Crystallography is different from spectroscopy.

Spectroscopy – Measures physical properties as interpretable data

(e.g. absorption frequency, molecular or fragment mass, bond bending frequency, magnetic resonance or chemical shift)

X-ray Crystallography – Measures a physical property (i.e. the data) in the form of the positions and intensities of the results of X-ray photons diffracting from a crystal.

The diffraction pattern is the Fourier transform of the electronic density (i.e. the structure) in the crystal however, while the intensities and positions can be measured, the phase information (ϕ) of the individual waves creating each diffraction spot in the pattern cannot be measured.

Electron density formula

ρ(xyz)=(1/V) Σ F(hkl)·exp [iϕ(hkl)]·exp [-2πi(hx +ky +lz)]

Hence, diffraction data need to be solved by a crystallographer using space groups and symmetry. Here is a schematic of a Patterson solution using heavy atom vectors.

It is the interpretation of the solved structure and not the data that is most useful to the structural scientist.

- confirmation of chemical identity, cocrystallized molecules, volume and contents of “void spaces”
- absolute chirality
- bond distances and angles
- torsion, twist angles, cis versus trans, endo versus exo
- H-bonding, n*-π interactions, π-π stacking
- planarity, aromaticity
- structural comparisons, overlays
- steric – cone, wedge, and bite angles of ligands
- other “bespoke” structural features important to your research

Dickinson, Cody F., Yang, Justin K., Yap, Glenn P. A., Tius, Marcus A. 2022,

“Modular Synthesis of a Semibuckminsterfullerene” Organic Letters 24(28), 5095-5098.