Source code for

'''Constant pressure/stress and temperature dynamics.

Combined Nose-Hoover and Parrinello-Rahman dynamics, creating an NPT
(or N,stress,T) ensemble.

The method is the one proposed by Melchionna et al. [1] and later
modified by Melchionna [2].  The differential equations are integrated
using a centered difference method [3].

 1. S. Melchionna, G. Ciccotti and B. L. Holian, "Hoover NPT dynamics
    for systems varying in shape and size", Molecular Physics 78, p. 533

 2. S. Melchionna, "Constrained systems and statistical distribution",
    Physical Review E, 61, p. 6165 (2000).

 3. B. L. Holian, A. J. De Groot, W. G. Hoover, and C. G. Hoover,
    "Time-reversible equilibrium and nonequilibrium isothermal-isobaric
    simulations with centered-difference Stoermer algorithms.", Physical
    Review A, 41, p. 4552 (1990).

import sys
import weakref

import numpy as np

from import MolecularDynamics
from ase import units

linalg = np.linalg

# Delayed imports:  If the trajectory object is reading a special ASAP version
# of HooverNPT, that class is imported from Asap.Dynamics.NPTDynamics.

[docs]class NPT(MolecularDynamics): classname = "NPT" # Used by the trajectory. _npt_version = 2 # Version number, used for Asap compatibility. def __init__(self, atoms, timestep, temperature=None, externalstress=None, ttime=None, pfactor=None, *, temperature_K=None, mask=None, trajectory=None, logfile=None, loginterval=1, append_trajectory=False): '''Constant pressure/stress and temperature dynamics. Combined Nose-Hoover and Parrinello-Rahman dynamics, creating an NPT (or N,stress,T) ensemble. The method is the one proposed by Melchionna et al. [1] and later modified by Melchionna [2]. The differential equations are integrated using a centered difference method [3]. See also NPTdynamics.tex The dynamics object is called with the following parameters: atoms: Atoms object The list of atoms. timestep: float The timestep in units matching eV, Å, u. temperature: float (deprecated) The desired temperature in eV. temperature_K: float The desired temperature in K. externalstress: float or nparray The external stress in eV/A^3. Either a symmetric 3x3 tensor, a 6-vector representing the same, or a scalar representing the pressure. Note that the stress is positive in tension whereas the pressure is positive in compression: giving a scalar p is equivalent to giving the tensor (-p, -p, -p, 0, 0, 0). ttime: float Characteristic timescale of the thermostat, in ASE internal units Set to None to disable the thermostat. WARNING: Not specifying ttime sets it to None, disabling the thermostat. pfactor: float A constant in the barostat differential equation. If a characteristic barostat timescale of ptime is desired, set pfactor to ptime^2 * B (where ptime is in units matching eV, Å, u; and B is the Bulk Modulus, given in eV/Å^3). Set to None to disable the barostat. Typical metallic bulk moduli are of the order of 100 GPa or 0.6 eV/A^3. WARNING: Not specifying pfactor sets it to None, disabling the barostat. mask: None or 3-tuple or 3x3 nparray (optional) Optional argument. A tuple of three integers (0 or 1), indicating if the system can change size along the three Cartesian axes. Set to (1,1,1) or None to allow a fully flexible computational box. Set to (1,1,0) to disallow elongations along the z-axis etc. mask may also be specified as a symmetric 3x3 array indicating which strain values may change. Useful parameter values: * The same timestep can be used as in Verlet dynamics, i.e. 5 fs is fine for bulk copper. * The ttime and pfactor are quite critical[4], too small values may cause instabilites and/or wrong fluctuations in T / p. Too large values cause an oscillation which is slow to die. Good values for the characteristic times seem to be 25 fs for ttime, and 75 fs for ptime (used to calculate pfactor), at least for bulk copper with 15000-200000 atoms. But this is not well tested, it is IMPORTANT to monitor the temperature and stress/pressure fluctuations. References: 1) S. Melchionna, G. Ciccotti and B. L. Holian, Molecular Physics 78, p. 533 (1993). 2) S. Melchionna, Physical Review E 61, p. 6165 (2000). 3) B. L. Holian, A. J. De Groot, W. G. Hoover, and C. G. Hoover, Physical Review A 41, p. 4552 (1990). 