"""Vibrational modes."""
import os
import os.path as op
import pickle
import sys
from math import sin, pi, sqrt, log
import numpy as np
import ase.units as units
from ase.io.trajectory import Trajectory
from ase.parallel import world, paropen
from ase.utils import opencew, pickleload
from ase.calculators.singlepoint import SinglePointCalculator
[docs]class Vibrations:
"""Class for calculating vibrational modes using finite difference.
The vibrational modes are calculated from a finite difference
approximation of the Hessian matrix.
The *summary()*, *get_energies()* and *get_frequencies()* methods all take
an optional *method* keyword. Use method='Frederiksen' to use the method
described in:
T. Frederiksen, M. Paulsson, M. Brandbyge, A. P. Jauho:
"Inelastic transport theory from first-principles: methodology and
applications for nanoscale devices", Phys. Rev. B 75, 205413 (2007)
atoms: Atoms object
The atoms to work on.
indices: list of int
List of indices of atoms to vibrate. Default behavior is
to vibrate all atoms.
name: str
Name to use for files.
delta: float
Magnitude of displacements.
nfree: int
Number of displacements per atom and cartesian coordinate, 2 and 4 are
supported. Default is 2 which will displace each atom +delta and
-delta for each cartesian coordinate.
Example:
>>> from ase import Atoms
>>> from ase.calculators.emt import EMT
>>> from ase.optimize import BFGS
>>> from ase.vibrations import Vibrations
>>> n2 = Atoms('N2', [(0, 0, 0), (0, 0, 1.1)],
... calculator=EMT())
>>> BFGS(n2).run(fmax=0.01)
BFGS: 0 16:01:21 0.440339 3.2518
BFGS: 1 16:01:21 0.271928 0.8211
BFGS: 2 16:01:21 0.263278 0.1994
BFGS: 3 16:01:21 0.262777 0.0088
>>> vib = Vibrations(n2)
>>> vib.run()
Writing vib.eq.pckl
Writing vib.0x-.pckl
Writing vib.0x+.pckl
Writing vib.0y-.pckl
Writing vib.0y+.pckl
Writing vib.0z-.pckl
Writing vib.0z+.pckl
Writing vib.1x-.pckl
Writing vib.1x+.pckl
Writing vib.1y-.pckl
Writing vib.1y+.pckl
Writing vib.1z-.pckl
Writing vib.1z+.pckl
>>> vib.summary()
---------------------
# meV cm^-1
---------------------
0 0.0 0.0
1 0.0 0.0
2 0.0 0.0
3 2.5 20.4
4 2.5 20.4
5 152.6 1230.8
---------------------
Zero-point energy: 0.079 eV
>>> vib.write_mode(-1) # write last mode to trajectory file
"""
def __init__(self, atoms, indices=None, name='vib', delta=0.01, nfree=2):
assert nfree in [2, 4]
self.atoms = atoms
self.calc = atoms.calc
if indices is None:
indices = range(len(atoms))
self.indices = np.asarray(indices)
self.name = name
self.delta = delta
self.nfree = nfree
self.H = None
self.ir = None
[docs] def run(self):
"""Run the vibration calculations.
This will calculate the forces for 6 displacements per atom +/-x,
+/-y, +/-z. Only those calculations that are not already done will be
started. Be aware that an interrupted calculation may produce an empty
file (ending with .pckl), which must be deleted before restarting the
job. Otherwise the forces will not be calculated for that
displacement.
Note that the calculations for the different displacements can be done
simultaneously by several independent processes. This feature relies
on the existence of files and the subsequent creation of the file in
case it is not found.
If the program you want to use does not have a calculator in ASE, use
``iterdisplace`` to get all displaced structures and calculate the forces
on your own.
"""
if op.isfile(self.name + '.all.pckl'):
raise RuntimeError(
'Cannot run calculation. ' +
self.name + '.all.pckl must be removed or split in order ' +
'to have only one sort of data structure at a time.')
for dispName, atoms in self.iterdisplace(inplace=True):
filename = dispName + '.pckl'
fd = opencew(filename)
if fd is not None:
self.calculate(atoms, filename, fd)
[docs] def iterdisplace(self, inplace=False):
"""Yield name and atoms object for initial and displaced structures.
Use this to export the structures for each single-point calculation
to an external program instead of using ``run()``. Then save the
calculated gradients to <name>.pckl and continue using this instance.
