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Generalized Coordination Number

This module allows for the computation of the Generalized Coordination Number (GCN) for an atomic system.

The GCN is a descriptor expanding on the better known Coordination Number (CN, the number of neighbours for each atom)

Functions

Calculates the atop Generalized Coordination Number (GCN) for a site. The GCN is defined as the sum of the coordination numbers of the neighbors of each atom divided by the maximum typical coordination number in the specific system (gcn_max).

Parameters

  • coords : ndarray Array of the coordinates of the atoms forming the system.
  • cut_off : float The cutoff distance for determining nearest neighbors.
  • gcn_max : float, optional Maximum typical coordination number in the specific system (default is 18.0). -strained : bool, optional iF True computes the strained aGCN (default is False). pbc : bool, optional Whether to apply periodic boundary conditions. Defaults to False. box : np.ndarray, optional Simulation box size (either [Lx, Ly, Lz] or [[xmin, xmax], [ymin, ymax], [zmin, zmax]] or 3 cell vectors (shape (3,3) - slower)). kwargs: thr_cn: int, optional An atom is considered in the surface if its CN < thr_cn dbulk: float, optional Bulk distance for strained aGCN (default is 0), has to be provided if strained is True

Returns

  • ndarray: Values of the atop GCN.
Source code in snow/descriptors/coordination.py 
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def agcn_calculator(coords, cut_off, gcn_max = 12.0, strained: bool = False, pbc: bool = False, box = None, **kwargs):
    """
    Calculates the atop Generalized Coordination Number (GCN) for a site. The GCN is defined as the sum of the coordination numbers of the neighbors
    of each atom divided by the maximum typical coordination number in the specific system (gcn_max).

    Parameters
    ----------
    - coords : ndarray
        Array of the coordinates of the atoms forming the system.
    - cut_off : float
        The cutoff distance for determining nearest neighbors.
    - gcn_max : float, optional
        Maximum typical coordination number in the specific system (default is 18.0).
    -strained : bool, optional
        iF True computes the strained aGCN (default is False).
    pbc : bool, optional
        Whether to apply periodic boundary conditions. Defaults to False.
    box : np.ndarray, optional
        Simulation box size (either [Lx, Ly, Lz] or [[xmin, xmax], [ymin, ymax], [zmin, zmax]] or 3 cell vectors (shape (3,3) - slower)).
    kwargs:
        thr_cn: int, optional
            An atom is considered in the surface if its CN < thr_cn
        dbulk: float, optional
            Bulk distance for strained aGCN (default is 0), has to be provided if strained is True

    Returns
    -------
    - ndarray: Values of the atop GCN.
    """
    neigh_list, coord_numbers = coordination_number(coords, cut_off, neigh_list=True, pbc=pbc, box=box)
    n_atoms = len(coord_numbers)
    agcn = np.zeros(n_atoms)
    sites=[]

    thr_cn = kwargs.get('thr_cn', None)
    dbulk = kwargs.get('dbulk', 0)

    for i, atom_neighbors in enumerate(neigh_list):
        if thr_cn is not None and coord_numbers[i] >= thr_cn:
            continue
        sites.append(coords[i])
        if strained:
            sgcn=0
            for nb in neigh_list[i]:
                for nnb in neigh_list[nb]:
                    d_nb_nnb= np.linalg.norm(coords[nb] - coords[nnb])
                    sgcn += dbulk/d_nb_nnb
            self_sgcn=0
            for nb in neigh_list[i]:
                break
                d_nb_nnb= np.linalg.norm(coords[nb] - coords[i])
                self_sgcn += dbulk/d_nb_nnb
            agcn[i]=((sgcn-self_sgcn)/gcn_max)
        else:
            agcn_i = sum(coord_numbers[neigh] for neigh in atom_neighbors)# - coord_numbers[i]
            agcn[i]=(agcn_i / gcn_max)

    return sites, agcn