Exemplo n.º 1
0
    def __init__(self, calc, gamma=True, symmetry=False, e_ph=False,
                 communicator=serial_comm):
        """Inititialize class with a list of atoms.

        The atoms object must contain a converged ground-state calculation.

        The set of q-vectors in which the dynamical matrix will be calculated
        is determined from the ``symmetry`` kwarg. For now, only time-reversal
        symmetry is used to generate the irrecducible BZ.

        Add a little note on parallelization strategy here.

        Parameters
        ----------
        calc: str or Calculator
            Calculator containing a ground-state calculation.
        gamma: bool
            Gamma-point calculation with respect to the q-vector of the
            dynamical matrix. When ``False``, the Monkhorst-Pack grid from the
            ground-state calculation is used.
        symmetry: bool
            Use symmetries to reduce the q-vectors of the dynamcial matrix
            (None, False or True). The different options are equivalent to the
            options in a ground-state calculation.
        e_ph: bool
            Save the derivative of the effective potential.
        communicator: Communicator
            Communicator for parallelization over k-points and real-space
            domain.
            
        """

        # XXX
        assert symmetry in [None, False], "Spatial symmetries not allowed yet"

        self.symmetry = symmetry

        if isinstance(calc, str):
            self.calc = GPAW(calc, communicator=serial_comm, txt=None)
        else:
            self.calc = calc

        # Make sure localized functions are initialized
        self.calc.set_positions()
        # Note that this under some circumstances (e.g. when called twice)
        # allocates a new array for the P_ani coefficients !!

        # Store useful objects
        self.atoms = self.calc.get_atoms()
        # Get rid of ``calc`` attribute
        self.atoms.calc = None
 
        # Boundary conditions
        pbc_c = self.calc.atoms.get_pbc()

        if np.all(pbc_c == False):
            self.gamma = True
            self.dtype = float
            kpts = None
            # Multigrid Poisson solver
            poisson_solver = PoissonSolver()
        else:
            if gamma:
                self.gamma = True
                self.dtype = float
                kpts = None
            else:
                self.gamma = False
                self.dtype = complex
                # Get k-points from ground-state calculation
                kpts = self.calc.input_parameters.kpts
                
            # FFT Poisson solver
            poisson_solver = FFTPoissonSolver(dtype=self.dtype)

        # K-point descriptor for the q-vectors of the dynamical matrix
        # Note, no explicit parallelization here.
        self.kd = KPointDescriptor(kpts, 1)
        self.kd.set_symmetry(self.atoms, self.calc.wfs.setups,
                             usesymm=symmetry)
        self.kd.set_communicator(serial_comm)

        # Number of occupied bands
        nvalence = self.calc.wfs.nvalence
        nbands = nvalence / 2 + nvalence % 2
        assert nbands <= self.calc.wfs.bd.nbands

        # Extract other useful objects
        # Ground-state k-point descriptor - used for the k-points in the
        # ResponseCalculator
        # XXX replace communicators when ready to parallelize
        kd_gs = self.calc.wfs.kd
        gd = self.calc.density.gd
        kpt_u = self.calc.wfs.kpt_u
        setups = self.calc.wfs.setups
        dtype_gs = self.calc.wfs.dtype
        
        # WaveFunctions
        wfs = WaveFunctions(nbands, kpt_u, setups, kd_gs, gd, dtype=dtype_gs)

        # Linear response calculator
        self.response_calc = ResponseCalculator(self.calc, wfs,
                                                dtype=self.dtype)
        
        # Phonon perturbation
        self.perturbation = PhononPerturbation(self.calc, self.kd,
                                               poisson_solver,
                                               dtype=self.dtype)

        # Dynamical matrix
        self.dyn = DynamicalMatrix(self.atoms, self.kd, dtype=self.dtype)

        # Electron-phonon couplings
        if e_ph:
            self.e_ph = ElectronPhononCoupling(self.atoms, gd, self.kd,
                                               dtype=self.dtype)
        else:
            self.e_ph = None
                                               
        # Initialization flag
        self.initialized = False

        # Parallel communicator for parallelization over kpts and domain
        self.comm = communicator
Exemplo n.º 2
0
    def __init__(self,
                 calc,
                 gamma=True,
                 symmetry=False,
                 e_ph=False,
                 communicator=serial_comm):
        """Inititialize class with a list of atoms.

        The atoms object must contain a converged ground-state calculation.

        The set of q-vectors in which the dynamical matrix will be calculated
        is determined from the ``symmetry`` kwarg. For now, only time-reversal
        symmetry is used to generate the irrecducible BZ.

        Add a little note on parallelization strategy here.

