Shape descriptors

What they are

A rotation invariant description of a shape. In essence, these are rotation invariants calculated from the coefficients of the spherical harmonic transform of a shape function, which in our case is either the radius (distance from the origin) of an isosurface as a function of the spherical angles theta and phi.

References:

How to calculate shape descriptors

Molecules in crystals

from chmpy import Crystal
c = Crystal.load("tests/test_files/acetic_acid.cif")

# calculate shape descriptors for each molecule in the asymmetric unit
desc = c.molecular_shape_descriptors()

Atoms in crystals

Likewise, atomic shape descriptors can be conveniently calculated directly from the Crystal object:

from chmpy import Crystal
c = Crystal.load("tests/test_files/acetic_acid.cif")

# calculate shape descriptors for each atom in the asymmetric unit
desc = c.atomic_shape_descriptors()

Isolated molecules

Hirshfeld surfaces typically only have a sensible definition in a crystal (or at least in a environment where the molecule is not isolated). As such, the more sensible descriptor to utilise may be one of the Promolecule density isosurface.

This can be readily calculated using the Molecule object:

from chmpy import Molecule
m = Molecule.load("tests/test_files/water.xyz")
desc = m.shape_descriptors()

# use EEM calculated charges to describe the shape and the ESP
# up to maximum angular momentum 16
desc_with_esp = m.shape_descriptors(l_max=16, with_property="esp")

However, another useful descriptor of atomic environments is a Hirshfeld-type descriptor in a molecule, where in order to 'close' the exterior of the surface we introduce a background density, as follows:

from chmpy import Molecule
m = Molecule.load("tests/test_files/water.xyz")
# with the default background density
desc = m.atomic_shape_descriptors()

# or with, a larger background density, contracting the atoms
desc = m.atomic_shape_descriptors(background=0.0001)