4) F. D. Di Tolla and M. Ronchetti, Physical Review E 48, p. 1726 (1993). ''' MolecularDynamics.__init__(self, atoms, timestep, trajectory, logfile, loginterval, append_trajectory=append_trajectory) # self.atoms = atoms # self.timestep = timestep if externalstress is None and pfactor is not None: raise TypeError("Missing 'externalstress' argument.") self.zero_center_of_mass_momentum(verbose=1) self.temperature = units.kB * self._process_temperature( temperature, temperature_K, 'eV') self.set_stress(externalstress) self.set_mask(mask) self.eta = np.zeros((3, 3), float) self.zeta = 0.0 self.zeta_integrated = 0.0 self.initialized = 0 self.ttime = ttime self.pfactor_given = pfactor self._calculateconstants() self.timeelapsed = 0.0 self.frac_traceless = 1
[docs] def set_temperature(self, temperature=None, *, temperature_K=None): """Set the temperature. Parameters: temperature: float (deprecated) The new temperature in eV. Deprecated, use ``temperature_K``. temperature_K: float (keyword-only argument) The new temperature, in K. """ self.temperature = units.kB * self._process_temperature( temperature, temperature_K, 'eV') self._calculateconstants()
[docs] def set_stress(self, stress): """Set the applied stress. Must be a symmetric 3x3 tensor, a 6-vector representing a symmetric 3x3 tensor, or a number representing the pressure. Use with care, it is better to set the correct stress when creating the object. """ if np.isscalar(stress): stress = np.array([-stress, -stress, -stress, 0.0, 0.0, 0.0]) else: stress = np.array(stress) if stress.shape == (3, 3): if not self._issymmetric(stress): raise ValueError( "The external stress must be a symmetric tensor.") stress = np.array((stress[0, 0], stress[1, 1], stress[2, 2], stress[1, 2], stress[0, 2], stress[0, 1])) elif stress.shape != (6,): raise ValueError("The external stress has the wrong shape.") self.externalstress = stress
[docs] def set_mask(self, mask): """Set the mask indicating dynamic elements of the computational box. If set to None, all elements may change. If set to a 3-vector of ones and zeros, elements which are zero specify directions along which the size of the computational box cannot change. For example, if mask = (1,1,0) the length of the system along the z-axis cannot change, although xz and yz shear is still possible. May also be specified as a symmetric 3x3 array indicating which strain values may change. Use with care, as you may "freeze in" a fluctuation in the strain rate. """ if mask is None: mask = np.ones((3,)) if not hasattr(mask, "shape"): mask = np.array(mask) if mask.shape != (3,) and mask.shape != (3, 3): raise RuntimeError('The mask has the wrong shape ' + '(must be a 3-vector or 3x3 matrix)') else: mask = np.not_equal(mask, 0) # Make sure it is 0/1 if mask.shape == (3,): self.mask = np.outer(mask, mask) else: self.mask = mask
[docs] def set_fraction_traceless(self, fracTraceless): """set what fraction of the traceless part of the force on eta is kept. By setting this to zero, the volume may change but the shape may not. """ self.frac_traceless = fracTraceless
[docs] def get_strain_rate(self): """Get the strain rate as an upper-triangular 3x3 matrix. This includes the fluctuations in the shape of the computational box. """ return np.array(self.eta, copy=1)
[docs] def set_strain_rate(self, rate): """Set the strain rate. Must be an upper triangular 3x3 matrix. If you set a strain rate along a direction that is "masked out" (see ``set_mask``), the strain rate along that direction will be maintained constantly. """ if not (rate.shape == (3, 3) and self._isuppertriangular(rate)): raise ValueError("Strain rate must be an upper triangular matrix.") self.eta = rate if self.initialized: # Recalculate h_past and eta_past so they match the current value. self._initialize_eta_h()
[docs] def get_time(self): "Get the elapsed time." return self.timeelapsed
[docs] def run(self, steps): """Perform a number of time steps.""" if not self.initialized: self.initialize() else: if self.have_the_atoms_been_changed(): raise NotImplementedError( "You have modified the atoms since the last timestep.") for i in range(steps): self.step() self.nsteps += 1 self.call_observers()
