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This chapter discusses the methods for determining the structure of crystals. Topics covered include diffraction techniques, determination of modulated phases and composites, structure determination of quasi-crystals, and diffraction by an imperfect crystal.

Organic molecules can provide an almost infinite variability in shape and electrical polarisation, and the solid state has a high degree of structuring and anisotropy. These are the reasons why much is expected from structure-activity relationships in solid-state chemistry, with promise for constructing a wide range of diverse materials. Moreover, since molecules in solids are blocked into a fixed conformation, and rotation and translation are forbidden, one may expect to be able to construct many different buildings with the same bricks, and one may fancy that the same organic compound can make a piece of rubbish in one crystal and a touchstone in another. This chapter discusses crystal polymorphism and crystal structure and how they are predicted, taxonomy of organic crystals, phenomenology of crystal polymorphism, analysis of crystal polymorphism by Pixel and quantum chemical calculations, construction of crystal structures by computers, molecular clusters with one symmetry operator, pros and cons of the Prom algorithm, and computer prediction of crystal structure.

Structure correlation studies were first carried out on intramolecular parameters, a classic work of which involved molecular deformations at a carbonyl center as a function of the intermolecular distance to an incoming nucleophile. In further applications, the term ‘structure correlation’ was extended to include all studies in which molecular or crystal properties are analysed in a systematic way over the database, to reveal correlations between structural or energetic properties of crystallised molecules. This chapter discusses correlation studies in organic solids, the Cambridge Structural Database (CSD) of organic crystals, structure correlation, retrieval of crystal and molecular structures from the CSD, the SubHeat database, geometrical categorisation of intermolecular bonding, space analysis of molecular packing modes, empty space versus filled space, close packing in crystals, calculation of intermolecular energies in crystals, basic concepts on lattice energies, sublimation entropies and vapor pressures of crystals, general-purpose force fields for organic crystals, correlation between molecular and crystal properties, and acceptable crystal structures.

This chapter reviews the weak hydrogen bond in supramolecular chemistry by focusing on the relevance of these interactions in the analysis, design, and synthesis of the structures of molecular assemblies, most notably crystals. Supramolecular chemistry signifies chemistry beyond the molecule and deals with implications of the fact that molecules can recognise one another via intermolecular interactions, typically in condensed media. This field has grown into two distinct branches: the study of supermolecules in solution and in the solid state, mainly in crystal structures. The most important distinction between these two situations is not structural but lies in the lifetime of the interactions − supramolecular association in the crystal is time-stable whereas in solution it is not. The present chapter mainly concentrates on solid-state supramolecular systems, and discusses the role of weak hydrogen bonds in inclusion complexes such as crown ethers, oligoaryl hosts, and cyclodextrins (cycloamyloses). The promises and problems of crystal engineering are also considered, together with drug design and biological recognition.

The number of RNA crystal structures has increased in an exponential manner mainly due to the fact that RNA is increasingly viewed as a predominant part of biological processes such as translation, ribozyme catalysis, and gene regulation, riboswitches, and mRNA-protein interactions, for which the gap in structural knowledge is still deep despite the determination of the crystal structure of the ribosome. Structural studies of the ubiquitous roles of RNA at all levels of cellular processes are starting to be supported by technological developments which enable high-throughput crystallography (HTC). Recently, robotics has entered the field of crystallization. Despite the high cost of these robots, they are highly valuable because they significantly shorten the time to set up experiments as well as multiply the number of possible tests by a 100-fold, just by going to the nanolitre scale in terms of liquid sample handling. They also allow samples to be tested that are too scarce for the usual microlitre-scale techniques. Furthermore, they reduce handling time, which can then be spent on more valuable tasks such as macromolecule purification or structure solving. This chapter presents guidelines to purify and set up RNA oligonucleotides crystallization experiments using a robot. An overview of crystallization robots available on the market will also be given with their advantages and drawbacks.

This chapter looks at the known crystal structures of fatty acids, including saturated and unsaturated chain materials. Structures of keto-, hydroxyl-, and methyl-branched fatty acids are also presented to understand how such branches might be tolerated within a methylene subcell packing region. Methyl branches are excluded. Depending on chain length and parity, polymorphism is an important consideration.

Thermodynamics governs the relative stability of crystal forms. The energetics are a compromise between intra- and intermolecular interactions. This chapter deals first with the former, including a discussion of the connection between molecular shape (conformation) and energetic, and methods for computationally estimating both energy differences and absolute thermodynamic quantities. This is followed by a similar discussion for intermolecular interactions. These principles are then applied to the phenomenon of conformational polymorphism, wherein a molecule can adopt different conformations in different crystal structures. Some examples of the treatment of conformational polymorphs are given. The chapter concludes with a discussion of the state-of-the-art computational prediction of crystal structures, in particular of the possible existence of polymorphs of a given molecular material.

