def test_qmmm_acn():
import numpy as np
import ase.units as units
from ase import Atoms
from ase.calculators.acn import (ACN, m_me, r_cn, r_mec,
sigma_me, sigma_c, sigma_n,
epsilon_me, epsilon_c, epsilon_n)
from ase.calculators.qmmm import SimpleQMMM, LJInteractionsGeneral, EIQMMM
from ase.constraints import FixLinearTriatomic
from ase.optimize import BFGS
# From https://www.sciencedirect.com/science/article/pii/S0166128099002079
eref = 4.9 * units.kcal / units.mol
dref = 3.368
aref = 79.1
sigma = np.array([sigma_me, sigma_c, sigma_n])
epsilon = np.array([epsilon_me, epsilon_c, epsilon_n])
inter = LJInteractionsGeneral(sigma, epsilon, sigma, epsilon, 3)
for calc in [ACN(),
SimpleQMMM([0, 1, 2], ACN(), ACN(), ACN()),
SimpleQMMM([0, 1, 2], ACN(), ACN(), ACN(), vacuum=3.0),
EIQMMM([0, 1, 2], ACN(), ACN(), inter),
EIQMMM([0, 1, 2], ACN(), ACN(), inter, vacuum=3.0),
EIQMMM([3, 4, 5], ACN(), ACN(), inter, vacuum=3.0)]:
dimer = Atoms('CCNCCN',
[(-r_mec, 0, 0),
(0, 0, 0),
(r_cn, 0, 0),
(r_mec, 3.7, 0),
(0, 3.7, 0),
(-r_cn, 3.7, 0)])
masses = dimer.get_masses()
masses[::3] = m_me
dimer.set_masses(masses)
dimer.calc = calc
fixd = FixLinearTriatomic(triples=[(0, 1, 2), (3, 4, 5)])
dimer.set_constraint(fixd)
opt = BFGS(dimer, maxstep=0.04,
trajectory=calc.name + '.traj', logfile=calc.name + 'd.log')
opt.run(0.001, steps=1000)
e0 = dimer.get_potential_energy()
d0 = dimer.get_distance(1, 4)
a0 = dimer.get_angle(2, 1, 4)
fmt = '{0:>25}: {1:.3f} {2:.3f} {3:.1f}'
print(fmt.format(calc.name, -e0, d0, a0))
assert abs(e0 + eref) < 0.013
assert abs(d0 - dref) < 0.224
assert abs(a0 - aref) < 2.9
print(fmt.format('reference', eref, dref, aref))
def test_rattle():
i = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
for calc in [
TIP3P(),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P()),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i)
]:
dimer = s22('Water_dimer')
for m in [0, 3]:
dimer.set_angle(m + 1, m, m + 2, angleHOH)
dimer.set_distance(m, m + 1, rOH, fix=0)
dimer.set_distance(m, m + 2, rOH, fix=0)
fixOH1 = [(3 * i, 3 * i + 1) for i in range(2)]
fixOH2 = [(3 * i, 3 * i + 2) for i in range(2)]
fixHH = [(3 * i + 1, 3 * i + 2) for i in range(2)]
dimer.set_constraint(FixBondLengths(fixOH1 + fixOH2 + fixHH))
dimer.calc = calc
e = dimer.get_potential_energy()
md = VelocityVerlet(dimer,
8.0 * units.fs,
trajectory=calc.name + '.traj',
logfile=calc.name + '.log',
loginterval=5)
md.run(25)
de = dimer.get_potential_energy() - e
assert abs(de - -0.028) < 0.001
def test_rattle_linear():
"""Test RATTLE and QM/MM for rigid linear acetonitrile."""
