Building neighborlists¶
A neighbor list is a collision detector for spheres: Given a number of spheres of different radius located at different points, it calculates the pairs of spheres that overlap.
ASE provides two implementations of neighbor lists. The newer
linearlyscaling function
ase.neighborlist.neighbor_list()
and
the older quadraticallyscaling class
ase.neighborlist.NeighborList
. The latter will likely
use the former as a backend in the future for linear scaling.
For flexibility, both implementations provide a “primitive”
interface which accepts arrays as arguments rather than the
more complex ase.atoms.Atoms
objects.

ase.neighborlist.
neighbor_list
(quantities, a, cutoff, self_interaction=False, max_nbins=1000000.0)[source]¶ Compute a neighbor list for an atomic configuration.
Atoms outside periodic boundaries are mapped into the box. Atoms outside nonperiodic boundaries are included in the neighbor list but complexity of neighbor list search for those can become n^2.
The neighbor list is sorted by first atom index ‘i’, but not by second atom index ‘j’.
Parameters:
 quantities: str
Quantities to compute by the neighbor list algorithm. Each character in this string defines a quantity. They are returned in a tuple of the same order. Possible quantities are:
 ‘i’ : first atom index
 ‘j’ : second atom index
 ‘d’ : absolute distance
 ‘D’ : distance vector
 ‘S’ : shift vector (number of cell boundaries crossed by the bond between atom i and j). With the shift vector S, the distances D between atoms can be computed from: D = a.positions[j]a.positions[i]+S.dot(a.cell)
 a: ase.Atoms
 Atomic configuration.
 cutoff: float or dict
Cutoff for neighbor search. It can be:
 A single float: This is a global cutoff for all elements.
 A dictionary: This specifies cutoff values for element pairs. Specification accepts element numbers of symbols. Example: {(1, 6): 1.1, (1, 1): 1.0, (‘C’, ‘C’): 1.85}
 A list/array with a per atom value: This specifies the radius of an atomic sphere for each atoms. If spheres overlap, atoms are within each others neighborhood.
 self_interaction: bool
 Return the atom itself as its own neighbor if set to true. Default: False
 max_nbins: int
 Maximum number of bins used in neighbor search. This is used to limit the maximum amount of memory required by the neighbor list.
Returns:
 i, j, …: array
 Tuple with arrays for each quantity specified above. Indices in \(i\) are returned in ascending order 0..len(a), but the order of (i,j) pairs is not guaranteed.
Examples:
Examples assume Atoms object a and numpy imported as np.
Coordination counting:
i = neighbor_list('i', a, 1.85) coord = np.bincount(i)
Coordination counting with different cutoffs for each pair of species:
i = neighbor_list('i', a, {('H', 'H'): 1.1, ('C', 'H'): 1.3, ('C', 'C'): 1.85}) coord = np.bincount(i)
Pair distribution function:
d = neighbor_list('d', a, 10.00) h, bin_edges = np.histogram(d, bins=100) pdf = h/(4*np.pi/3*(bin_edges[1:]**3  bin_edges[:1]**3)) * a.get_volume()/len(a)
Pair potential:
i, j, d, D = neighbor_list('ijdD', a, 5.0) energy = (C/d**6).sum() pair_forces = (6*C/d**5 * (D/d).T).T forces_x = np.bincount(j, weights=pair_forces[:, 0], minlength=len(a))  np.bincount(i, weights=pair_forces[:, 0], minlength=len(a)) forces_y = np.bincount(j, weights=pair_forces[:, 1], minlength=len(a))  np.bincount(i, weights=pair_forces[:, 1], minlength=len(a)) forces_z = np.bincount(j, weights=pair_forces[:, 2], minlength=len(a))  np.bincount(i, weights=pair_forces[:, 2], minlength=len(a))
Dynamical matrix for a pair potential stored in a block sparse format:
from scipy.sparse import bsr_matrix i, j, dr, abs_dr = neighbor_list('ijDd', atoms) energy = (dr.T / abs_dr).T dynmat = (dde * (energy.reshape(1, 3, 1) * energy.reshape(1, 1, 3)).T).T (de / abs_dr * (np.eye(3, dtype=energy.dtype)  (energy.reshape(1, 3, 1) * energy.reshape(1, 1, 3))).T).T dynmat_bsr = bsr_matrix((dynmat, j, first_i), shape=(3*len(a), 3*len(a))) dynmat_diag = np.empty((len(a), 3, 3)) for x in range(3): for y in range(3): dynmat_diag[:, x, y] = np.bincount(i, weights=dynmat[:, x, y]) dynmat_bsr += bsr_matrix((dynmat_diag, np.arange(len(a)), np.arange(len(a) + 1)), shape=(3 * len(a), 3 * len(a)))

