import numpy as np
from ase.calculators.calculator import Calculator
from ase.neighborlist import neighbor_list
def fcut(r, r0, r1):
"""
Piecewise quintic C^{2,1} regular polynomial for use as a smooth cutoff.
Ported from JuLIP.jl, https://github.com/JuliaMolSim/JuLIP.jl
Parameters
----------
r0 - inner cutoff radius
r1 - outder cutoff radius
"""""
s = 1.0 - (r - r0) / (r1 - r0)
return (s >= 1.0) + ((s > 0.0) & (s < 1.0)) * (
6.0 * s**5 - 15.0 * s**4 + 10.0 * s**3
)
def fcut_d(r, r0, r1):
"""
Derivative of fcut() function defined above
"""
s = 1 - (r - r0) / (r1 - r0)
return -(
((s > 0.0) & (s < 1.0))
* (30 * s**4 - 60 * s**3 + 30 * s**2)
/ (r1 - r0)
)
[docs]class MorsePotential(Calculator):
"""Morse potential.
Default values chosen to be similar as Lennard-Jones.
"""
implemented_properties = ['energy', 'forces']
default_parameters = {'epsilon': 1.0,
'rho0': 6.0,
'r0': 1.0,
'rcut1': 1.9,
'rcut2': 2.7}
nolabel = True
def __init__(self, **kwargs):
"""
Parameters
----------
epsilon: float
Absolute minimum depth, default 1.0
r0: float
Minimum distance, default 1.0
rho0: float
Exponential prefactor. The force constant in the potential minimum
is k = 2 * epsilon * (rho0 / r0)**2, default 6.0
"""
Calculator.__init__(self, **kwargs)
def calculate(self, atoms=None, properties=['energy'],
system_changes=['positions', 'numbers', 'cell',
'pbc', 'charges', 'magmoms']):
Calculator.calculate(self, atoms, properties, system_changes)
epsilon = self.parameters.epsilon
rho0 = self.parameters.rho0
r0 = self.parameters.r0
rcut1 = self.parameters.rcut1 * r0
rcut2 = self.parameters.rcut2 * r0
forces = np.zeros((len(self.atoms), 3))
preF = - 2 * epsilon * rho0 / r0
i, j, d, D = neighbor_list('ijdD', atoms, rcut2)
dhat = (D / d[:, None]).T
expf = np.exp(rho0 * (1.0 - d / r0))
fc = fcut(d, rcut1, rcut2)
E = epsilon * expf * (expf - 2)
dE = preF * expf * (expf - 1) * dhat
energy = 0.5 * (E * fc).sum()
F = (dE * fc + E * fcut_d(d, rcut1, rcut2) * dhat).T
for dim in range(3):
forces[:, dim] = np.bincount(i, weights=F[:, dim],
minlength=len(atoms))
self.results['energy'] = energy
self.results['forces'] = forces