Models of thermal motion in small-molecule crystallography

Abstract

This review commemorates the centenary of the Debye–Waller factor, highlighting its significance in quantifying the impact of thermal vibrations on scattering intensities as well as on crystal properties in small-molecule crystallography. It provides an introduction to thermal motion and displacement parameters, offering insights for chemists and crystallographers.

The Debye–Waller factor, introduced a century ago, remains a fundamental component in the refinement of crystal structures against X-ray, neutron and electron diffraction data. This review marks its centenary by exploring its applications in small-molecule crystallography. We provide a historical overview of the development of the Debye–Waller factor and its foundations in lattice dynamics. The review discusses the practical use of anisotropic displacement parameters and their role in accurate structure determination. We also address the challenges and advancements in modelling thermal motion and disorder, the role of multi-temperature measurements and modern computational approaches.