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# Source code for ase.vibrations.vibrations

    # -*- coding: utf-8 -*-
    """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, basestring
    from ase.calculators.singlepoint import SinglePointCalculator

    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.get_calculator()
            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
            self.ram = None

        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)

        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

        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 self.ram:
                freq, noninPol, pol = self.get_polarizability()
            if world.rank == 0:
                if self.ir and self.ram:
                    pickle.dump([forces, dipole, freq, noninPol, pol], fd, protocol=2)
                    sys.stdout.write(
                        'Writing %s, dipole moment = (%.6f %.6f %.6f)\n' %
                        (filename, dipole[0], dipole[1], dipole[2]))
                elif self.ir and not self.ram:
                    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()

        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

        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)

        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

        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

        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)

        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, basestring):
                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

        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

        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]))
            p = self.atoms.positions.copy()
            n %= 3 * len(self.indices)
            traj = Trajectory('%s.%d.traj' % (self.name, n), 'w')
            calc = self.atoms.get_calculator()
            self.atoms.set_calculator()
            for x in np.linspace(0, 2 * pi, nimages, endpoint=False):
                self.atoms.set_positions(p + sin(x) * mode)
                traj.write(self.atoms)
            self.atoms.set_positions(p)
            self.atoms.set_calculator(calc)
            traj.close()

        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.set_calculator(calc)
            self.atoms.edit()

        def write_jmol(self):
            """Writes file for viewing of the modes with jmol."""

            fd = open(self.name + '.xyz', 'w')
            symbols = self.atoms.get_chemical_symbols()
            f = self.get_frequencies()
            for n in range(3 * len(self.indices)):
                fd.write('%6d\n' % len(self.atoms))
                if f[n].imag != 0:
                    c = 'i'
                    f[n] = f[n].imag
                else:
                    c = ' '
                fd.write('Mode #%d, f = %.1f%s cm^-1' % (n, f[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]))
            fd.close()

        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]

        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
            fd = open(out, 'w')
            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]))
            fd.close()

Documentation v: 3.19.0

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