"""This module implements a class for (true) time-dependent density
functional theory calculations.
"""
from __future__ import print_function
import time
from math import log
import numpy as np
from gpaw.calculator import GPAW
from gpaw.mixer import DummyMixer
from gpaw.preconditioner import Preconditioner
from gpaw.tddft.units import (attosec_to_autime, autime_to_attosec,
aufrequency_to_eV)
from gpaw.tddft.utils import MultiBlas
from gpaw.tddft.bicgstab import BiCGStab
from gpaw.tddft.cscg import CSCG
from gpaw.tddft.propagators import \
ExplicitCrankNicolson, \
SemiImplicitCrankNicolson, \
EhrenfestPAWSICN,\
EhrenfestHGHSICN,\
EnforcedTimeReversalSymmetryCrankNicolson, \
SemiImplicitTaylorExponential, \
SemiImplicitKrylovExponential, \
AbsorptionKick
from gpaw.tddft.tdopers import \
TimeDependentHamiltonian, \
TimeDependentOverlap, \
TimeDependentWaveFunctions, \
TimeDependentDensity, \
AbsorptionKickHamiltonian
from gpaw.wavefunctions.fd import FD
from gpaw.tddft.spectrum import photoabsorption_spectrum
photoabsorption_spectrum = photoabsorption_spectrum
# T^-1
# Bad preconditioner
class KineticEnergyPreconditioner:
def __init__(self, gd, kin, dtype):
self.preconditioner = Preconditioner(gd, kin, dtype)
self.preconditioner.allocate()
def apply(self, kpt, psi, psin):
for i in range(len(psi)):
psin[i][:] = self.preconditioner(psi[i], kpt.phase_cd, None, None)
# S^-1
class InverseOverlapPreconditioner:
"""Preconditioner for TDDFT."""
def __init__(self, overlap):
self.overlap = overlap
def apply(self, kpt, psi, psin):
self.overlap.apply_inverse(psi, psin, kpt)
# ^^^^^^^^^^
class FDTDDFTMode(FD):
def __call__(self, *args, **kwargs):
reuse_wfs_method = kwargs.pop('reuse_wfs_method', None)
assert reuse_wfs_method is None
return TimeDependentWaveFunctions(self.nn, *args, **kwargs)
[docs]class TDDFT(GPAW):
"""Time-dependent density functional theory calculation based on GPAW.
This class is the core class of the time-dependent density functional
theory implementation and is the only class which a user has to use.
"""
def __init__(self, filename,
td_potential=None, propagator='SICN', calculate_energy=True,
propagator_kwargs=None, solver='CSCG', tolerance=1e-8,
**kwargs):
"""Create TDDFT-object.
Parameters:
filename: string
File containing ground state or time-dependent state to propagate
td_potential: class, optional
Function class for the time-dependent potential. Must have a method
'strength(time)' which returns the strength of the linear potential
to each direction as a vector of three floats.
propagator: {'SICN','ETRSCN','ECN','SITE','SIKE4','SIKE5','SIKE6'}
Name of the time propagator for the Kohn-Sham wavefunctions
solver: {'CSCG','BiCGStab'}
Name of the iterative linear equations solver for time propagation
tolerance: float
Tolerance for the linear solver
The following parameters can be used: `txt`, `parallel`, `communicator`
`mixer` and `dtype`. The internal parameters `mixer` and `dtype` are
strictly used to specify a dummy mixer and complex type respectively.
"""
# Set initial time
self.time = 0.0
# Set initial kick strength
self.kick_strength = np.array([0.0, 0.0, 0.0], dtype=float)
# Set initial value of iteration counter
self.niter = 0
# Parallelization dictionary should default to strided bands
self.default_parallel = GPAW.default_parallel.copy()
self.default_parallel['stridebands'] = True
self.default_parameters = GPAW.default_parameters.copy()
self.default_parameters['mixer'] = DummyMixer()