"""
atoms = self.atoms if inplace else self.atoms.copy()
yield self.name + '.eq', atoms
for dispName, a, i, disp in self.displacements():
if not inplace:
atoms = self.atoms.copy()
pos0 = atoms.positions[a, i]
atoms.positions[a, i] += disp
yield dispName, atoms
if inplace:
atoms.positions[a, i] = pos0
[docs] def iterimages(self):
"""Yield initial and displaced structures."""
for name, atoms in self.iterdisplace():
yield atoms
def displacements(self):
for a in self.indices:
for i in range(3):
for sign in [-1, 1]:
for ndis in range(1, self.nfree // 2 + 1):
dispName = ('%s.%d%s%s' %
(self.name, a, 'xyz'[i],
ndis * ' +-'[sign]))
disp = ndis * sign * self.delta
yield dispName, a, i, disp
def calculate(self, atoms, filename, fd):
forces = self.calc.get_forces(atoms)
if self.ir:
dipole = self.calc.get_dipole_moment(atoms)
if world.rank == 0:
if self.ir:
pickle.dump([forces, dipole], fd, protocol=2)
sys.stdout.write(
'Writing %s, dipole moment = (%.6f %.6f %.6f)\n' %
(filename, dipole[0], dipole[1], dipole[2]))
else:
pickle.dump(forces, fd, protocol=2)
sys.stdout.write('Writing %s\n' % filename)
fd.close()
sys.stdout.flush()
[docs] def clean(self, empty_files=False, combined=True):
"""Remove pickle-files.
Use empty_files=True to remove only empty files and
combined=False to not remove the combined file.
"""
if world.rank != 0:
return 0
n = 0
filenames = [self.name + '.eq.pckl']
if combined:
filenames.append(self.name + '.all.pckl')
for dispName, a, i, disp in self.displacements():
filename = dispName + '.pckl'
filenames.append(filename)
for name in filenames:
if op.isfile(name):
if not empty_files or op.getsize(name) == 0:
os.remove(name)
n += 1
return n
[docs] def combine(self):
"""Combine pickle-files to one file ending with '.all.pckl'.
The other pickle-files will be removed in order to have only one sort
of data structure at a time.
"""
if world.rank != 0:
return 0
filenames = [self.name + '.eq.pckl']
for dispName, a, i, disp in self.displacements():
filename = dispName + '.pckl'
filenames.append(filename)
combined_data = {}
for name in filenames:
if not op.isfile(name) or op.getsize(name) == 0:
raise RuntimeError('Calculation is not complete. ' +
name + ' is missing or empty.')
with open(name, 'rb') as fl:
f = pickleload(fl)
combined_data.update({op.basename(name): f})
filename = self.name + '.all.pckl'
fd = opencew(filename)
if fd is None:
raise RuntimeError(
'Cannot write file ' + filename +
'. Remove old file if it exists.')
else:
pickle.dump(combined_data, fd, protocol=2)
fd.close()
return self.clean(combined=False)
[docs] def split(self):
"""Split combined pickle-file.
The combined pickle-file will be removed in order to have only one
sort of data structure at a time.
"""
if world.rank != 0:
return 0
combined_name = self.name + '.all.pckl'
if not op.isfile(combined_name):
raise RuntimeError('Cannot find combined file: ' +
combined_name + '.')
with open(combined_name, 'rb') as fl:
combined_data = pickleload(fl)
filenames = [self.name + '.eq.pckl']
for dispName, a, i, disp in self.displacements():
filename = dispName + '.pckl'
filenames.append(filename)
if op.isfile(filename):
raise RuntimeError(
'Cannot split. File ' + filename + 'already exists.')
