii) with an IAM high-order refinement. Differences were visualized with the program PEANUT and were complemented by quantitative results from a Hirshfeld test. Influences of scale factor differences, and of refinement against F;2 versus F, have been investigated. Systematic errors were observed in the IAM, especially when only low-order data were available. Although these errors were reduced in high-order IAM refinements, they only disappeared in charge density--and likewise--invariom refinements.

CrystalExplorer: A Tool for Displaying Hirshfeld Surfaces and Visualising Intermolecular Interactions in Molecular Crystals

Crystal structure prediction on the basis of just the chemical formula has long been considered a formidable or even insoluble problem. Being able to solve this problem would open the possibilities to find new phases of planetary materials at extreme conditions [1,2], to solve structures where experimental data are insufficient, and to design new materials entirely on the computer (once the structure is known, it is relatively easy to predict many of its properties e.g., [3]). Essentially, the problem can be reduced to the problem of global optimization of the free energy of a crystal with respect to structural parameters. Recently, we addressed this problem and devised a new method based on a specifically devised and carefully tuned ab initio evolutionary algorithm, which we implemented in the USPEX code (Universal Structure Predictor: Evolutionary Xtallography, [4-6]). At given P-T conditions, USPEX finds the stable structure and a number of robust metastable structures. USPEX uses ab initio free energy as evaluation function and features local optimization and spatial heredity, as well as further operators such as mutation and permutation. This method has been widely tested and applied to solve a number of important problems. It turns out to be extremely efficient for predicting crystal structures with very different geometrical features and types of chemical bonding. In this talk I will discuss some of the applications of this method to a number of interesting materials (C, N, O, S, H2O, MgSiO3, CaCO3, MgCO3). Possible industrial applications will be discussed as well. Future developments of the method will be outlined.