# NB: TDDFT restart files contain additional information which
# will override the initial settings for time/kick/niter.
GPAW.__init__(self, filename, **kwargs)
assert isinstance(self.wfs, TimeDependentWaveFunctions)
assert isinstance(self.wfs.overlap, TimeDependentOverlap)
# Prepare for dipole moment file handle
self.dm_file = None
# Initialize wavefunctions and density
# (necessary after restarting from file)
if not self.initialized:
self.initialize()
self.set_positions()
# Don't be too strict
self.density.charge_eps = 1e-5
wfs = self.wfs
self.rank = wfs.world.rank
self.text = self.log
self.text('')
self.text('')
self.text('------------------------------------------')
self.text(' Time-propagation TDDFT ')
self.text('------------------------------------------')
self.text('')
self.text('Charge epsilon: ', self.density.charge_eps)
# Time-dependent variables and operators
self.td_potential = td_potential
self.td_hamiltonian = TimeDependentHamiltonian(self.wfs, self.spos_ac,
self.hamiltonian,
td_potential)
self.td_overlap = self.wfs.overlap # TODO remove this property
self.td_density = TimeDependentDensity(self)
# Solver for linear equations
self.text('Solver: ', solver)
if solver == 'BiCGStab':
self.solver = BiCGStab(gd=wfs.gd, timer=self.timer,
tolerance=tolerance)
elif solver == 'CSCG':
self.solver = CSCG(gd=wfs.gd, timer=self.timer,
tolerance=tolerance)
else:
raise RuntimeError('Solver %s not supported.' % solver)
# Preconditioner
# No preconditioner as none good found
self.text('Preconditioner: ', 'None')
self.preconditioner = None # TODO! check out SSOR preconditioning
# self.preconditioner = InverseOverlapPreconditioner(self.overlap)
# self.preconditioner = KineticEnergyPreconditioner(
# wfs.gd, self.td_hamiltonian.hamiltonian.kin, np.complex)
# Time propagator
self.text('Propagator: ', propagator)
if propagator_kwargs is None:
propagator_kwargs = {}
if propagator == 'ECN':
self.propagator = ExplicitCrankNicolson(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'SICN':
self.propagator = SemiImplicitCrankNicolson(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'EFSICN':
self.propagator = EhrenfestPAWSICN(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'EFSICN_HGH':
self.propagator = EhrenfestHGHSICN(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'ETRSCN':
self.propagator = EnforcedTimeReversalSymmetryCrankNicolson(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'SITE':
self.propagator = SemiImplicitTaylorExponential(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator == 'SIKE':
self.propagator = SemiImplicitKrylovExponential(
self.td_density,
self.td_hamiltonian, self.td_overlap, self.solver,
self.preconditioner, wfs.gd, self.timer, **propagator_kwargs)
elif propagator.startswith('SITE') or propagator.startswith('SIKE'):
raise DeprecationWarning('Use propagator_kwargs to specify degree.')
else:
raise RuntimeError('Time propagator %s not supported.' % propagator)
if self.rank == 0:
if wfs.kd.comm.size > 1:
if wfs.nspins == 2:
self.text('Parallelization Over Spin')
if wfs.gd.comm.size > 1:
self.text('Using Domain Decomposition: %d x %d x %d' %
tuple(wfs.gd.parsize_c))
if wfs.bd.comm.size > 1:
self.text('Parallelization Over bands on %d Processors' %
wfs.bd.comm.size)
self.text('States per processor = ', wfs.bd.mynbands)
self.hpsit = None
self.eps_tmp = None
self.mblas = MultiBlas(wfs.gd)
# Restarting an FDTD run generates hamiltonian.fdtd_poisson, which
# now overwrites hamiltonian.poisson
if hasattr(self.hamiltonian, 'fdtd_poisson'):
self.hamiltonian.poisson = self.hamiltonian.fdtd_poisson
self.hamiltonian.poisson.set_grid_descriptor(self.density.finegd)
# For electrodynamics mode
if self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT':
self.initialize_FDTD()
self.hamiltonian.poisson.print_messages(self.text)
self.log.flush()
self.calculate_energy = calculate_energy
if self.hamiltonian.xc.name.startswith('GLLB'):
self.text('GLLB model potential. Not updating energy.')