The structure and function of biological molecules is to a large degree determined by hydrogen bonding. This is the case for proteins, nucleic acids, carbohydrates, membranes and also the aqueous medium in which these components are held. The three-dimensional architecture of proteins and nucleic acids is stabilised by hydrogen bonds, biological recognition operates mainly by this mechanism, and the molecular mobility required for biological processes is directly connected with rapid formation and breaking of hydrogen bonds. This chapter discusses the weak hydrogen bond in biological structures, the crystal structures of biological molecules, problems associated with determining the crystallographic resolution problem, and weak hydrogen bonding in peptides and proteins, nucleic acids, carbohydrates, and water molecules.

The historical introduction covers the parallel developments in EM on inorganic and biological samples. Vainshtein, Pinsker and Zvyagin in Moscow solved structures from electron-diffraction patterns in the 1950s. Aaron Klug in 1968 pioneered computer image processing of EM images and realised that the crystallographic structure factor phase information can be read out directly in numbers from the Fourier transform. A few years later the EM optics was powerful enough to allow metals to be seen in oxides. The first determination of atomic coordinates in a crystal from EM images was done in 1984. Compared to X-ray crystallography, electron microscopy has some advantages; crystals a million times smaller (even defects) can be studied and the crystallographic structure factor phases can be read out numerically. Drawbacks are radiation damage (especially for organics) and multiple diffraction.

This chapter reconsiders the model for petroleum wax structure presented in Chapter 1 in light of the structural information presented in the intervening chapters. The earlier packing model is found to be deficient for various reasons: (a) the expectation that methyl branches can be accommodated into the methylene subcell region, (b) that there can be solvent molecules at the chain layer interfaces, (c) that the type of layer packing is ill-defined. Indeed, single crystal evidence from electron diffraction clearly shows that there can be at least two types of solid solution packing in polydisperse arrays, depending on the absolute breadth of the chain length distribution (but not the polydispersity index). Finally, important areas are indicated where more research is needed, including the determination of unknown crystal structures of rather simple molecules such as the symmetric wax esters.

This chapter reviews the crystal structures of lipid alcohols. As with the paraffins, the influence of polymethylene chain length and parity of crystal structure is presented. Binary phase behaviour is shown to be somewhat different from that of n-paraffins due to the existence of a polar ‘headgroup’ that is stabilized in a hydrogen bonded chain network. The crystal structures of cholesterol and two oxidized derivatives are presented, including the binary behaviour of the former parent with either derivative.

The weak hydrogen bond was first identified in 1935, but it was only in the early 1990s that it really permeated into the consciousness of chemists and biologists. It only seems natural that this interaction was explored first using spectroscopy, followed by crystallography. In structural supramolecular chemistry, a crystal structure is often not the result of hierarchic interaction preferences but a convolution of a large number of strong and weak interactions, each of which affect the rest intimately. Methods for codification of crystal structures must take this into account if they are to be accurate and useful. Of course, the goal of a subject like crystal engineering is to design systems where the interaction preferences are hierarchic, or in other words where the interaction interference is at a minimum. However, most crystal structures are not so predictable and the challenge posed by weak hydrogen bonding effects to the dogma of crystal engineering remains a real one.

Global optimisation methods that involve the assessment of multiple trial crystal structures against measured diffraction data offer a powerful alternative to Direct methods of structure solution. This chapter describes the problem of searching an N-dimensional hypersurface, populated with a great many function minima, for the global minimum that corresponds to the true crystal structure. Key factors discussed include model construction, agreement factor calculation and estimating the likelihood of success. Various global optimisation methods including simulated annealing and genetic algorithms are covered, and the chapter is illustrated with numerous examples of solved molecular crystal structures.

This chapter presents the crystal structures of cholesteryl esters, revealing how chain length and/or unsaturation influence the favoured layer packing of these molecules. Favoured polymorphs are given as well as domains for co-solubility. The single crystal structures of binary solid solutions are discussed, revealing how the packing rules found for the n-paraffin binaries are mostly irrelevant, because the cholesteryl ring moiety is confined to a discrete region of the layer packing. Favoured packing sites are found for the different chain lengths.

This chapter reviews the crystal structures of fatty acid esters of linear fatty alcohols, revealing that no complete structure exists for a symmetric chain ester. Chain branching influences on layer packing are shown. The binary phase diagrams of esters with n-paraffins are presented, revealing how symmetric esters prefer tilted chain layer packing that are incompatible with n-paraffins of the same chain length, whereas asymmetric esters may be co-soluble. The arrangement of ester chains in natural waxes, including those from insects, is discussed.