"""Langevin dynamics class."""
import numpy as np
from ase.md.md import MolecularDynamics
from ase.parallel import world
[docs]class Langevin(MolecularDynamics):
"""Langevin (constant N, V, T) molecular dynamics.
Usage: Langevin(atoms, dt, temperature, friction)
atoms
The list of atoms.
dt
The time step.
temperature
The desired temperature, in energy units.
friction
A friction coefficient, typically 1e-4 to 1e-2.
fixcm
If True, the position and momentum of the center of mass is
kept unperturbed. Default: True.
rng
Random number generator, by default numpy.random. Must have a
standard_normal method matching the signature of
numpy.random.standard_normal.
The temperature and friction are normally scalars, but in principle one
quantity per atom could be specified by giving an array.
RATTLE constraints can be used with these propagators, see:
E. V.-Eijnden, and G. Ciccotti, Chem. Phys. Lett. 429, 310 (2006)
The propagator is Equation 23 (Eq. 39 if RATTLE constraints are used)
of the above reference. That reference also contains another
propagator in Eq. 21/34; but that propagator is not quasi-symplectic
and gives a systematic offset in the temperature at large time steps.
This dynamics accesses the atoms using Cartesian coordinates."""
# Helps Asap doing the right thing. Increment when changing stuff:
_lgv_version = 3
def __init__(self, atoms, timestep, temperature, friction, fixcm=True,
trajectory=None, logfile=None, loginterval=1,
communicator=world, rng=np.random, append_trajectory=False):
self.temp = temperature
self.fr = friction
self.fixcm = fixcm # will the center of mass be held fixed?
self.communicator = communicator
self.rng = rng
MolecularDynamics.__init__(self, atoms, timestep, trajectory,
logfile, loginterval,
append_trajectory=append_trajectory)
self.updatevars()
def todict(self):
d = MolecularDynamics.todict(self)
d.update({'temperature': self.temp,
'friction': self.fr,
'fix-cm': self.fixcm})
return d
def set_temperature(self, temperature):
self.temp = temperature
self.updatevars()
def set_friction(self, friction):
self.fr = friction
self.updatevars()
def set_timestep(self, timestep):
self.dt = timestep
self.updatevars()
def updatevars(self):
dt = self.dt
T = self.temp
fr = self.fr
masses = self.masses
sigma = np.sqrt(2 * T * fr / masses)
self.c1 = dt / 2. - dt * dt * fr / 8.
self.c2 = dt * fr / 2 - dt * dt * fr * fr / 8.
self.c3 = np.sqrt(dt) * sigma / 2. - dt**1.5 * fr * sigma / 8.
self.c5 = dt**1.5 * sigma / (2 * np.sqrt(3))
self.c4 = fr / 2. * self.c5
# Works in parallel Asap, #GLOBAL number of atoms:
self.natoms = self.atoms.get_number_of_atoms()
def step(self, f=None):
atoms = self.atoms
natoms = len(atoms)
if f is None:
f = atoms.get_forces()
# This velocity as well as xi, eta and a few other variables are stored
# as attributes, so Asap can do its magic when atoms migrate between
# processors.
self.v = atoms.get_velocities()
self.xi = self.rng.standard_normal(size=(natoms, 3))
self.eta = self.rng.standard_normal(size=(natoms, 3))
# When holonomic constraints for rigid linear triatomic molecules are
# present, ask the constraints to redistribute xi and eta within each
# triple defined in the constraints. This is needed to achieve the
# correct target temperature.
for constraint in self.atoms.constraints:
if hasattr(constraint, 'redistribute_forces_md'):
constraint.redistribute_forces_md(atoms, self.xi, rand=True)
constraint.redistribute_forces_md(atoms, self.eta, rand=True)
if self.communicator is not None:
self.communicator.broadcast(self.xi, 0)
self.communicator.broadcast(self.eta, 0)
# First halfstep in the velocity.
self.v += (self.c1 * f / self.masses - self.c2 * self.v +
self.c3 * self.xi - self.c4 * self.eta)
# Full step in positions
x = atoms.get_positions()
if self.fixcm:
old_cm = atoms.get_center_of_mass()
# Step: x^n -> x^(n+1) - this applies constraints if any.
atoms.set_positions(x + self.dt * self.v + self.c5 * self.eta)
if self.fixcm:
new_cm = atoms.get_center_of_mass()
d = old_cm - new_cm
# atoms.translate(d) # Does not respect constraints
atoms.set_positions(atoms.get_positions() + d)
# recalc velocities after RATTLE constraints are applied
self.v = (self.atoms.get_positions() - x -
self.c5 * self.eta) / self.dt
f = atoms.get_forces(md=True)
# Update the velocities
self.v += (self.c1 * f / self.masses - self.c2 * self.v +
self.c3 * self.xi - self.c4 * self.eta)
if self.fixcm: # subtract center of mass vel
v_cm = self._get_com_velocity()
self.v -= v_cm
# Second part of RATTLE taken care of here
atoms.set_momenta(self.v * self.masses)
return f
def _get_com_velocity(self):
"""Return the center of mass velocity.
Internal use only. This function can be reimplemented by Asap.
"""
return np.dot(self.masses.flatten(), self.v) / self.masses.sum()