100 Years of X-Ray Crystallography

ABSTRACT The developments in crystallography, since it was first covered in Science Progress in 1917, following the formulation of the Bragg equation, are described. The advances in instrumentation and data analysis, coupled with the application of computational methods to data analysis, have enabled the solution of molecular structures from the simplest binary systems to the most complex of biological structures. These developments are shown to have had major impacts in the development of chemical bonding theory and in offering an increasing understanding of enzyme-substrate interactions. The advent of Synchrotron radiation sources has opened a new chapter in this multi-disciplinary field of science. Keywords: bonding, crystal structure, data analysis, DNA, electron density, powder diffraction, ribosome, symmetry, synchrotron, unit cell 1. Introduction 1.1 Historical The year 2017 is a rather suitable point to chart the developments in X-ray crystallography bearing in mind that the Nobel Prize in Physics in 1915 was awarded to the father and son team of William Henry Bragg and William Lawrence Bragg (Figure l) (1). It is significant that, since then, crystallography has been (and remains) one of the most multidisciplinary sciences that links together frontier areas of research and has, directly or indirectly, produced the largest number of Nobel Laureates throughout the history of the awards, with 29 Prizes for 48 Laureates up to the present day. The Braggs had built (2) on the discovery by Max von Laue of the phenomenon of the diffraction of X-rays in crystals, the latter having recognised that the wavelength of X-rays matched the spacing of atoms within solids (2). The diffraction pattern from the NaCl crystal is shown in Figure 2. A report of the Braggs' award was made in Science Progress in 1916 (3). The initial discovery left some difficult problems in that not only the space lattices, but also the wavelengths and the intensity distribution wavelengths in the spectra of the X-rays, were unknown quantities. W.L. Bragg found that the phenomenon could be treated mathematically as a reflection by the successive parallel planes that may be placed so as to pass through the lattice points (Figure 3). In this way, the ratio between the wavelengths and the distances of these planes from each other could be calculated from the angle of reflection. The Bragg formula (Bragg's law) can be written: n[lambda] = 2d sin [theta] (1) The Braggs focused their initial efforts on the simplest structures, i.e. the alkali metal halides, demonstrating the face-centred cubic lattice of NaCl, KBr and KI and the simple cubic lattice of CsCl. In the first, a metal atom is surrounded by six halide ions and each halide ions, and in the second structure each ion has eight neighbours. The Braggs' investigation of diamond revealed the tetrahedral nature of the environment of each carbon atom (1). Since these original discoveries, X-ray crystallography has become one of the most important scientific techniques for determining the structure of molecules from the smallest to the largest. This article traces its development over the 100 years following the publication of Braggs' law. 2. Terminology While it is not the aim here to enable readers to solve X-ray structures, it is necessary to introduce some of the terms and parameters used in X-ray diffraction. 2.1 Unit cell A crystal lattice is built made up of identical 3-dimensional units which are repeated by translation in the X-, Y- and Z-directions. The unit cell (Figure 4) can be thought of as the fundamental structural pattern from which the crystal is constructed. Unit cells are classified into seven crystal systems by noting the rotational symmetry elements they possess; thus a tetragonal unit cell has one four-fold axis and a cubic unit cell has four three-fold axes arranged tetrahedrally. …