def have_the_atoms_been_changed(self): "Checks if the user has modified the positions or momenta of the atoms" limit = 1e-10 h = self._getbox() if max(abs((h - self.h).ravel())) > limit: self._warning("The computational box has been modified.") return 1 expected_r = + 0.5, h) err = max(abs((expected_r - self.atoms.get_positions()).ravel())) if err > limit: self._warning("The atomic positions have been modified: " + str(err)) return 1 return 0 def step(self): """Perform a single time step. Assumes that the forces and stresses are up to date, and that the positions and momenta have not been changed since last timestep. """ # Assumes the following variables are OK # q_past, q, q_future, p, eta, eta_past, zeta, zeta_past, h, h_past # # q corresponds to the current positions # p must be equal to self.atoms.GetCartesianMomenta() # h must be equal to self.atoms.GetUnitCell() # # print "Making a timestep" dt = self.dt h_future = self.h_past + 2 * dt *, self.eta) if self.pfactor_given is None: deltaeta = np.zeros(6, float) else: stress = self.stresscalculator() deltaeta = -2 * dt * (self.pfact * linalg.det(self.h) * (stress - self.externalstress)) if self.frac_traceless == 1: eta_future = self.eta_past + self.mask * \ self._makeuppertriangular(deltaeta) else: trace_part, traceless_part = self._separatetrace( self._makeuppertriangular(deltaeta)) eta_future = self.eta_past + trace_part + self.frac_traceless * traceless_part deltazeta = 2 * dt * self.tfact * (self.atoms.get_kinetic_energy() - self.desiredEkin) zeta_future = self.zeta_past + deltazeta # Advance time # print "Max change in scaled positions:", max(abs(self.q_future.flat - self.q.flat)) # print "Max change in basis set", max(abs((h_future - self.h).flat)) self.timeelapsed += dt self.h_past = self.h self.h = h_future self.inv_h = linalg.inv(self.h) self.q_past = self.q self.q = self.q_future self._setbox_and_positions(self.h, self.q) self.eta_past = self.eta self.eta = eta_future self.zeta_past = self.zeta self.zeta = zeta_future self._synchronize() # for parallel simulations. self.zeta_integrated += dt * self.zeta force = self.forcecalculator() self._calculate_q_future(force) self.atoms.set_momenta( - self.q_past, self.h / (2 * dt)) * self._getmasses()) # self.stresscalculator() def forcecalculator(self): return self.atoms.get_forces(md=True) def stresscalculator(self): return self.atoms.get_stress(include_ideal_gas=True)
[docs] def initialize(self): """Initialize the dynamics. The dynamics requires positions etc for the two last times to do a timestep, so the algorithm is not self-starting. This method performs a 'backwards' timestep to generate a configuration before the current. This is called automatically the first time ``run()`` is called. """ # print "Initializing the NPT dynamics." dt = self.dt atoms = self.atoms self.h = self._getbox() if not self._isuppertriangular(self.h): print("I am", self) print("self.h:") print(self.h) print("Min:", min((self.h[1, 0], self.h[2, 0], self.h[2, 1]))) print("Max:", max((self.h[1, 0], self.h[2, 0], self.h[2, 1]))) raise NotImplementedError( "Can (so far) only operate on lists of atoms where the computational box is an upper triangular matrix.") self.inv_h = linalg.inv(self.h) # The contents of the q arrays should migrate in parallel simulations. # self._make_special_q_arrays() self.q =, self.inv_h) - 0.5 # zeta and eta were set in __init__ self._initialize_eta_h() deltazeta = dt * self.tfact * (atoms.get_kinetic_energy() - self.desiredEkin) self.zeta_past = self.zeta - deltazeta self._calculate_q_past_and_future() self.initialized = 1
[docs] def get_gibbs_free_energy(self): """Return the Gibb's free energy, which is supposed to be conserved. Requires that the energies of the atoms are up to date. This is mainly intended as a diagnostic tool. If called before the first timestep, Initialize will be called. """ if not self.initialized: self.initialize() n = self._getnatoms() # tretaTeta = sum(diagonal(matrixmultiply(transpose(self.eta), # self.eta))) contractedeta = np.sum((self.eta * self.eta).ravel()) gibbs = (self.atoms.get_potential_energy() + self.atoms.get_kinetic_energy() - np.sum(self.externalstress[0:3]) * linalg.det(self.h) / 3.0) if self.ttime is not None: gibbs += (1.5 * n * self.temperature * (self.ttime * self.zeta)**2 + 3 * self.temperature * (n - 1) * self.zeta_integrated) else: assert self.zeta == 0.0 if self.pfactor_given is not None: gibbs += 0.5 / self.pfact * contractedeta else: assert contractedeta == 0.0 return gibbs