import numpy as np
from ase import Atoms
from ase.calculators.acn import (ACN, m_me, r_cn, r_mec, sigma_me, sigma_c,
sigma_n, epsilon_me, epsilon_c, epsilon_n)
from ase.calculators.qmmm import SimpleQMMM, EIQMMM, LJInteractionsGeneral
from ase.md.verlet import VelocityVerlet
from ase.constraints import FixLinearTriatomic
import ase.units as units
sigma = np.array([sigma_me, sigma_c, sigma_n])
epsilon = np.array([epsilon_me, epsilon_c, epsilon_n])
i = LJInteractionsGeneral(sigma, epsilon, sigma, epsilon, 3)
for calc in [
ACN(),
SimpleQMMM([0, 1, 2], ACN(), ACN(), ACN()),
EIQMMM([0, 1, 2], ACN(), ACN(), i)
]:
dimer = Atoms('CCNCCN', [(-r_mec, 0, 0), (0, 0, 0), (r_cn, 0, 0),
(r_mec, 3.7, 0), (0, 3.7, 0),
(-r_cn, 3.7, 0)])
masses = dimer.get_masses()
masses[::3] = m_me
dimer.set_masses(masses)
fixd = FixLinearTriatomic(triples=[(0, 1, 2), (3, 4, 5)])
dimer.set_constraint(fixd)
dimer.calc = calc
d1 = dimer[:3].get_all_distances()
d2 = dimer[3:].get_all_distances()
e = dimer.get_potential_energy()
md = VelocityVerlet(dimer,
2.0 * units.fs,
trajectory=calc.name + '.traj',
logfile=calc.name + '.log',
loginterval=20)
md.run(100)
de = dimer.get_potential_energy() - e
assert np.all(abs(dimer[:3].get_all_distances() - d1) < 1e-10)
assert np.all(abs(dimer[3:].get_all_distances() - d2) < 1e-10)
assert abs(de - -0.005) < 0.001
def test_orca_qmmm():
from ase.calculators.tip4p import TIP4P, epsilon0, sigma0
from ase.calculators.orca import ORCA
from ase.calculators.qmmm import EIQMMM, LJInteractions
from ase.data import s22
atoms = s22.create_s22_system('Water_dimer')
qmcalc = ORCA(label='water', orcasimpleinput='BLYP def2-SVP')
lj = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
atoms.calc = EIQMMM(selection=[0, 1, 2],
qmcalc=qmcalc,
mmcalc=TIP4P(),
interaction=lj,
output='orca_qmmm.log')
e = atoms.get_potential_energy()
assert abs(e + 2077.45445852) < 1.0
def test_qmmm_tip4p():
from math import cos, sin, pi
import numpy as np
#import matplotlib.pyplot as plt
import ase.units as units
from ase import Atoms
from ase.calculators.tip4p import TIP4P, epsilon0, sigma0, rOH, angleHOH
from ase.calculators.qmmm import (SimpleQMMM, EIQMMM, LJInteractions,
LJInteractionsGeneral)
from ase.constraints import FixInternals
from ase.optimize import BFGS
r = rOH
a = angleHOH * pi / 180
# From https://doi.org/10.1063/1.445869
eexp = 6.24 * units.kcal / units.mol
dexp = 2.75
aexp = 46
D = np.linspace(2.5, 3.5, 30)
i = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
# General LJ interaction object
sigma_mm = np.array([sigma0, 0, 0])
epsilon_mm = np.array([epsilon0, 0, 0])
sigma_qm = np.array([sigma0, 0, 0])
epsilon_qm = np.array([epsilon0, 0, 0])
ig = LJInteractionsGeneral(sigma_qm, epsilon_qm, sigma_mm, epsilon_mm, 3)
for calc in [
TIP4P(),
SimpleQMMM([0, 1, 2], TIP4P(), TIP4P(), TIP4P()),
SimpleQMMM([0, 1, 2], TIP4P(), TIP4P(), TIP4P(), vacuum=3.0),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), i),
EIQMMM([3, 4, 5], TIP4P(), TIP4P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), ig),
EIQMMM([3, 4, 5], TIP4P(), TIP4P(), ig, vacuum=3.0),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), ig, vacuum=3.0)
]:
dimer = Atoms('OH2OH2', [(0, 0, 0), (r * cos(a), 0, r * sin(a)),
(r, 0, 0), (0, 0, 0),
(r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0)])
dimer.calc = calc
E = []
F = []
for d in D:
dimer.positions[3:, 0] += d - dimer.positions[3, 0]
E.append(dimer.get_potential_energy())
F.append(dimer.get_forces())
F = np.array(F)
#plt.plot(D, E)
F1 = np.polyval(np.polyder(np.polyfit(D, E, 7)), D)
