Glossary of Terms

Hirshfeld Surface

The Hirshfeld surface of a molecule in a crystal is constructed by partitioning space in the crystal into regions where the electron distribution of a sum of spherical atoms for the molecule (the promolecule) dominates the corresponding sum over the crystal (the procrystal).

di and de

di is the distance from the Hirshfeld surface to the nearest nucleus inside the surface. de is the distance from the Hirshfeld surface to the nearest nucleus outside the surface.

Globularity, G

Is a measure of the degree to which the surface area differs from the value for a sphere of the same volume: $G = \frac{S_{sphere}}{S_{H}} = \frac{(36\pi)^{1/3}V_{H}^{2/3}}{S_{H}}$

where $S_{H}$ and $V_{H}$ are the surface area and volume of the Hirshfeld surface respectively.

Asphericity, $\Omega$

Is a measure of the anisotropy of an object and when applied to the atomic positions is defined by the equation: $\Omega = \frac{1}{2}\lbrace\sum_{i < j}(\lambda_{i} - \lambda_{j})^{2}\rbrace\lbrace\sum_{i}\lambda_{i}\rbrace^{-2}$

where $\lambda_{i}$ are the principle moments of inertia of the molecule. For the Hirshfeld surface we take each point on the surface by treating each point on the surface as an object with unit mass when determining the moments of inertia. $\Omega$ takes a value between 0.0 for an isotropic (spherical) object and 1.0 for an oblate (disk-shaped) object while a prolate (cigar-shaped) object will have $\Omega$ $\approx$0.25.

Shape Index, S

The shape index is a qualitative measure of shape.

Curvedness, C

The curvedness is a function of the root-mean-square curvature of the surface, with flat areas of the surface having a low curvedness and areas of sharp curvature having a high curvedness.