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Thermal properties of solid-state materials are a fundamental topic of studywith important practical implications. For example, anisotropic displacementparameters (ADPs) are routinely used in physics, chemistry, and crystallographyto quantify the thermal motion of atoms in crystals. ADPs are commonly derivedfrom diffraction experiments, but recent developments have also enabled theirfirst-principles prediction using periodic density functional theory (DFT).Here, we combine experiments and dispersion-corrected DFT to quantify latticethermal expansion and ADPs in crystalline {\alpha}-sulfur (S8), a prototypicalelemental solid that is controlled by the interplay of covalent and van derWaals interactions. We first report on single-crystal and powder X-raydiffraction (XRD) measurements that provide new and improved reference datafrom 10 K up to room temperature. We then use several populardispersion-corrected DFT methods to predict vibrational and thermal propertiesof {\alpha}-sulfur, including the anisotropic lattice thermal expansion.Hereafter, ADPs are derived in the commonly used harmonic approximation (in thecomputed zero-Kelvin structure) and also in the quasi-harmonic approximation(QHA) which takes the predicted lattice thermal expansion into account. At thePBE+D3(BJ) level, the latter leads to excellent agreement with experiments.Finally, more general implications of this study for realistic materialsmodeling at finite temperature are discussed.

Lattice thermal expansion and anisotropic displacements in {\alpha}-sulfur from diffraction experiments and first-principles theory