F2 = F[:, :3, 0].sum(1)
error = abs(F1 - F2).max()
assert error < 0.01
dimer.constraints = FixInternals(bonds=[(r, (0, 1)), (r, (0, 2)),
(r, (3, 4)), (r, (3, 5))],
angles=[(a, (2, 0, 1)),
(a, (5, 3, 4))])
opt = BFGS(dimer,
maxstep=0.04,
trajectory=calc.name + '.traj',
logfile=calc.name + 'd.log')
opt.run(0.01)
e0 = dimer.get_potential_energy()
d0 = dimer.get_distance(0, 3)
R = dimer.positions
v1 = R[2] - R[3]
v2 = R[3] - (R[5] + R[4]) / 2
a0 = np.arccos(
np.dot(v1, v2) /
(np.dot(v1, v1) * np.dot(v2, v2))**0.5) / np.pi * 180
fmt = '{0:>23}: {1:.3f} {2:.3f} {3:.3f} {4:.1f}'
print(fmt.format(calc.name, -min(E), -e0, d0, a0))
assert abs(e0 + eexp) < 0.002
assert abs(d0 - dexp) < 0.006
assert abs(a0 - aexp) < 2.5
print(fmt.format('reference', 9.999, eexp, dexp, aexp))
from ase import Atoms
from ase.calculators.acn import (ACN, m_me, r_cn, r_mec, sigma_me, sigma_c,
sigma_n, epsilon_me, epsilon_c, epsilon_n)
from ase.calculators.qmmm import SimpleQMMM, EIQMMM, LJInteractionsGeneral
from ase.md.verlet import VelocityVerlet
from ase.constraints import FixLinearTriatomic
import ase.units as units
sigma = np.array([sigma_me, sigma_c, sigma_n])
epsilon = np.array([epsilon_me, epsilon_c, epsilon_n])
i = LJInteractionsGeneral(sigma, epsilon, sigma, epsilon, 3)
for calc in [
ACN(),
SimpleQMMM([0, 1, 2], ACN(), ACN(), ACN()),
EIQMMM([0, 1, 2], ACN(), ACN(), i)
]:
dimer = Atoms('CCNCCN', [(-r_mec, 0, 0), (0, 0, 0), (r_cn, 0, 0),
(r_mec, 3.7, 0), (0, 3.7, 0), (-r_cn, 3.7, 0)])
masses = dimer.get_masses()
masses[::3] = m_me
dimer.set_masses(masses)
fixd = FixLinearTriatomic(triples=[(0, 1, 2), (3, 4, 5)])
dimer.set_constraint(fixd)
dimer.calc = calc
D = np.linspace(2.5, 3.5, 30)
i = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
# General LJ interaction object
sigma_mm = np.array([0, 0, sigma0])
epsilon_mm = np.array([0, 0, epsilon0])
sigma_qm = np.array([0, 0, sigma0])
epsilon_qm = np.array([0, 0, epsilon0])
ig = LJInteractionsGeneral(sigma_qm, epsilon_qm, sigma_mm, epsilon_mm, 3)
for calc in [TIP3P(),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P()),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P(), vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i),
EIQMMM([3, 4, 5], TIP3P(), TIP3P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), ig),
EIQMMM([3, 4, 5], TIP3P(), TIP3P(), ig, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), ig, vacuum=3.0)]:
dimer = Atoms('H2OH2O',
[(r * cos(a), 0, r * sin(a)),
(r, 0, 0),
(0, 0, 0),
(r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0),
(0, 0, 0)])
dimer.calc = calc
E = []
interaction = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
for selection in [[0, 1, 2], [3, 4, 5]]:
name = ''.join(str(i) for i in selection)
dimer = Atoms('OH2OH2', [(0, 0, 0), (-r * cos(a / 2), r * sin(a / 2), 0),
(-r * cos(a / 2), -r * sin(a / 2), 0), (0, 0, 0),
(-r * cos(a), 0, r * sin(a)), (-r, 0, 0)])
dimer.positions[3:, 0] += 2.8
dimer.constraints = FixBondLengths([
((selection[i] + 3) % 6, (selection[i - 1] + 3) % 6) for i in range(3)
])
dimer.calc = EIQMMM(selection,
GPAW(txt=name + '.txt', h=0.16),
TIP4P(),
interaction,
vacuum=4,
embedding=Embedding(rc=0.2, rc2=20, width=1),
output=name + '.out')
opt = LBFGS(dimer, trajectory=name + '.traj')
opt.run(0.02)
monomer = dimer[selection]
monomer.center(vacuum=4)
monomer.calc = GPAW(txt=name + 'M.txt', h=0.16)
opt = PreconLBFGS(monomer, precon=Exp(A=3), trajectory=name + 'M.traj')
opt.run(0.02)
e0 = monomer.get_potential_energy()
be = dimer.get_potential_energy() - e0
d = dimer.get_distance(0, 3)