        Parameters
        ----------
        calc: str or Calculator
            Calculator containing a ground-state calculation.
        gamma: bool
            Gamma-point calculation with respect to the q-vector of the
            dynamical matrix. When ``False``, the Monkhorst-Pack grid from the
            ground-state calculation is used.
        symmetry: bool
            Use symmetries to reduce the q-vectors of the dynamcial matrix
            (None, False or True). The different options are equivalent to the
            old style options in a ground-state calculation (see usesymm).
        e_ph: bool
            Save the derivative of the effective potential.
        communicator: Communicator
            Communicator for parallelization over k-points and real-space
            domain.
        """

        # XXX
        assert symmetry in [None, False], "Spatial symmetries not allowed yet"

        if isinstance(calc, str):
            self.calc = GPAW(calc, communicator=serial_comm, txt=None)
        else:
            self.calc = calc

        cell_cv = self.calc.atoms.get_cell()
        setups = self.calc.wfs.setups
        # XXX - no clue how to get magmom - ignore it for the moment
        # m_av = magmom_av.round(decimals=3)  # round off
        # id_a = zip(setups.id_a, *m_av.T)
        id_a = setups.id_a

        if symmetry is None:
            self.symmetry = Symmetry(id_a,
                                     cell_cv,
                                     point_group=False,
                                     time_reversal=False)
        else:
            self.symmetry = Symmetry(id_a,
                                     cell_cv,
                                     point_group=False,
                                     time_reversal=True)

        # Make sure localized functions are initialized
        self.calc.set_positions()
        # Note that this under some circumstances (e.g. when called twice)
        # allocates a new array for the P_ani coefficients !!

        # Store useful objects
        self.atoms = self.calc.get_atoms()
        # Get rid of ``calc`` attribute
        self.atoms.calc = None

        # Boundary conditions
        pbc_c = self.calc.atoms.get_pbc()

        if np.all(pbc_c == False):
            self.gamma = True
            self.dtype = float
            kpts = None
            # Multigrid Poisson solver
            poisson_solver = PoissonSolver()
        else:
            if gamma:
                self.gamma = True
                self.dtype = float
                kpts = None
            else:
                self.gamma = False
                self.dtype = complex
                # Get k-points from ground-state calculation
                kpts = self.calc.input_parameters.kpts

            # FFT Poisson solver
            poisson_solver = FFTPoissonSolver(dtype=self.dtype)

        # K-point descriptor for the q-vectors of the dynamical matrix
        # Note, no explicit parallelization here.
        self.kd = KPointDescriptor(kpts, 1)
        self.kd.set_symmetry(self.atoms, self.symmetry)
        self.kd.set_communicator(serial_comm)

        # Number of occupied bands
        nvalence = self.calc.wfs.nvalence
        nbands = nvalence // 2 + nvalence % 2
        assert nbands <= self.calc.wfs.bd.nbands

        # Extract other useful objects
        # Ground-state k-point descriptor - used for the k-points in the
        # ResponseCalculator
        # XXX replace communicators when ready to parallelize
        kd_gs = self.calc.wfs.kd
        gd = self.calc.density.gd
        kpt_u = self.calc.wfs.kpt_u
        setups = self.calc.wfs.setups
        dtype_gs = self.calc.wfs.dtype

        # WaveFunctions
        wfs = WaveFunctions(nbands, kpt_u, setups, kd_gs, gd, dtype=dtype_gs)

        # Linear response calculator
        self.response_calc = ResponseCalculator(self.calc,
                                                wfs,
                                                dtype=self.dtype)

        # Phonon perturbation
        self.perturbation = PhononPerturbation(self.calc,
                                               self.kd,
                                               poisson_solver,
                                               dtype=self.dtype)

        # Dynamical matrix
        self.dyn = DynamicalMatrix(self.atoms, self.kd, dtype=self.dtype)

        # Electron-phonon couplings
        if e_ph:
            self.e_ph = ElectronPhononCoupling(self.atoms,
                                               gd,
                                               self.kd,
                                               dtype=self.dtype)
        else:
            self.e_ph = None

        # Initialization flag
        self.initialized = False

        # Parallel communicator for parallelization over kpts and domain
        self.comm = communicator
Exemplo n.º 3
0
class PhononCalculator:
    """This class defines the interface for phonon calculations."""
    
    def __init__(self, calc, gamma=True, symmetry=False, e_ph=False,
                 communicator=serial_comm):
        """Inititialize class with a list of atoms.

        The atoms object must contain a converged ground-state calculation.

        The set of q-vectors in which the dynamical matrix will be calculated
        is determined from the ``symmetry`` kwarg. For now, only time-reversal
        symmetry is used to generate the irrecducible BZ.

        Add a little note on parallelization strategy here.

