gamma=1e-3,
max_displacement=0.01)
i = 0
while system.analysis.min_dist() < min_dist and i < warm_n_times:
print("minimization: {:+.2e}".format(system.analysis.energy()["total"]))
system.integrator.run(warm_steps)
i += 1
print("minimization: {:+.2e}".format(system.analysis.energy()["total"]))
print()
system.integrator.set_vv()
# activate thermostat
system.thermostat.set_langevin(kT=temperature, gamma=1.0, seed=42)
widom = reaction_ensemble.WidomInsertion(temperature=temperature, seed=77)
# add insertion reaction
insertion_reaction_id = 0
widom.add_reaction(reactant_types=[],
reactant_coefficients=[],
product_types=[1, 2],
product_coefficients=[1, 1],
default_charges={
1: -1,
2: +1
})
print(widom.get_status())
system.setup_type_map([0, 1, 2])
n_iterations = 100
class WidomInsertionTest(ut.TestCase):
"""Test the implementation of the widom insertion.
The excess chemical potential is calculated for identical particles in
a 20 cubed box with a single particle, interacting via a LJ-potential
(cut-off at 5 sigma)."""
N0 = 1
TEMPERATURE = 0.5
TYPE_HA = 0
CHARGE_HA = 0
LJ_EPS = 1.0
LJ_SIG = 1.0
LJ_CUT = 5
BOX_L = 2 * LJ_CUT
LJ_SHIFT = lj_potential(LJ_CUT, LJ_EPS, LJ_SIG, LJ_CUT + 1, 0.0)
radius = np.linspace(1e-10, LJ_CUT, 1000)
# numerical integration for radii smaller than the cut-off in spherical
# coordinates
integrateUpToCutOff = 4 * np.pi * np.trapz(radius**2 * np.exp(
-lj_potential(radius, LJ_EPS, LJ_SIG, LJ_CUT, LJ_SHIFT) / TEMPERATURE),
x=radius)
# numerical solution for V_lj=0 => corresponds to the volume (as exp(0)=1)
integreateRest = (BOX_L**3 - 4.0 / 3.0 * np.pi * LJ_CUT**3)
# calculate excess chemical potential of the system, see Frenkel Smith,
# p 174. Note: He uses scaled coordinates, which is why we need to divide
# by the box volume
target_mu_ex = -TEMPERATURE * \
np.log((integrateUpToCutOff + integreateRest) / BOX_L**3)
system = espressomd.System(box_l=np.ones(3) * BOX_L)
system.cell_system.set_n_square()
system.seed = system.cell_system.get_state()['n_nodes'] * [2]
np.random.seed(69) # make reaction code fully deterministic
system.cell_system.skin = 0.4
volume = np.prod(system.box_l) # cuboid box
Widom = reaction_ensemble.WidomInsertion(temperature=TEMPERATURE, seed=1)
def setUp(self):
self.system.part.add(id=0,
pos=0.5 * self.system.box_l,
type=self.TYPE_HA)
self.system.non_bonded_inter[self.TYPE_HA,
self.TYPE_HA].lennard_jones.set_params(
epsilon=self.LJ_EPS,
sigma=self.LJ_SIG,
cutoff=self.LJ_CUT,
shift="auto")
self.Widom.add_reaction(reactant_types=[],
reactant_coefficients=[],
product_types=[self.TYPE_HA],
product_coefficients=[1],
default_charges={self.TYPE_HA: self.CHARGE_HA})
def test_widom_insertion(self):
system = WidomInsertionTest.system
Widom = WidomInsertionTest.Widom
target_mu_ex = WidomInsertionTest.target_mu_ex
system.seed = system.cell_system.get_state()['n_nodes'] * [
np.random.randint(5)
]
num_samples = 100000
for _ in range(num_samples):
# 0 for insertion reaction
Widom.measure_excess_chemical_potential(0)
mu_ex = Widom.measure_excess_chemical_potential(0)
deviation_mu_ex = abs(mu_ex[0] - target_mu_ex)
# error
self.assertLess(
deviation_mu_ex - 1e-3,
0.0,
msg=
"\nExcess chemical potential for single LJ-particle computed via widom insertion gives a wrong value.\n"
+ " average mu_ex: " + str(mu_ex[0]) + " mu_ex_std_err: " +
str(mu_ex[1]) + " target_mu_ex: " + str(target_mu_ex))
# Warmup Integration Loop
act_min_dist = system.analysis.min_dist()
i = 0
while (i < warm_n_times):
print(i, "warmup")
system.integrator.run(steps=warm_steps)
i += 1
#Increase LJ cap
lj_cap = lj_cap + 10
system.force_cap = lj_cap
# remove force capping
system.force_cap = 0
unimportant_K_diss = 0.0088
RE = reaction_ensemble.WidomInsertion(
temperature=temperature, exclusion_radius=1.0)
RE.add_reaction(gamma=unimportant_K_diss, reactant_types=[], reactant_coefficients=[], product_types=[
1, 2], product_coefficients=[1, 1], default_charges={1: -1, 2: +1})
print(RE.get_status())
system.setup_type_map([0, 1, 2])
for i in range(10000):
for j in range(30):
RE.measure_excess_chemical_potential(0) # 0 for insertion reaction
system.integrator.run(steps=2)
system.integrator.run(steps=500)
if(i % 100 == 0):
print("mu_ex_pair", RE.measure_excess_chemical_potential(0))
#0 for insertion reaction
print("HA", system.number_of_particles(type=0), "A-",
system.number_of_particles(type=1), "H+", system.number_of_particles(type=2))
