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"""TIP3P potential."""
import numpy as np
import ase.units as units
from ase.calculators.calculator import Calculator, all_changes
qH = 0.417
sigma0 = 3.15061
epsilon0 = 0.1521 * units.kcal / units.mol
rOH = 0.9572
angleHOH = 104.52
thetaHOH = 104.52 / 180 * np.pi # we keep this for backwards compatibility
class TIP3P(Calculator):
implemented_properties = ['energy', 'forces']
nolabel = True
pcpot = None
def __init__(self, rc=5.0, width=1.0):
"""TIP3P potential.
rc: float
Cutoff radius for Coulomb part.
width: float
Width for cutoff function for Coulomb part.
"""
self.rc = rc
self.width = width
Calculator.__init__(self)
self.sites_per_mol = 3
def calculate(self, atoms=None,
properties=['energy'],
system_changes=all_changes):
Calculator.calculate(self, atoms, properties, system_changes)
R = self.atoms.positions.reshape((-1, 3, 3))
Z = self.atoms.numbers
pbc = self.atoms.pbc
cell = self.atoms.cell.diagonal()
nh2o = len(R)
assert (self.atoms.cell == np.diag(cell)).all(), 'not orthorhombic'
assert ((cell >= 2 * self.rc) | ~pbc).all(), 'cutoff too large' # ???
if Z[0] == 8:
o = 0
else:
o = 2
assert (Z[o::3] == 8).all()
assert (Z[(o + 1) % 3::3] == 1).all()
assert (Z[(o + 2) % 3::3] == 1).all()
charges = np.array([qH, qH, qH])
charges[o] *= -2
energy = 0.0
forces = np.zeros((3 * nh2o, 3))
for m in range(nh2o - 1):
DOO = R[m + 1:, o] - R[m, o]
shift = np.zeros_like(DOO)
for i, periodic in enumerate(pbc):
if periodic:
L = cell[i]
shift[:, i] = (DOO[:, i] + L / 2) % L - L / 2 - DOO[:, i]
DOO += shift
d2 = (DOO**2).sum(1)
d = d2**0.5
x1 = d > self.rc - self.width
x2 = d < self.rc
x12 = np.logical_and(x1, x2)
y = (d[x12] - self.rc + self.width) / self.width
t = np.zeros(len(d)) # cutoff function
t[x2] = 1.0
t[x12] -= y**2 * (3.0 - 2.0 * y)
dtdd = np.zeros(len(d))
dtdd[x12] -= 6.0 / self.width * y * (1.0 - y)
c6 = (sigma0**2 / d2)**3
c12 = c6**2
e = 4 * epsilon0 * (c12 - c6)
energy += np.dot(t, e)
F = (24 * epsilon0 * (2 * c12 - c6) / d2 * t -
e * dtdd / d)[:, np.newaxis] * DOO
forces[m * 3 + o] -= F.sum(0)
forces[m * 3 + 3 + o::3] += F
for j in range(3):
D = R[m + 1:] - R[m, j] + shift[:, np.newaxis]
r2 = (D**2).sum(axis=2)
r = r2**0.5
e = charges[j] * charges / r * units.Hartree * units.Bohr
energy += np.dot(t, e).sum()
F = (e / r2 * t[:, np.newaxis])[:, :, np.newaxis] * D
FOO = -(e.sum(1) * dtdd / d)[:, np.newaxis] * DOO
forces[(m + 1) * 3 + o::3] += FOO
forces[m * 3 + o] -= FOO.sum(0)
forces[(m + 1) * 3:] += F.reshape((-1, 3))
forces[m * 3 + j] -= F.sum(axis=0).sum(axis=0)
if self.pcpot:
e, f = self.pcpot.calculate(np.tile(charges, nh2o),
self.atoms.positions)
energy += e
forces += f
self.results['energy'] = energy
self.results['forces'] = forces
def embed(self, charges):
"""Embed atoms in point-charges."""
self.pcpot = PointChargePotential(charges)
return self.pcpot
def check_state(self, atoms, tol=1e-15):
system_changes = Calculator.check_state(self, atoms, tol)
if self.pcpot and self.pcpot.mmpositions is not None:
system_changes.append('positions')
return system_changes
def add_virtual_sites(self, positions):
return positions # no virtual sites
def redistribute_forces(self, forces):
return forces
def get_virtual_charges(self, atoms):
charges = np.empty(len(atoms))
charges[:] = qH
if atoms.numbers[0] == 8:
charges[::3] = -2 * qH
else:
charges[2::3] = -2 * qH
return charges
class PointChargePotential:
def __init__(self, mmcharges):
"""Point-charge potential for TIP3P.
Only used for testing QMMM.
"""
self.mmcharges = mmcharges
self.mmpositions = None
self.mmforces = None
def set_positions(self, mmpositions, com_pv=None):
self.mmpositions = mmpositions
def calculate(self, qmcharges, qmpositions):
energy = 0.0
self.mmforces = np.zeros_like(self.mmpositions)
qmforces = np.zeros_like(qmpositions)
for C, R, F in zip(self.mmcharges, self.mmpositions, self.mmforces):
d = qmpositions - R
r2 = (d**2).sum(1)
e = units.Hartree * units.Bohr * C * r2**-0.5 * qmcharges
energy += e.sum()
f = (e / r2)[:, np.newaxis] * d
qmforces += f
F -= f.sum(0)
self.mmpositions = None
return energy, qmforces
def get_forces(self, calc):
return self.mmforces
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