Mark A. Spackman

Hirshfeld surface analysis

In the last few years the analysis of molecular crystal structures using tools based on Hirshfeld surfaces has rapidly gained in popularity. This approach represents an attempt to venture beyond the current paradigm—internuclear distances and angles, crystal packing diagrams with molecules represented via various models, and the identification of close contacts deemed to be important—and to view molecules as “organic wholes”, thereby fundamentally altering the discussion of intermolecular interactions through an unbiased identification of all close contacts.

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.

A novel definition of a molecule in a crystal

Abstract A new method for dividing a crystalline electron distribution into molecular fragments is proposed, based on Hirshfelds partitioning scheme. Unlike other approaches, the method partitions the crystal into smooth molecular volumes as well as intermolecular voids of low electron density. To compare the new method with several other schemes which subdivide a crystal into molecules, numerical integration is performed on two model electron densities (one representing a superposition of isolated molecules, the other interacting molecules) for ice VIII, formamide and urea. The new scheme is simply to apply, aesthetically appealing, and offers some promise in routine partitioning of crystalline electron densities or in computer graphics to provide additional insight into molecular packing in crystals.

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.

A simple quantitative model of hydrogen bonding

A simple model for the computation of intermolecular interactions is described. It consists of atom–atom potentials for the representation of repulsion and dispersion energies, and an evaluation of the electrostatic energy in terms of partitioned multipole moments of the monomer electron distributions. Applications are given in detail for hydrogen‐bonded dimers of the molecules HF, HCl, CO, N2, Cl2, HCN, CO2, N2O, OCS, HCCH, NCCN, and HCCCN, and the results compared with ab initio and experimental results. Hydrogen bond energies are obtained to better than 4 kJ mol−1, intermolecular separations to typically better than 0.15 A, and intermolecular angles within 5°, all compared with experiment. Force constants and vibrational frequencies are also well reproduced.

Atom–atom potentials via electron gas theory

The Gordon–Kim electron gas model is used to derive a set of short range repulsive potentials for homoatomic pairs containing atoms up to Kr. These potentials correlate extremely well with experimental van der Waals and nonbonded radii. Single exponential fits to the repulsive potentials are given, and are combined with an approximate dispersion energy term derived from experimental and theoretical atomic dipole polarizabilities and C6 constants to form a set of internally consistent atom–atom potentials of the exp‐6 form.

Three new co-crystals of hydroquinone: crystal structures and Hirshfeld surface analysis of intermolecular interactions

Hydroquinone (benzene-1,4-diol or quinol) is reported here to form co-crystals in different ratios with propan-2-ol, N,N-dimethylacetamide (DMA) and N,N-diethylformamide (DEF). Investigation of intermolecular interactions and crystal packing via Hirshfeld surface analysis reveals that more than two-thirds of the close contacts are associated with relatively weak H⋯H, C⋯H and H⋯C interactions. The use of Hirshfeld surfaces in combination with fingerprint plots demonstrates that these weak interactions are important for both local packing and crystal packing. The complexes highlight the way in which electrostatic complementarity to a large extent governs the hydrogen bonding pattern in molecular crystals.