for name in filenames:
fd = opencew(name)
try:
pickle.dump(combined_data[op.basename(name)], fd, protocol=2)
except KeyError:
pickle.dump(combined_data[name], fd, protocol=2) # Old version
fd.close()
os.remove(combined_name)
return 1 # One file removed
def read(self, method='standard', direction='central'):
self.method = method.lower()
self.direction = direction.lower()
assert self.method in ['standard', 'frederiksen']
assert self.direction in ['central', 'forward', 'backward']
def load(fname, combined_data=None):
if combined_data is None:
with open(fname, 'rb') as fl:
f = pickleload(fl)
else:
try:
f = combined_data[op.basename(fname)]
except KeyError:
f = combined_data[fname] # Old version
if not hasattr(f, 'shape') and not hasattr(f, 'keys'):
# output from InfraRed
return f[0]
return f
n = 3 * len(self.indices)
H = np.empty((n, n))
r = 0
if op.isfile(self.name + '.all.pckl'):
# Open the combined pickle-file
combined_data = load(self.name + '.all.pckl')
else:
combined_data = None
if direction != 'central':
feq = load(self.name + '.eq.pckl', combined_data)
for a in self.indices:
for i in 'xyz':
name = '%s.%d%s' % (self.name, a, i)
fminus = load(name + '-.pckl', combined_data)
fplus = load(name + '+.pckl', combined_data)
if self.method == 'frederiksen':
fminus[a] -= fminus.sum(0)
fplus[a] -= fplus.sum(0)
if self.nfree == 4:
fminusminus = load(name + '--.pckl', combined_data)
fplusplus = load(name + '++.pckl', combined_data)
if self.method == 'frederiksen':
fminusminus[a] -= fminusminus.sum(0)
fplusplus[a] -= fplusplus.sum(0)
if self.direction == 'central':
if self.nfree == 2:
H[r] = .5 * (fminus - fplus)[self.indices].ravel()
else:
H[r] = H[r] = (-fminusminus +
8 * fminus -
8 * fplus +
fplusplus)[self.indices].ravel() / 12.0
elif self.direction == 'forward':
H[r] = (feq - fplus)[self.indices].ravel()
else:
assert self.direction == 'backward'
H[r] = (fminus - feq)[self.indices].ravel()
H[r] /= 2 * self.delta
r += 1
H += H.copy().T
self.H = H
m = self.atoms.get_masses()
if 0 in [m[index] for index in self.indices]:
raise RuntimeError('Zero mass encountered in one or more of '
'the vibrated atoms. Use Atoms.set_masses()'
' to set all masses to non-zero values.')
self.im = np.repeat(m[self.indices]**-0.5, 3)
omega2, modes = np.linalg.eigh(self.im[:, None] * H * self.im)
self.modes = modes.T.copy()
# Conversion factor:
s = units._hbar * 1e10 / sqrt(units._e * units._amu)
self.hnu = s * omega2.astype(complex)**0.5
[docs] def get_energies(self, method='standard', direction='central', **kw):
"""Get vibration energies in eV."""
if (self.H is None or method.lower() != self.method or
direction.lower() != self.direction):
self.read(method, direction, **kw)
return self.hnu
[docs] def get_frequencies(self, method='standard', direction='central'):
"""Get vibration frequencies in cm^-1."""
s = 1. / units.invcm
return s * self.get_energies(method, direction)
[docs] def summary(self, method='standard', direction='central', freq=None,
log=sys.stdout):
"""Print a summary of the vibrational frequencies.
Parameters:
method : string
Can be 'standard'(default) or 'Frederiksen'.
direction: string
Direction for finite differences. Can be one of 'central'
(default), 'forward', 'backward'.
freq : numpy array
Optional. Can be used to create a summary on a set of known
frequencies.
log : if specified, write output to a different location than
stdout. Can be an object with a write() method or the name of a
file to create.
"""
if isinstance(log, str):
log = paropen(log, 'a')
write = log.write
s = 0.01 * units._e / units._c / units._hplanck
if freq is not None:
hnu = freq / s
else:
hnu = self.get_energies(method, direction)
write('---------------------\n')
write(' # meV cm^-1\n')
write('---------------------\n')
for n, e in enumerate(hnu):
if e.imag != 0:
c = 'i'
e = e.imag
else:
c = ' '
e = e.real
write('%3d %6.1f%s %7.1f%s\n' % (n, 1000 * e, c, s * e, c))
write('---------------------\n')
write('Zero-point energy: %.3f eV\n' %
self.get_zero_point_energy(freq=freq))
def get_zero_point_energy(self, freq=None):
if freq is None:
return 0.5 * self.hnu.real.sum()
else:
s = 0.01 * units._e / units._c / units._hplanck
return 0.5 * freq.real.sum() / s
[docs] def get_mode(self, n):
"""Get mode number ."""