ase.neighborlist.
primitive_neighbor_list
(quantities, pbc, cell, positions, cutoff, numbers=None, self_interaction=False, use_scaled_positions=False, max_nbins=1000000.0)[source]¶ Compute a neighbor list for an atomic configuration.
Atoms outside periodic boundaries are mapped into the box. Atoms outside nonperiodic boundaries are included in the neighbor list but complexity of neighbor list search for those can become n^2.
The neighbor list is sorted by first atom index ‘i’, but not by second atom index ‘j’.
Parameters:
 quantities: str
Quantities to compute by the neighbor list algorithm. Each character in this string defines a quantity. They are returned in a tuple of the same order. Possible quantities are
 ‘i’ : first atom index
 ‘j’ : second atom index
 ‘d’ : absolute distance
 ‘D’ : distance vector
 ‘S’ : shift vector (number of cell boundaries crossed by the bond between atom i and j). With the shift vector S, the distances D between atoms can be computed from: D = positions[j]positions[i]+S.dot(cell)
 pbc: array_like
 3tuple indicating giving periodic boundaries in the three Cartesian directions.
 cell: 3x3 matrix
 Unit cell vectors.
 positions: list of xyzpositions
 Atomic positions. Anything that can be converted to an ndarray of shape (n, 3) will do: [(x1,y1,z1), (x2,y2,z2), …]. If use_scaled_positions is set to true, this must be scaled positions.
 cutoff: float or dict
Cutoff for neighbor search. It can be:
 A single float: This is a global cutoff for all elements.
 A dictionary: This specifies cutoff values for element pairs. Specification accepts element numbers of symbols. Example: {(1, 6): 1.1, (1, 1): 1.0, (‘C’, ‘C’): 1.85}
 A list/array with a per atom value: This specifies the radius of an atomic sphere for each atoms. If spheres overlap, atoms are within each others neighborhood.
 self_interaction: bool
 Return the atom itself as its own neighbor if set to true. Default: False
 use_scaled_positions: bool
 If set to true, positions are expected to be scaled positions.
 max_nbins: int
 Maximum number of bins used in neighbor search. This is used to limit the maximum amount of memory required by the neighbor list.
Returns:
 i, j, … : array
 Tuple with arrays for each quantity specified above. Indices in \(i\) are returned in ascending order 0..len(a)1, but the order of (i,j) pairs is not guaranteed.

class
ase.neighborlist.
NeighborList
(cutoffs, skin=0.3, sorted=False, self_interaction=True, bothways=False, primitive=<class 'ase.neighborlist.PrimitiveNeighborList'>)[source]¶ Neighbor list object.
 cutoffs: list of float
 List of cutoff radii  one for each atom. If the spheres (defined by their cutoff radii) of two atoms overlap, they will be counted as neighbors.
 skin: float
 If no atom has moved more than the skindistance since the
last call to the
update()
method, then the neighbor list can be reused. This will save some expensive rebuilds of the list, but extra neighbors outside the cutoff will be returned.  self_interaction: bool
 Should an atom return itself as a neighbor?
 bothways: bool
 Return all neighbors. Default is to return only “half” of the neighbors.
Example:
nl = NeighborList([2.3, 1.7]) nl.update(atoms) indices, offsets = nl.get_neighbors(0)

class
ase.neighborlist.
PrimitiveNeighborList
(cutoffs, skin=0.3, sorted=False, self_interaction=True, bothways=False, use_scaled_positions=False)[source]¶ Neighbor list that works without Atoms objects.
This is less fancy, but can be used to avoid conversions between scaled and nonscaled coordinates which may affect cell offsets through rounding errors.