Quasigraph is an open-source toolkit designed for generating chemical and geometric descriptors to be used in machine learning models.

Installation

The easiest method to install quasigraph is by utilizing pip:

$ pip install quasigraph

Getting started

from ase.build import molecule
from quasigraph import QuasiGraph

# Initialize an Atoms object for methanol (CH3OH) using ASE's molecule function
atoms = molecule('CH3OH')

# Instantiate a QuasiGraph object containing chemical and coordination numbers
qgr = QuasiGraph(atoms)

# Convert the QuasiGraph object into a pandas DataFrame
df = qgr.get_dataframe()

# Convert the QuasiGraph object into a vector
vector = qgr.get_vector()

Descriptor

The descriptor can be separated into two parts, a chemical part and a geometric part.

Chemical part

The chemical part of the descriptor employs the Mendeleev library, incorporating atomic details like the valence electron concentration, covalent radius, atomic radius, Pauling electronegativity and electron affinitity for every element within the object.

For example, for methanol (CH₃OH) we have the table:

Geometric part

The geometric part involves identifying all bonds and computing the coordination numbers for each atom, indicated as CN. Additionally, the generalized coordination number (GCN)¹ is determined by summing the coordination numbers of the neighboring ligands for each atom and normalizing this sum by the highest coordination number found in the molecule.

Figure 1 - Schematic representation of the methanol molecule, indicating the chemical symbol and coordination number (CN) for every atom.

For example, for methanol (CH₃OH) we have the geometric data, as shown in Fig. 1.

Continuous bond information (optional)

By default the geometric part is CN and GCN. The geometric_features argument selects any of the per-atom features below; the chemical columns come first, then the geometric ones in the order given.

from quasigraph import QuasiGraph, GEOMETRIC_FEATURES

qgr = QuasiGraph(atoms, geometric_features=GEOMETRIC_FEATURES)
qgr.get_dataframe()   # ... CN, GCN, CN_smooth, bond_mean, bond_min, bond_max, bond_std, bond_strain

Covalent radii are the Pyykkö values from Mendeleev. Metallic bonds are typically 10–20 % longer than the sum of these radii, so in a perfect fcc metal CN_smooth is roughly 0.65 × CN and bond_strain ≈ 0.15; the useful information is the variation between sites.

Adsorption-site environment

For a target that depends on one atom, such as the adsorption free energy of a hydrogen atom, get_site_environment aggregates the descriptor over the neighbour shells of that atom on the bond graph and returns a fixed-length, named vector that does not depend on the number of atoms or their order:

qgr = QuasiGraph(atoms, geometric_features=GEOMETRIC_FEATURES)
env = qgr.get_site_environment("H", shells=2, elements=["Ag", "Au", "Cu", "Pd", "Pt"])  # pandas Series
vector = qgr.get_site_vector("H", shells=2, elements=["Ag", "Au", "Cu", "Pd", "Pt"])   # numpy array

site is an atom index or a chemical symbol that occurs once in the structure. The Series contains site_<feature> for the site atom itself and, for each shell k (atoms k bonds away from the site): shell<k>_n, shell<k>_n_<El> (counts per element in elements), shell<k>_dist_mean/min/max (distance from the site), shell<k>_<feature>_mean for chemical features and shell<k>_<feature>_mean/min/max for geometric features. Pass the same elements list for every structure of a dataset so all vectors have the same length; an empty shell contributes zeros.

Package structure

• quasigraph.quasigraph.QuasiGraph – user-facing class; wraps an ASE Atoms object and exposes get_dataframe() / get_vector() plus the attributes cn, gcn, bonded_atoms, bonds, adjacency, distances (non-periodic) and distances_tensor (periodic).
• quasigraph.geometry – pure NumPy functions for distances, bonds, CN and GCN (distance_matrix, distance_tensor, bonds_from_distance_matrix, coordination_numbers, generalized_coordination_numbers, ...). They take plain arrays and can be reused without ASE.
• quasigraph.elements – chemical features taken from the Mendeleev library. Database lookups are cached per element symbol (get_element, get_feature), so the cost of a Mendeleev query is paid once per element per process instead of once per atom.
• quasigraph.ptable – hand-curated tables (VEC, CONFIG) not available in Mendeleev.

License

This is an open source code under MIT License.

Acknowledgements

We thank financial support from FAPESP (Grant No. 2022/14549-3), INCT Materials Informatics (Grant No. 406447/2022-5), and CNPq (Grant No. 311324/2020-7).