mode = np.zeros((len(self.atoms), 3))
mode[self.indices] = (self.modes[n] * self.im).reshape((-1, 3))
return mode
[docs] def write_mode(self, n=None, kT=units.kB * 300, nimages=30):
"""Write mode number n to trajectory file. If n is not specified,
writes all non-zero modes."""
if n is None:
for index, energy in enumerate(self.get_energies()):
if abs(energy) > 1e-5:
self.write_mode(n=index, kT=kT, nimages=nimages)
return
mode = self.get_mode(n) * sqrt(kT / abs(self.hnu[n]))
pos0 = self.atoms.get_positions()
n %= 3 * len(self.indices)
atoms = self.atoms.copy()
with Trajectory('%s.%d.traj' % (self.name, n), 'w') as traj:
for x in np.linspace(0, 2 * pi, nimages, endpoint=False):
atoms.set_positions(pos0 + sin(x) * mode)
traj.write(atoms)
def show_as_force(self, n, scale=0.2):
mode = self.get_mode(n) * len(self.hnu) * scale
calc = SinglePointCalculator(self.atoms, forces=mode)
self.atoms.calc = calc
self.atoms.edit()
[docs] def write_jmol(self):
"""Writes file for viewing of the modes with jmol."""
with open(self.name + '.xyz', 'w') as fd:
self._write_jmol(fd)
def _write_jmol(self, fd):
symbols = self.atoms.get_chemical_symbols()
freq = self.get_frequencies()
for n in range(3 * len(self.indices)):
fd.write('%6d\n' % len(self.atoms))
if freq[n].imag != 0:
c = 'i'
freq[n] = freq[n].imag
else:
c = ' '
fd.write('Mode #%d, f = %.1f%s cm^-1' % (n, freq[n], c))
if self.ir:
fd.write(', I = %.4f (D/Å)^2 amu^-1.\n' % self.intensities[n])
else:
fd.write('.\n')
mode = self.get_mode(n)
for i, pos in enumerate(self.atoms.positions):
fd.write('%2s %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f \n' %
(symbols[i], pos[0], pos[1], pos[2],
mode[i, 0], mode[i, 1], mode[i, 2]))
[docs] def fold(self, frequencies, intensities,
start=800.0, end=4000.0, npts=None, width=4.0,
type='Gaussian', normalize=False):
"""Fold frequencies and intensities within the given range
and folding method (Gaussian/Lorentzian).
The energy unit is cm^-1.
normalize=True ensures the integral over the peaks to give the
intensity.
"""
lctype = type.lower()
assert lctype in ['gaussian', 'lorentzian']
if not npts:
npts = int((end - start) / width * 10 + 1)
prefactor = 1
if lctype == 'lorentzian':
intensities = intensities * width * pi / 2.
if normalize:
prefactor = 2. / width / pi
else:
sigma = width / 2. / sqrt(2. * log(2.))
if normalize:
prefactor = 1. / sigma / sqrt(2 * pi)
# Make array with spectrum data
spectrum = np.empty(npts)
energies = np.linspace(start, end, npts)
for i, energy in enumerate(energies):
energies[i] = energy
if lctype == 'lorentzian':
spectrum[i] = (intensities * 0.5 * width / pi /
((frequencies - energy)**2 +
0.25 * width**2)).sum()
else:
spectrum[i] = (intensities *
np.exp(-(frequencies - energy)**2 /
2. / sigma**2)).sum()
return [energies, prefactor * spectrum]
[docs] def write_dos(self, out='vib-dos.dat', start=800, end=4000,
npts=None, width=10,
type='Gaussian', method='standard', direction='central'):
"""Write out the vibrational density of states to file.
First column is the wavenumber in cm^-1, the second column the
folded vibrational density of states.
Start and end points, and width of the Gaussian/Lorentzian
should be given in cm^-1."""
frequencies = self.get_frequencies(method, direction).real
intensities = np.ones(len(frequencies))
energies, spectrum = self.fold(frequencies, intensities,
start, end, npts, width, type)
# Write out spectrum in file.
outdata = np.empty([len(energies), 2])
outdata.T[0] = energies
outdata.T[1] = spectrum
with open(out, 'w') as fd:
fd.write('# %s folded, width=%g cm^-1\n' % (type.title(), width))
fd.write('# [cm^-1] arbitrary\n')
for row in outdata:
fd.write('%.3f %15.5e\n' %
(row[0], row[1]))