X-ray Determination Of Molecular Structure

• Type of physical science: Chemistry
• Field of study: Chemistry of molecules: structure

X-ray crystallography is the science that describes and interprets the diffraction of X-rays by crystalline substances. Such diffraction patterns can be used to identify the structure of a molecule and have led to the development of many important structural concepts in a wide variety of sciences.

Overview

X-rays are defined as short-wavelength electromagnetic radiation produced by transitions of electrons in the inner orbitals of atoms, or by the deceleration of high-energy electrons. The wavelength range is from approximately 0.1 angstroms to 100 angstroms. For analytical purposes, the X-ray can be obtained in one of three ways: by bombarding a metal target with a stream of electrons; by subjecting a target to a primary beam of electrons in order to produce a secondary beam of fluorescent X-rays; or by using a radioactive source that, upon decay, yields an X-ray beam.

Primarily, the interest in X-rays as a means of determining molecular structure arises from the fact that a crystalline material will produce a unique and regular diffraction pattern when subjected to X-radiation. A crystalline substance is defined as a homogeneous solid having an ordered internal atomic arrangement and a definite composition. Since no two chemical materials form structures in which the spacing of both the atoms and the planes in which they sit is identical, X-ray diffraction patterns can be used to determine the structure of the original diffracting molecule.

The term crystal, Greek for ice, refers to a regular three-dimensional arrangement of atoms, ions, or molecules. This regularity gives rise to what is called the unit cell, which essentially outlines the simplest repeating unit found in a crystal. A simple analogy for the unit cell would be to consider the regular, repeating brick units in the wall of a house. The wall would be considered the crystal structure, with each brick representing a unit cell. Each wall in the house could, therefore, be described by the repeating dimensions of the individual bricks that make it up.

A unit cell is defined by six parameters. These parameters express the characteristics of the size and shape of the cell. Three parameters (a, b, and c) describe the sides of the cell, while the remaining three (α, β, and γ) describe the angles between those sides. The possible combinations of these parameters result in a variety of shapes that a unit cell or crystal might assume. Analysis has shown that there are seven crystal systems in which a unit cell may exist. These possibilities are pictured in Figure 1. Notice that for some, the unit contains the same atom at the corners of the cell but not in the center of the face (the side of the cell formed by imaginary lines connecting the atoms) or the center of the body of the cell. These cells are referred to as primitive cells (P). Those in which the same type of atom occupies the corners of the cell and the intersection of the diagonals through the body of the cell are given the name body-centered cells (I). Others, called face-centered cells (F), have the same type of atom occupying the corners and the intersection of all diagonals through a face of the cell. Finally, the end-centered cell (C) is that in which the corners of the cell and the centers of two opposite faces are occupied by the same atom. In all, fourteen varieties of a unit cell exist and are called the Bravais lattices (named for August Bravais).

A second concept fundamental to the use of X-rays in structural determination is that of diffraction. Diffraction is the bending of waves into the shadow regions of obstacles. This might at first glance appear to be a rather obscure concept, but, as an example, consider a sound heard around the corner of a building from where a person is standing. The sound waves could not have followed a straight-line path. In fact, they have spread out into the geometric shadow regions of the building’s edge. The same effect describes the experience of viewing a bright light through a common wire mesh similar to those used in sorting powders. When the light hits the mesh, it is scattered and spreads around the mesh into its shadow region, creating a fuzzy pattern of light of varying intensity that can be seen on a screen behind the mesh. This blurring of the light results from the interference of the rays with one another as they are scattered by the mesh.

When X-rays fall on a body, the atoms scatter the incident radiation in much the same manner. In a crystalline structure, where the atoms are arranged in a regular pattern, there exists a definite phase relationship between the scattered rays from the neighboring atoms. If a monochromatic X-ray beam falls on a crystal, the rays are diffracted by the atomic planes within the crystal.

Each reflected ray interacts with the other reflected rays. If the rays are out of phase, they tend to destroy one another, with the net result being no emerging ray or a dark spot. Constructive interference of the rays, in which reflected rays reinforce one another, is known to occur when the conditions of Bragg’s equation (n λ = 2d sin θ) are met. Where λ is the wavelength of the incident X-ray beam, d is the distance between crystal planes, and θ is the angle of the incident ray.

Consequently, a crystal will generate a series of diffraction lines from each plane for a series of wavelengths. The sum of these lines is a diffraction pattern of light and dark spots, from which it is possible to determine the different distances between the crystal planes as well as the angles between the planes. Based on such information, the physical dimensions of the crystal can be deduced.

Applications

X-ray diffraction methods are one means of providing the details of molecular structure. They play a major role in numerous aspects of modern science, from biochemistry to engineering. Empirical drug design, molecular modeling, protein-substrate interactions, and numerous other applications all depend on the identification of a molecule’s structure. Materials scientists, whose research deals with the relationship between a material’s structure and its properties, are especially dependent on X-ray methods. Material engineering is concerned with the modification of properties and the performance of the modified material. The ability to determine a material’s structure—not only the crystal structure but also the electronic structure and the structure of boundaries and interfaces—is fundamental to such an operation.

Typically, a diffraction pattern is obtained by mounting a crystal so that it may be subjected to X-radiation. The crystal is oriented, usually by computer-controlled instrumentation, about different axes successively so that a complete distribution of reflected X-ray beams is obtained from each plane of the crystal. This process will give a complete diffraction pattern.

Figure 2 shows a typical diffraction pattern for an inorganic salt crystal. By careful measurement of the distances between the spots and by consideration of the intensities of these spots, the crystal can be identified.