        Parameters
        ----------
        calc: str or Calculator
            Calculator containing a ground-state calculation.
        gamma: bool
            Gamma-point calculation with respect to the q-vector of the
            dynamical matrix. When ``False``, the Monkhorst-Pack grid from the
            ground-state calculation is used.
        symmetry: bool
            Use symmetries to reduce the q-vectors of the dynamcial matrix
            (None, False or True). The different options are equivalent to the
            options in a ground-state calculation.
        e_ph: bool
            Save the derivative of the effective potential.
        communicator: Communicator
            Communicator for parallelization over k-points and real-space
            domain.
            
        """

        # XXX
        assert symmetry in [None, False], "Spatial symmetries not allowed yet"

        self.symmetry = symmetry

        if isinstance(calc, str):
            self.calc = GPAW(calc, communicator=serial_comm, txt=None)
        else:
            self.calc = calc

        # Make sure localized functions are initialized
        self.calc.set_positions()
        # Note that this under some circumstances (e.g. when called twice)
        # allocates a new array for the P_ani coefficients !!

        # Store useful objects
        self.atoms = self.calc.get_atoms()
        # Get rid of ``calc`` attribute
        self.atoms.calc = None
 
        # Boundary conditions
        pbc_c = self.calc.atoms.get_pbc()

        if np.all(pbc_c == False):
            self.gamma = True
            self.dtype = float
            kpts = None
            # Multigrid Poisson solver
            poisson_solver = PoissonSolver()
        else:
            if gamma:
                self.gamma = True
                self.dtype = float
                kpts = None
            else:
                self.gamma = False
                self.dtype = complex
                # Get k-points from ground-state calculation
                kpts = self.calc.input_parameters.kpts
                
            # FFT Poisson solver
            poisson_solver = FFTPoissonSolver(dtype=self.dtype)

        # K-point descriptor for the q-vectors of the dynamical matrix
        # Note, no explicit parallelization here.
        self.kd = KPointDescriptor(kpts, 1)
        self.kd.set_symmetry(self.atoms, self.calc.wfs.setups,
                             usesymm=symmetry)
        self.kd.set_communicator(serial_comm)

        # Number of occupied bands
        nvalence = self.calc.wfs.nvalence
        nbands = nvalence / 2 + nvalence % 2
        assert nbands <= self.calc.wfs.bd.nbands

        # Extract other useful objects
        # Ground-state k-point descriptor - used for the k-points in the
        # ResponseCalculator
        # XXX replace communicators when ready to parallelize
        kd_gs = self.calc.wfs.kd
        gd = self.calc.density.gd
        kpt_u = self.calc.wfs.kpt_u
        setups = self.calc.wfs.setups
        dtype_gs = self.calc.wfs.dtype
        
        # WaveFunctions
        wfs = WaveFunctions(nbands, kpt_u, setups, kd_gs, gd, dtype=dtype_gs)

        # Linear response calculator
        self.response_calc = ResponseCalculator(self.calc, wfs,
                                                dtype=self.dtype)
        
        # Phonon perturbation
        self.perturbation = PhononPerturbation(self.calc, self.kd,
                                               poisson_solver,
                                               dtype=self.dtype)

        # Dynamical matrix
        self.dyn = DynamicalMatrix(self.atoms, self.kd, dtype=self.dtype)

        # Electron-phonon couplings
        if e_ph:
            self.e_ph = ElectronPhononCoupling(self.atoms, gd, self.kd,
                                               dtype=self.dtype)
        else:
            self.e_ph = None
                                               
        # Initialization flag
        self.initialized = False

        # Parallel communicator for parallelization over kpts and domain
        self.comm = communicator

    def initialize(self):
        """Initialize response calculator and perturbation."""

        # Get scaled atomic positions
        spos_ac = self.atoms.get_scaled_positions()

        self.perturbation.initialize(spos_ac)
        self.response_calc.initialize(spos_ac)

        self.initialized = True
        
    def __getstate__(self): 
        """Method used when pickling.

        Bound method attributes cannot be pickled and must therefore be deleted
        before an instance is dumped to file.

        """

        # Get state of object and take care of troublesome attributes
        state = dict(self.__dict__)
        state['kd'].__dict__['comm'] = serial_comm
        state.pop('calc')
        state.pop('perturbation')
        state.pop('response_calc')
        
        return state

    def run(self, qpts_q=None, clean=False, name=None, path=None):
        """Run calculation for atomic displacements and update matrix.

        Parameters
        ----------
        qpts: List
            List of q-points indices for which the dynamical matrix will be
            calculated (only temporary).