print(name, be, d)
def test_qmmm(testdir):
r = rOH
a = angleHOH * pi / 180
# From https://doi.org/10.1063/1.445869
eexp = 6.50 * units.kcal / units.mol
dexp = 2.74
aexp = 27
D = np.linspace(2.5, 3.5, 30)
i = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
# General LJ interaction object
sigma_mm = np.array([0, 0, sigma0])
epsilon_mm = np.array([0, 0, epsilon0])
sigma_qm = np.array([0, 0, sigma0])
epsilon_qm = np.array([0, 0, epsilon0])
ig = LJInteractionsGeneral(sigma_qm, epsilon_qm, sigma_mm, epsilon_mm, 3)
for calc in [
TIP3P(),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P()),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P(), vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i),
EIQMMM([3, 4, 5], TIP3P(), TIP3P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), ig),
EIQMMM([3, 4, 5], TIP3P(), TIP3P(), ig, vacuum=3.0),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), ig, vacuum=3.0)
]:
dimer = Atoms('H2OH2O',
[(r * cos(a), 0, r * sin(a)), (r, 0, 0), (0, 0, 0),
(r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0), (0, 0, 0)])
dimer.calc = calc
E = []
F = []
for d in D:
dimer.positions[3:, 0] += d - dimer.positions[5, 0]
E.append(dimer.get_potential_energy())
F.append(dimer.get_forces())
F = np.array(F)
F1 = np.polyval(np.polyder(np.polyfit(D, E, 7)), D)
F2 = F[:, :3, 0].sum(1)
error = abs(F1 - F2).max()
assert error < 0.01
dimer.constraints = FixInternals(bonds=[(r, (0, 2)), (r, (1, 2)),
(r, (3, 5)), (r, (4, 5))],
angles_deg=[
(np.degrees(a), (0, 2, 1)),
(np.degrees(a), (3, 5, 4))
])
opt = GPMin(dimer,
trajectory=calc.name + '.traj',
logfile=calc.name + 'd.log')
opt.run(0.01)
e0 = dimer.get_potential_energy()
d0 = dimer.get_distance(2, 5)
R = dimer.positions
v1 = R[1] - R[5]
v2 = R[5] - (R[3] + R[4]) / 2
a0 = np.arccos(
np.dot(v1, v2) /
(np.dot(v1, v1) * np.dot(v2, v2))**0.5) / np.pi * 180
fmt = '{0:>20}: {1:.3f} {2:.3f} {3:.3f} {4:.1f}'
print(fmt.format(calc.name, -min(E), -e0, d0, a0))
assert abs(e0 + eexp) < 0.002
assert abs(d0 - dexp) < 0.01
assert abs(a0 - aexp) < 4
print(fmt.format('reference', 9.999, eexp, dexp, aexp))
def test_turbomole_qmmm():
"""Test the Turbomole calculator in simple QMMM and
explicit interaction QMMM simulations."""
r = rOH
a = angleHOH * pi / 180
D = np.linspace(2.5, 3.5, 30)
interaction = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
qm_par = {'esp fit': 'kollman', 'multiplicity': 1}
for calc in [
TIP3P(),
SimpleQMMM([0, 1, 2], Turbomole(**qm_par), TIP3P(), TIP3P()),
SimpleQMMM([0, 1, 2],
Turbomole(**qm_par),
TIP3P(),
TIP3P(),
vacuum=3.0),
EIQMMM([0, 1, 2], Turbomole(**qm_par), TIP3P(), interaction),
EIQMMM([3, 4, 5],
Turbomole(**qm_par),
TIP3P(),
interaction,
vacuum=3.0),
EIQMMM([0, 1, 2],
Turbomole(**qm_par),
TIP3P(),
interaction,
vacuum=3.0)
]:
dimer = Atoms('H2OH2O',
[(r * cos(a), 0, r * sin(a)), (r, 0, 0), (0, 0, 0),
(r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0), (0, 0, 0)])
dimer.calc = calc
E = []
F = []
for d in D:
dimer.positions[3:, 0] += d - dimer.positions[5, 0]
E.append(dimer.get_potential_energy())
F.append(dimer.get_forces())
F = np.array(F)
F1 = np.polyval(np.polyder(np.polyfit(D, E, 7)), D)
F2 = F[:, :3, 0].sum(1)
error = abs(F1 - F2).max()
assert error < 0.9
dimer.set_constraint(
FixInternals(bonds=[(r, (0, 2)), (r, (1, 2)), (r, (3, 5)),
(r, (4, 5))],
angles_deg=[(angleHOH, (0, 2, 1)),
(angleHOH, (3, 5, 4))]))
opt = BFGS(dimer,
trajectory=calc.name + '.traj',
logfile=calc.name + 'd.log')
opt.run(0.01)
e0 = dimer.get_potential_energy()
d0 = dimer.get_distance(2, 5)
