X-Ray Crystallography, Basic Principles

Definition

X-ray crystallography reveals the spatial structure of molecules by measuring how they scatter X-ray radiation when arranged in a crystal lattice. Two broad fields may be distinguished: small molecule crystallography deals with a small number of atom positions and typically well-ordered crystals, while macromolecular (usually protein) crystallography determines a much larger number of atomic positions, usually despite considerable crystalline disorder.

Their common goal is to calculate the electron density distribution in the crystal from measured X-ray diffraction intensities. The electron density and diffraction intensities are represented by mathematical functions, which may be interconverted variously using the Fourier transform, convolution and complex productoperations if the phases of the diffracted X-rays are known. Because the phases are not directly measurable, the dilemma known as the “phase problem” arises. Several methods exist that enable phase estimation and...