def _sw_angle_interaction(dR12,
dR13,
gamma=1.2,
sigma=2.0951,
cutoff=1.8 * 2.0951):
"""The angular interaction for the Stillinger-Weber potential.
This function is defined only for interaction with a pair of
neighbors. We then vmap this function three times below to make
it work on the whole system of atoms.
Args:
dR12: A d-dimensional vector that specifies the displacement
of the first neighbor. This potential is usually used in three
dimensions.
dR13: A d-dimensional vector that specifies the displacement
of the second neighbor.
gamma: A scalar used to fit the angle interaction.
sigma: A scalar that sets the distance scale between neighbors.
cutoff: The cutoff beyond which the interactions are not
considered. The default value should not be changed for the
default SW potential.
Returns:
Angular interaction energy for one pair of neighbors.
"""
a = cutoff / sigma
dr12 = space.distance(dR12)
dr13 = space.distance(dR13)
dr12 = np.where(dr12 < cutoff, dr12, 0)
dr13 = np.where(dr13 < cutoff, dr13, 0)
term1 = np.exp(gamma / (dr12 / sigma - a) + gamma / (dr13 / sigma - a))
cos_angle = quantity.angle_between_two_vectors(dR12, dR13)
term2 = (cos_angle + 1. / 3)**2
within_cutoff = (dr12 > 0) & (dr13 > 0) & (np.linalg.norm(dR12 - dR13) >
1e-5)
return np.where(within_cutoff, term1 * term2, 0)
def single_pair_angular_symmetry_function(dR12, dR13, eta, lam, zeta,
cutoff_distance):
"""Computes the angular symmetry function due to one pair of neighbors."""
dR23 = dR12 - dR13
dr12_2 = space.square_distance(dR12)
dr13_2 = space.square_distance(dR13)
dr23_2 = space.square_distance(dR23)
dr12 = space.distance(dR12)
dr13 = space.distance(dR13)
dr23 = space.distance(dR23)
triplet_squared_distances = dr12_2 + dr13_2 + dr23_2
triplet_cutoff = reduce(
lambda x, y: x * _behler_parrinello_cutoff_fn(y, cutoff_distance),
[dr12, dr13, dr23], 1.0)
result = 2.0 ** (1.0 - zeta) * (
1.0 + lam * quantity.angle_between_two_vectors(dR12, dR13)) ** zeta * \
np.exp(-eta * triplet_squared_distances) * triplet_cutoff
return result