def get_center_of_mass_momentum(self): "Get the center of mass momentum." return self.atoms.get_momenta().sum(0)
[docs] def zero_center_of_mass_momentum(self, verbose=0): "Set the center of mass momentum to zero." cm = self.get_center_of_mass_momentum() abscm = np.sqrt(np.sum(cm * cm)) if verbose and abscm > 1e-4: self._warning( self.classname + ": Setting the center-of-mass momentum to zero " "(was %.6g %.6g %.6g)" % tuple(cm)) self.atoms.set_momenta(self.atoms.get_momenta() - cm / self._getnatoms())
def attach_atoms(self, atoms): """Assign atoms to a restored dynamics object. This function must be called to set the atoms immediately after the dynamics object has been read from a trajectory. """ try: self.atoms except AttributeError: pass else: raise RuntimeError("Cannot call attach_atoms on a dynamics " "which already has atoms.") MolecularDynamics.__init__(self, atoms, self.dt) limit = 1e-6 h = self._getbox() if max(abs((h - self.h).ravel())) > limit: raise RuntimeError( "The unit cell of the atoms does not match the unit cell stored in the file.") self.inv_h = linalg.inv(self.h) self.q =, self.inv_h) - 0.5 self._calculate_q_past_and_future() self.initialized = 1
[docs] def attach(self, function, interval=1, *args, **kwargs): """Attach callback function or trajectory. At every *interval* steps, call *function* with arguments *args* and keyword arguments *kwargs*. If *function* is a trajectory object, its write() method is attached, but if *function* is a BundleTrajectory (or another trajectory supporting set_extra_data(), said method is first used to instruct the trajectory to also save internal data from the NPT dynamics object. """ if hasattr(function, "set_extra_data"): # We are attaching a BundleTrajectory or similar function.set_extra_data("npt_init", WeakMethodWrapper(self, "get_init_data"), once=True) function.set_extra_data("npt_dynamics", WeakMethodWrapper(self, "get_data")) MolecularDynamics.attach(self, function, interval, *args, **kwargs)
def get_init_data(self): "Return the data needed to initialize a new NPT dynamics." return {'dt': self.dt, 'temperature': self.temperature, 'desiredEkin': self.desiredEkin, 'externalstress': self.externalstress, 'mask': self.mask, 'ttime': self.ttime, 'tfact': self.tfact, 'pfactor_given': self.pfactor_given, 'pfact': self.pfact, 'frac_traceless': self.frac_traceless} def get_data(self): "Return data needed to restore the state." return {'eta': self.eta, 'eta_past': self.eta_past, 'zeta': self.zeta, 'zeta_past': self.zeta_past, 'zeta_integrated': self.zeta_integrated, 'h': self.h, 'h_past': self.h_past, 'timeelapsed': self.timeelapsed} @classmethod def read_from_trajectory(cls, trajectory, frame=-1, atoms=None): """Read dynamics and atoms from trajectory (Class method). Simultaneously reads the atoms and the dynamics from a BundleTrajectory, including the internal data of the NPT dynamics object (automatically saved when attaching a BundleTrajectory to an NPT object). Arguments: trajectory The filename or an open BundleTrajectory object. frame (optional) Which frame to read. Default: the last. atoms (optional, internal use only) Pre-read atoms. Do not use. """ if isinstance(trajectory, str): if trajectory.endswith('/'): trajectory = trajectory[:-1] if trajectory.endswith('.bundle'): from import BundleTrajectory trajectory = BundleTrajectory(trajectory) else: raise ValueError( f"Cannot open '{trajectory}': unsupported file format") # trajectory is now a BundleTrajectory object (or compatible) if atoms is None: atoms = trajectory[frame] init_data = trajectory.read_extra_data('npt_init', 0) frame_data = trajectory.read_extra_data('npt_dynamics', frame) dyn = cls(atoms, timestep=init_data['dt'], temperature=init_data['temperature'], externalstress=init_data['externalstress'], ttime=init_data['ttime'], pfactor=init_data['pfactor_given'], mask=init_data['mask']) dyn.desiredEkin = init_data['desiredEkin'] dyn.tfact = init_data['tfact'] dyn.pfact = init_data['pfact'] dyn.frac_traceless = init_data['frac_traceless'] for k, v in frame_data.items(): setattr(dyn, k, v) return (dyn, atoms) def _getbox(self): "Get the computational box." return self.atoms.get_cell() def _getmasses(self): "Get