def test_kinetic_energy_calculations():
atoms = 5
T = 298.15
E_kin = kinetic_energy_for_temperature(atoms, T)
T_calc = temperature_for_kinetic_energy(atoms, E_kin)
assert T == pytest.approx(T_calc)
def test_fixed_dof_kinetic_energy():
atoms = 5
T = 298.15
E_kin_ref = kinetic_energy_for_temperature(atoms, T)
fully_fixed = 3 * atoms
E_kin_fully_fixed = kinetic_energy_for_temperature(atoms,
T,
fixed_dof=fully_fixed)
assert E_kin_fully_fixed == 0.
translation_fixed = 3
T_trans_fixed = temperature_for_kinetic_energy(atoms,
E_kin_ref,
fixed_dof=translation_fixed)
assert T_trans_fixed > T
def test_scale_velocities_to_temperatue():
atoms = 5
masses = np.ones(atoms)
T = 298.15
E_ref = kinetic_energy_for_temperature(atoms, T) # in Bohr
v_unscaled = 2 * (np.random.rand(atoms, 3) - 0.5)
v_scaled = scale_velocities_to_temperatue(masses, v_unscaled, T)
E_scaled = kinetic_energy_from_velocities(masses, v_scaled)
assert E_scaled == pytest.approx(E_ref)
def test_get_mb_velocities_for_geom(remove_com, remove_rot):
geom = geom_loader("lib:benzene.xyz")
T = 298.15
fixed_dof = 0
if remove_com:
fixed_dof += 3
if remove_rot:
fixed_dof += 3
v = get_mb_velocities_for_geom(geom,
T,
remove_com=remove_com,
remove_rot=remove_rot) # in Bohr/fs
E_kin = kinetic_energy_from_velocities(geom.masses, v)
E_ref = kinetic_energy_for_temperature(len(geom.atoms),
T,
fixed_dof=fixed_dof) # in Bohr
assert E_kin == pytest.approx(E_ref)
def md(geom,
v0,
steps,
dt,
remove_com_v=True,
thermostat=None,
T=298.15,
timecon=100,
term_funcs=None,
constraints=None,
constraint_kwargs=None,
verbose=True):
"""Velocity verlet integrator.
Parameters
----------
geom : Geometry
The system for which the dynamics are to be run.
v0 : np.array, floats
Initial velocities in Bohr/fs.
steps : float
Number of simulation steps.
dt : float
Timestep in fs.
remove_com_v : bool, default=True
Remove center-of-mass velocity.
thermostat : str, optional, default None
Which and whether to use a thermostat.
T : float, optional, default=None
Desired temperature in thermostated runs.
timecon : float
Timeconsanst of the thermostat in fs.
term_funcs : dict, optional
Iterable of functions that are called with the atomic
coordinates in every MD cycle and result in termination
constraints : 2d iterable, optional
2D iterable containing atom indices describing constrained
bond lengths.
of the MD integration when they evaluate to true.
constraint_kwargs : dict, optional
Keyword arguments for the constraint algorithm.
verbose : bool, default=True
Do additional printing when True.
"""
assert geom.coord_type == "cart"
if term_funcs is None:
term_funcs = dict()
if verbose:
t_ps = steps * dt * 1e-3 # Total simulation time
print(
f"Doing {steps} steps of {dt:.4f} fs for a total of {t_ps:.2f} ps."
)
energy_forces_getter = energy_forces_getter_closure(geom)
if constraint_kwargs is None:
constraint_kwargs = dict()
if remove_com_v and (not thermostat):
print(
"Center of mass velocity removal requested, but thermostat is disabled. "
"Disabling velocity removal.")
remove_com_v = False
# Fixed degrees of freedom
fixed_dof = 0
if remove_com_v:
fixed_dof += 3
constrained_md = constraints is not None
# Get RATTLE function from closure for constrained MD
if constrained_md:
fixed_dof += len(constraints)
rattle = rattle_closure(geom,
constraints,
dt,
energy_forces_getter=energy_forces_getter,
**constraint_kwargs)
if thermostat is not None:
thermo_func = THERMOSTATS[thermostat]
tau_t = dt / timecon
sigma = kinetic_energy_for_temperature(len(geom.atoms),
T,
fixed_dof=fixed_dof)
# In amu
masses = geom.masses
masses_rep = geom.masses_rep
total_mass = masses.sum()
x = geom.cart_coords
# v is given in Bohr/fs
v = v0
a_prev = np.zeros_like(x)
xs = list()
Ts = list()
E_tots = list()
E_pot, forces = energy_forces_getter(geom.coords)
t_cur = 0
terminate = False
terminate_key = None
T_avg = 0
log(logger, f"Running MD with Δt={dt:.2f} fs for {steps} steps.")
for step in range(steps):
xs.append(x.copy())
E_kin = kinetic_energy_from_velocities(masses, v.reshape(-1, 3))
T = temperature_for_kinetic_energy(len(masses),
E_kin,
fixed_dof=fixed_dof)
T_avg += T
Ts.append(T)
E_tot = E_pot + E_kin
E_tots.append(E_tot)
status_msg = (
f"Step {step:05d} {t_cur*1e-3: >6.2f} ps E={E_tot: >8.6f} E_h "
f"T={T: >8.2f} K <T>={T_avg/(step+1): >8.2f}")
if (step % 25) == 0:
log(logger, status_msg)
if verbose: print(status_msg)
if thermostat:
E_kin_new = thermo_func(E_kin, sigma, v.size - fixed_dof, tau_t)
scale = (E_kin_new / E_kin)**0.5
v *= scale
# RATTLE algorithm
if constrained_md:
x, v, E_pot, forces = rattle(x, v, forces)
# Simple Velocity-Verlet integration
else:
E_pot, forces = energy_forces_getter(geom.coords)
# Acceleration, convert from Hartree / (Bohr * amu) to Bohr/fs²
a = forces / masses_rep * FORCE2ACC
v += .5 * (a + a_prev) * dt
if remove_com_v:
v -= v * masses_rep / total_mass
# v*dt = Bohr/fs * fs -> Bohr
# a*dt**2 = Bohr/fs² * fs² -> Bohr
x += v * dt + .5 * a * dt**2
a_prev = a
# Update coordinates
geom.coords = x
for name, func in term_funcs.items():
if func(x.reshape(-1, 3)):
terminate = True
terminate_key = name
break
if terminate:
log(logger,
f"Termination function '{name}' evaluted to True. Breaking.")
break
if check_for_stop_sign():
break
# Advance time
t_cur += dt
log(logger, "")
md_result = MDResult(
coords=np.array(xs),
t_ps=t_cur * 1e-3,
step=step,
terminated=terminate_key,
T=np.array(Ts),
E_tot=np.array(E_tots),
)
return md_result