One method is to construct from a diffraction pattern a series of rays drawn perpendicular from a common point to each plane of the crystal. Such a drawing is called the reciprocal lattice because the distance of each point from the origin is reciprocal to the interplanar spacing of the plane it represents. These points define a geometric construction known as the Ewald sphere, which yields, in two dimensions, a pattern of circles. The pattern for a particular species is generally consistent but may vary with polymorphism or experimental conditions. An alternate method is to replace the single crystal with a large collection of very small crystals that are randomly oriented. Such a method is called a powder method, and the resulting pattern is called a powder diffraction diagram.

The powder diffraction diagram is sufficient data if the identification of a sample is the only information required. Qualitative identification of the substance can be made by matching the diffraction pattern to known patterns. Computer matching of diffraction patterns has significantly improved such structural identifications. It is common to run the unknown sample and then compare the diffraction pattern to those of standards. The method simply requires that a library of standard patterns be available. A second means of qualitative identification entails the measurement of the distance between the planes of the crystal, the d-value. These values are calculated from the diffraction diagram of the unknown substance and again compared with those in a data file. The file is arranged so that it can be searched first by the distance between the crystal planes and then according to the intensity of the reflections. A correct match requires agreement in both of these areas.

If the unknown substance contains a mixture of components, each must be identified separately. One way of doing this is to treat a list of d-values and intensities as a single component, and then match as many of the reflections as possible to a known substance. After a suitable match is made for this component, these lines are omitted, and the remaining lines are matched. This requires that the intensities of the remaining reflections are adjusted to indicate their brightness, as in the pure component. The same matching procedure is followed for the second component.

A more complete structural analysis of a molecule or crystal would include a precise location of all atoms involved. X-ray diffraction methods are capable of determining the placement of an atom to within one-hundredth of an angstrom. This allows for the actual reconstruction of the crystal or molecular lattice. It also provides a means of calculating such parameters as the angle between bonds and the distance between the atoms involved in a bond. Advancements such as time-resolved X-ray crystallography and X-ray free-electron lasers (XFELs) now allow scientists to observe molecular structures in motion and capture intermediate stages of chemical reactions.

X-ray diffraction is adaptable to quantitative work as well as qualitative identification; however, this process is difficult, and complications are abundant. The intensities of a diffraction pattern are proportional to the fraction of the material present in a mixture. Theoretically, this should allow for the same calibration-type processes common to other absorption methods; however, the intensity measurement and the direct comparison of those measurements are most difficult. Interferences are frequently encountered. Internal standards are sometimes used, but they cannot solve all the problems. At the present time, X-ray diffraction is used for both qualitative identification and quantitative phase analysis, although quantitative work can still be complex. Developments in artificial intelligence now assist in interpreting diffraction data, automating structure determination, and identifying errors in structural models.

Context

The first X-ray photograph was taken in 1895. Since that time, X-ray techniques have developed into one of the most informative experimental methods available to the scientific community. Given their capability to describe not only the macroscopic picture of molecular structure but also the microscopic properties, such as the geometric realities within that structure, X-ray methods have aided and improved many science and engineering techniques.

The initial application of X-ray techniques to chemical structural identification is credited to Max von Laue, who, in 1912, realized that the crystal’s internal regularity was a potential source of diffraction. Following this, William H. Bragg and Lawrence Bragg extended Laue’s work to link the intensities of the diffraction pattern with the atomic arrangement of the molecule.

Most of the early work in X-ray crystallography focused on the structures of known compounds. X-ray methods were applied to the research of bond angles, bond forces, and bond lengths. The Nobel Prizes in Chemistry in 1936 (Peter Debye) and 1954 (Linus Pauling) are examples of the importance of structural chemistry. Debye was recognized for his investigations of dipole moments and the diffraction of X-rays and electrons in gases, while Pauling was recognized for his research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances. The field of physics has also benefited from X-ray methods, as witnessed in three Nobel Prizes in Physics being awarded to Laue (1914), the Braggs (1915), and Clinton Joseph Davisson and George Paget Thompson (1937), for their experimental discovery of electron diffraction by crystals.

One of the most famous examples of the importance of X-ray crystallography to the scientific world is credited to James D. Watson, Francis Crick, and Maurice Wilkins for their discovery of the molecular structure of nucleic acid and its significance for information transfer in living materials. It was the diffraction pattern of DNA (deoxyribonucleic acid) that allowed Watson to conclude that the regularity of the molecule was a result of a helical nature. Their ability to interpret the diffraction pattern produced is nothing short of brilliant.

X-ray crystallography has continued to grow and enjoys a rather prominent position in many scientific fields. Many see crystallographic methods as a bridge between biological, physical, chemical, and materials sciences. Its importance as a means of structural identification cannot be stressed enough. In fact, when the 1985 Nobel Prize in Chemistry was awarded to Herbert A. Hauptman and Jerome Karle for their work on a direct-method approach to solving crystal structures, the award speech stated, “In order to understand the nature of chemical bonds, the functions of molecules in a biological context, and the mechanism and dynamics of reactions, knowledge of the exact molecular structure is absolutely essential.” It is likely, therefore, that X-ray diffraction will continue to be a fundamental and leading technique for structural concepts in the future.

Principal terms

CRYSTAL: a substance that is crystalline in three dimensions and bound by plane faces

CRYSTALLOGRAPHY: a branch of mineralogy involved mostly with the recognition, description, and classification of naturally occurring crystal species

DIFFRACTION: the spreading of waves as they move past an obstacle

INTERFERENCE: the superposition of two or more waves, resulting in a net displacement of their amplitudes; the resultant displacement is the sum of the original amplitudes

UNIT CELL: an imaginary solid figure drawn around a molecule in a crystal to indicate a repeating unit

X-RAY: radiation produced when streams of electrons are allowed to bombard a metal, falling between 3 x 10¹⁹ hertz and 3 x 10¹⁶ hertz on the electromagnetic spectrum

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