self.calculate_energy = False
def create_wave_functions(self, mode, *args, **kwargs):
mode = FDTDDFTMode(mode.nn, mode.interpolation, True)
GPAW.create_wave_functions(self, mode, *args, **kwargs)
[docs] def read(self, filename):
reader = GPAW.read(self, filename)
if 'tddft' in reader:
self.time = reader.tddft.time
self.niter = reader.tddft.niter
self.kick_strength = reader.tddft.kick_strength
[docs] def initialize(self, reading=False):
self.parameters.mixer = DummyMixer()
self.parameters.experimental['reuse_wfs_method'] = None
GPAW.initialize(self, reading=reading)
def _write(self, writer, mode):
GPAW._write(self, writer, mode)
writer.child('tddft').write(time=self.time,
niter=self.niter,
kick_strength=self.kick_strength)
# Electrodynamics requires extra care
def initialize_FDTD(self):
# Sanity check
assert(self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT')
self.hamiltonian.poisson.set_density(self.density)
# The propagate calculation_mode causes classical part to evolve
# in time when self.hamiltonian.poisson.solve(...) is called
self.hamiltonian.poisson.set_calculation_mode('propagate')
# During each time step, self.hamiltonian.poisson.solve may be called
# several times (depending on the used propagator). Using the
# attached observer one ensures that actual propagation takes
# place only once. This is because
# the FDTDPoissonSolver changes the calculation_mode from propagate to
# something else when the propagation is finished.
self.attach(self.hamiltonian.poisson.set_calculation_mode, 1,
'propagate')
[docs] def propagate(self, time_step, iterations, dipole_moment_file=None,
restart_file=None, dump_interval=100):
"""Propagates wavefunctions.
Parameters:
time_step: float
Time step in attoseconds (10^-18 s), e.g., 4.0 or 8.0
iterations: integer
Iterations, e.g., 20 000 as / 4.0 as = 5000
dipole_moment_file: string, optional
Name of the data file where to the time-dependent dipole
moment is saved
restart_file: string, optional
Name of the restart file
dump_interval: integer
After how many iterations restart data is dumped
"""
if self.rank == 0:
self.text()
self.text('Starting time: %7.2f as'
% (self.time * autime_to_attosec))
self.text('Time step: %7.2f as' % time_step)
header = """\
Simulation Total log10 Iterations:
Time time Energy (eV) Norm Propagator"""
self.text()
self.text(header)
# Convert to atomic units
time_step = time_step * attosec_to_autime
if dipole_moment_file is not None:
self.initialize_dipole_moment_file(dipole_moment_file)
# Set these as class properties for use of observers
self.time_step = time_step
self.dump_interval = dump_interval
niterpropagator = 0
self.tdmaxiter = self.niter + iterations
# Let FDTD part know the time step
if self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT':
self.hamiltonian.poisson.set_time(self.time)
self.hamiltonian.poisson.set_time_step(self.time_step)
self.timer.start('Propagate')
while self.niter < self.tdmaxiter:
norm = self.density.finegd.integrate(self.density.rhot_g)
# Write dipole moment at every iteration
if dipole_moment_file is not None:
self.update_dipole_moment_file(norm)
# print output (energy etc.) every 10th iteration
if self.niter % 10 == 0:
self.get_td_energy()
T = time.localtime()
if self.rank == 0:
iter_text = 'iter: %3d %02d:%02d:%02d %11.2f' \
' %13.6f %9.1f %10d'
self.text(iter_text %
(self.niter, T[3], T[4], T[5],
self.time * autime_to_attosec,
self.Etot * aufrequency_to_eV,
log(abs(norm) + 1e-16) / log(10),
niterpropagator))
self.log.flush()
# Propagate the Kohn-Shame wavefunctions a single timestep
niterpropagator = self.propagator.propagate(self.time, time_step)
self.time += time_step
self.niter += 1
# Call registered callback functions
self.call_observers(self.niter)
# Write restart data
if restart_file is not None and self.niter % dump_interval == 0:
self.write(restart_file, 'all')
if self.rank == 0:
print('Wrote restart file.')
print(self.niter, ' iterations done. Current time is ',
self.time * autime_to_attosec, ' as.')