the masses as an Nx1 array." return np.reshape(self.atoms.get_masses(), (-1, 1)) def _separatetrace(self, mat): """return two matrices, one proportional to the identity the other traceless, which sum to the given matrix """ tracePart = ((mat[0][0] + mat[1][1] + mat[2][2]) / 3.) * np.identity(3) return tracePart, mat - tracePart # A number of convenient helper methods def _warning(self, text): "Emit a warning." sys.stderr.write("WARNING: " + text + "\n") sys.stderr.flush() def _calculate_q_future(self, force): "Calculate future q. Needed in Timestep and Initialization." dt = self.dt id3 = np.identity(3) alpha = (dt * dt) * / self._getmasses(), self.inv_h) beta = dt *, + 0.5 * self.zeta * id3, self.inv_h)) inv_b = linalg.inv(beta + id3) self.q_future = * self.q +, beta - id3) + alpha, inv_b) def _calculate_q_past_and_future(self): def ekin(p, m=self.atoms.get_masses()): p2 = np.sum(p * p, -1) return 0.5 * np.sum(p2 / m) / len(m) p0 = self.atoms.get_momenta() m = self._getmasses() p = np.array(p0, copy=1) dt = self.dt for i in range(2): self.q_past = self.q - dt * / m, self.inv_h) self._calculate_q_future(self.atoms.get_forces(md=True)) p = - self.q_past, self.h / (2 * dt)) * m e = ekin(p) if e < 1e-5: # The kinetic energy and momenta are virtually zero return p = (p0 - p) + p0 def _initialize_eta_h(self): self.h_past = self.h - self.dt *, self.eta) if self.pfactor_given is None: deltaeta = np.zeros(6, float) else: deltaeta = (-self.dt * self.pfact * linalg.det(self.h) * (self.stresscalculator() - self.externalstress)) if self.frac_traceless == 1: self.eta_past = self.eta - self.mask * \ self._makeuppertriangular(deltaeta) else: trace_part, traceless_part = self._separatetrace( self._makeuppertriangular(deltaeta)) self.eta_past = self.eta - trace_part - self.frac_traceless * traceless_part def _makeuppertriangular(self, sixvector): "Make an upper triangular matrix from a 6-vector." return np.array(((sixvector[0], sixvector[5], sixvector[4]), (0, sixvector[1], sixvector[3]), (0, 0, sixvector[2]))) @staticmethod def _isuppertriangular(m) -> bool: "Check that a matrix is on upper triangular form." return m[1, 0] == m[2, 0] == m[2, 1] == 0.0 def _calculateconstants(self): "(Re)calculate some constants when pfactor, ttime or temperature have been changed." n = self._getnatoms() if self.ttime is None: self.tfact = 0.0 else: self.tfact = 2.0 / (3 * n * self.temperature * self.ttime * self.ttime) if self.pfactor_given is None: self.pfact = 0.0 else: self.pfact = 1.0 / (self.pfactor_given * linalg.det(self._getbox())) # self.pfact = 1.0/(n * self.temperature * self.ptime * self.ptime) self.desiredEkin = 1.5 * (n - 1) * self.temperature def _setbox_and_positions(self, h, q): """Set the computational box and the positions.""" self.atoms.set_cell(h) r = + 0.5, h) self.atoms.set_positions(r) # A few helper methods, which have been placed in separate methods # so they can be replaced in the parallel version. def _synchronize(self): """Synchronizes eta, h and zeta on all processors in a parallel simulation. In a parallel simulation, eta, h and zeta are communicated from the master to all slaves, to prevent numerical noise from causing them to diverge. In a serial simulation, do nothing. """ pass # This is a serial simulation object. Do nothing. def _getnatoms(self): """Get the number of atoms. In a parallel simulation, this is the total number of atoms on all processors. """ return len(self.atoms) def _make_special_q_arrays(self): """Make the arrays used to store data about the atoms. In a parallel simulation, these are migrating arrays. In a serial simulation they are ordinary Numeric arrays. """ natoms = len(self.atoms) self.q = np.zeros((natoms, 3), float) self.q_past = np.zeros((natoms, 3), float) self.q_future = np.zeros((natoms, 3), float)
class WeakMethodWrapper: """A weak reference to a method. Create an object storing a weak reference to an instance and the name of the method to call. When called, calls the method. Just storing a weak reference to a bound method would not work, as the bound method object would go away immediately. """ def __init__(self, obj, method): self.obj = weakref.proxy(obj) self.method = method def __call__(self, *args, **kwargs): m = getattr(self.obj, self.method) return m(*args, **kwargs)