R = dimer.positions
v1 = R[1] - R[5]
v2 = R[5] - (R[3] + R[4]) / 2
a0 = np.arccos(
np.dot(v1, v2) /
(np.dot(v1, v1) * np.dot(v2, v2))**0.5) / np.pi * 180
fmt = '{0:>20}: {1:.3f} {2:.3f} {3:.3f} {4:.1f}'
print(fmt.format(calc.name, -min(E), -e0, d0, a0))
import ase.units as units
from ase.calculators.tip3p import TIP3P, epsilon0, sigma0, rOH, angleHOH
from ase.calculators.qmmm import SimpleQMMM, EIQMMM, LJInteractions
from ase.data.s22 import create_s22_system as s22
from ase.md.verlet import VelocityVerlet
from ase.constraints import FixBondLengths
i = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
for calc in [
TIP3P(),
SimpleQMMM([0, 1, 2], TIP3P(), TIP3P(), TIP3P()),
EIQMMM([0, 1, 2], TIP3P(), TIP3P(), i)
]:
dimer = s22('Water_dimer')
for m in [0, 3]:
dimer.set_angle(m + 1, m, m + 2, angleHOH)
dimer.set_distance(m, m + 1, rOH, fix=0)
dimer.set_distance(m, m + 2, rOH, fix=0)
fixOH1 = [(3 * i, 3 * i + 1) for i in range(2)]
fixOH2 = [(3 * i, 3 * i + 2) for i in range(2)]
fixHH = [(3 * i + 1, 3 * i + 2) for i in range(2)]
dimer.set_constraint(FixBondLengths(fixOH1 + fixOH2 + fixHH))
dimer.calc = calc
e = dimer.get_potential_energy()
md = VelocityVerlet(dimer,
2.0 * units.fs,
from __future__ import print_function
from ase.data import s22
from ase.calculators.tip3p import TIP3P, epsilon0, sigma0
from ase.calculators.qmmm import EIQMMM, LJInteractions, Embedding
from gpaw import GPAW
# Create system
atoms = s22.create_s22_system('Water_dimer')
atoms.center(vacuum=4.0)
# Make QM atoms selection of first water molecule:
qm_idx = range(3)
# Set up interaction & embedding object
interaction = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
embedding = Embedding(rc=0.02) # Short range analytical potential cutoff
# Set up calculator
atoms.calc = EIQMMM(qm_idx,
GPAW(txt='qm.out'),
TIP3P(),
interaction,
embedding=embedding,
vacuum=None, # if None, QM cell = MM cell
output='qmmm.log')
print(atoms.get_potential_energy())
a = angleHOH * np.pi / 180
# From http://dx.doi.org/10.1063/1.445869
eexp = 6.24 * units.kcal / units.mol
dexp = 2.75
aexp = 46
D = np.linspace(2.5, 3.5, 30)
inter = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
for calc in [
TIP4P(),
SimpleQMMM([0, 1, 2], TIP4P(), TIP4P(), TIP4P()),
SimpleQMMM([0, 1, 2], TIP4P(), TIP4P(), TIP4P(), vacuum=3.0),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), inter),
EIQMMM([0, 1, 2], TIP4P(), TIP4P(), inter, vacuum=3.0),
EIQMMM([3, 4, 5], TIP4P(), TIP4P(), inter, vacuum=3.0)
]:
dimer = Atoms('OH2OH2', [(0, 0, 0), (r * cos(a), 0, r * sin(a)), (r, 0, 0),
(0, 0, 0), (r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0)])
dimer.calc = calc
E = []
F = []
for d in D:
dimer.positions[3:, 0] += d - dimer.positions[3, 0]
E.append(dimer.get_potential_energy())
F.append(dimer.get_forces())
F = np.array(F)
r = rOH
a = angleHOH * pi / 180
D = np.linspace(2.5, 3.5, 30)
interaction = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
qm_par = {'esp fit': 'kollman', 'multiplicity': 1}
for calc in [
TIP3P(),
SimpleQMMM([0, 1, 2], Turbomole(**qm_par), TIP3P(), TIP3P()),
SimpleQMMM([0, 1, 2],
Turbomole(**qm_par),
TIP3P(),
TIP3P(),
vacuum=3.0),
EIQMMM([0, 1, 2], Turbomole(**qm_par), TIP3P(), interaction),
EIQMMM([3, 4, 5],
Turbomole(**qm_par),
TIP3P(),
interaction,
vacuum=3.0),
EIQMMM([0, 1, 2],
Turbomole(**qm_par),
TIP3P(),
interaction,
vacuum=3.0)
]:
dimer = Atoms('H2OH2O', [(r * cos(a), 0, r * sin(a)), (r, 0, 0), (0, 0, 0),
(r * cos(a / 2), r * sin(a / 2), 0),
(r * cos(a / 2), -r * sin(a / 2), 0), (0, 0, 0)])
dimer.calc = calc