self.timer.stop('Propagate')
# Write final results and close dipole moment file
if dipole_moment_file is not None:
# TODO final iteration is propagated, but nothing is updated
# norm = self.density.finegd.integrate(self.density.rhot_g)
# self.finalize_dipole_moment_file(norm)
self.finalize_dipole_moment_file()
# Finalize FDTDPoissonSolver
if self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT':
self.hamiltonian.poisson.finalize_propagation()
# Call registered callback functions
self.call_observers(self.niter, final=True)
if restart_file is not None:
self.write(restart_file, 'all')
def initialize_dipole_moment_file(self, dipole_moment_file):
if self.rank == 0:
if self.dm_file is not None and not self.dm_file.closed:
raise RuntimeError('Dipole moment file is already open')
if self.time == 0.0:
mode = 'w'
else:
# We probably continue from restart
mode = 'a'
self.dm_file = open(dipole_moment_file, mode)
# If the dipole moment file is empty, add a header
if self.dm_file.tell() == 0:
header = '# Kick = [%22.12le, %22.12le, %22.12le]\n' \
% (self.kick_strength[0], self.kick_strength[1],
self.kick_strength[2])
header += '# %15s %15s %22s %22s %22s\n' \
% ('time', 'norm', 'dmx', 'dmy', 'dmz')
self.dm_file.write(header)
self.dm_file.flush()
def update_dipole_moment_file(self, norm):
dm = self.density.finegd.calculate_dipole_moment(self.density.rhot_g)
if self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT':
dm += self.hamiltonian.poisson.get_classical_dipole_moment()
if self.rank == 0:
line = '%20.8lf %20.8le %22.12le %22.12le %22.12le\n' \
% (self.time, norm, dm[0], dm[1], dm[2])
self.dm_file.write(line)
self.dm_file.flush()
def finalize_dipole_moment_file(self, norm=None):
if norm is not None:
self.update_dipole_moment_file(norm)
if self.rank == 0:
self.dm_file.close()
self.dm_file = None
def update_eigenvalues(self):
kpt_u = self.wfs.kpt_u
if self.hpsit is None:
self.hpsit = self.wfs.gd.zeros(len(kpt_u[0].psit_nG),
dtype=complex)
if self.eps_tmp is None:
self.eps_tmp = np.zeros(len(kpt_u[0].eps_n),
dtype=complex)
# self.Eband = sum_i <psi_i|H|psi_j>
for kpt in kpt_u:
self.td_hamiltonian.apply(kpt, kpt.psit_nG, self.hpsit,
calculate_P_ani=False)
self.mblas.multi_zdotc(self.eps_tmp, kpt.psit_nG,
self.hpsit, len(kpt_u[0].psit_nG))
self.eps_tmp *= self.wfs.gd.dv
kpt.eps_n[:] = self.eps_tmp.real
self.occupations.calculate_band_energy(self.wfs)
H = self.td_hamiltonian.hamiltonian
# Nonlocal
self.Enlkin = H.xc.get_kinetic_energy_correction()
# PAW
self.Ekin = H.e_kinetic0 + self.occupations.e_band + self.Enlkin
self.e_coulomb = H.e_coulomb
self.Eext = H.e_external
self.Ebar = H.e_zero
self.Exc = H.e_xc
self.Etot = self.Ekin + self.e_coulomb + self.Ebar + self.Exc
[docs] def get_td_energy(self):
"""Calculate the time-dependent total energy"""
if not self.calculate_energy:
self.Etot = 0.0
return 0.0
self.td_overlap.update(self.wfs)
self.td_density.update()
self.td_hamiltonian.update(self.td_density.get_density(),
self.time)
self.update_eigenvalues()
return self.Etot
def set_absorbing_boundary(self, absorbing_boundary):
self.td_hamiltonian.set_absorbing_boundary(absorbing_boundary)
# exp(ip.r) psi
[docs] def absorption_kick(self, kick_strength):
"""Delta absorption kick for photoabsorption spectrum.
Parameters:
kick_strength: [float, float, float]
Strength of the kick, e.g., [0.0, 0.0, 1e-3]
"""
if self.rank == 0:
self.text('Delta kick = ', kick_strength)
self.kick_strength = np.array(kick_strength)
abs_kick_hamiltonian = AbsorptionKickHamiltonian(
self.wfs, self.spos_ac,
np.array(kick_strength, float))
abs_kick = AbsorptionKick(self.wfs, abs_kick_hamiltonian,
self.td_overlap, self.solver,
self.preconditioner, self.wfs.gd, self.timer)
abs_kick.kick()
# Kick the classical part, if it is present
if self.hamiltonian.poisson.get_description() == 'FDTD+TDDFT':
self.hamiltonian.poisson.set_kick(kick = self.kick_strength)