        """

        if not self.initialized:
            self.initialize()

        if self.gamma:
            qpts_q = [0]
        elif qpts_q is None:
            qpts_q = range(self.kd.nibzkpts)
        else:
            assert isinstance(qpts_q, list)

        # Update name and path attributes
        self.set_name_and_path(name=name, path=path)
        # Get string template for filenames
        filename_str = self.get_filename_string()

        # Delay the ranks belonging to the same k-point/domain decomposition
        # equally
        time.sleep(rank // self.comm.size)

        # XXX Make a single ground_state_contributions member function
        # Ground-state contributions to the force constants
        self.dyn.density_ground_state(self.calc)
        # self.dyn.wfs_ground_state(self.calc, self.response_calc)
        
        # Calculate linear response wrt q-vectors and displacements of atoms
        for q in qpts_q:
            
            if not self.gamma:
                self.perturbation.set_q(q)

            # First-order contributions to the force constants
            for a in self.dyn.indices:
                for v in [0, 1, 2]:

                    # Check if the calculation has already been done
                    filename = filename_str % (q, a, v)
                    # Wait for all sub-ranks to enter
                    self.comm.barrier()
                    
                    if os.path.isfile(os.path.join(self.path, filename)):
                        continue

                    if self.comm.rank == 0:
                        fd = open(os.path.join(self.path, filename), 'w')

                    # Wait for all sub-ranks here
                    self.comm.barrier()
                    
                    components = ['x', 'y', 'z']
                    symbols = self.atoms.get_chemical_symbols()
                    print "q-vector index: %i" % q
                    print "Atom index: %i" % a
                    print "Atomic symbol: %s" % symbols[a]
                    print "Component: %s" % components[v]

                    # Set atom and cartesian component of perturbation
                    self.perturbation.set_av(a, v)
                    # Calculate linear response
                    self.response_calc(self.perturbation)

                    # Calculate row of the matrix of force constants
                    self.dyn.calculate_row(self.perturbation,
                                           self.response_calc)

                    # Write force constants to file
                    if self.comm.rank == 0:
                        self.dyn.write(fd, q, a, v)
                        fd.close()
                        
                    # Store effective potential derivative
                    if self.e_ph is not None:
                        v1_eff_G = self.perturbation.v1_G + \
                                   self.response_calc.vHXC1_G
                        self.e_ph.v1_eff_qavG.append(v1_eff_G)

                    # Wait for the file-writing rank here
                    self.comm.barrier()

        # XXX
        # Check that all files are valid and collect in a single file
        # Remove the files
        if clean:
            self.clean()
            
    def get_atoms(self):
        """Return atoms."""

        return self.atoms
    
    def get_dynamical_matrix(self):
        """Return reference to ``dyn`` attribute."""
        
        return self.dyn

    def get_filename_string(self):
        """Return string template for force constant filenames."""

        name_str = (self.name + '.' + 'q_%%0%ii_' % len(str(self.kd.nibzkpts)) +
                    'a_%%0%ii_' % len(str(len(self.atoms))) + 'v_%i' + '.pckl')

        return name_str
    
    def set_atoms(self, atoms):
        """Set atoms to be included in the calculation.

        Parameters
        ----------
        atoms: list
            Can be either a list of strings, ints or ...
            
        """
        
        assert isinstance(atoms, list)
        
        if isinstance(atoms[0], str):
            assert np.all([isinstance(atom, str) for atom in atoms])
            sym_a = self.atoms.get_chemical_symbols()
            # List for atomic indices
            indices = []
            for type in atoms:
                indices.extend([a for a, atom in enumerate(sym_a)
                                if atom == type])
        else:
            assert np.all([isinstance(atom, int) for atom in atoms])
            indices = atoms
            
        self.dyn.set_indices(indices)

    def set_name_and_path(self, name=None, path=None):
        """Set name and path of the force constant files.

        name: str
            Base name for the files which the elements of the matrix of force
            constants will be written to.
        path: str
            Path specifying the directory where the files will be dumped.
            
        """

        if name is None:
            self.name = 'phonon.' + self.atoms.get_chemical_formula()
        else:
            self.name = name
        # self.name += '.nibzkpts_%i' % self.kd.nibzkpts
        
        if path is None:
            self.path = '.'
        else:
            self.path = path

        # Set corresponding attributes in the ``dyn`` attribute
        filename_str = self.get_filename_string()
        self.dyn.set_name_and_path(filename_str, self.path)
            
    def clean(self):
        """Delete generated files."""

        filename_str = self.get_filename_string()
        
        for q in range(self.kd.nibzkpts):
            for a in range(len(self.atoms)):
                for v in [0, 1, 2]:
                    filename = filename_str % (q, a, v)
                    if os.path.isfile(os.path.join(self.path, filename)):
                        os.remove(filename)
                        
    def band_structure(self, path_kc, modes=False, acoustic=True):
        """Calculate phonon dispersion along a path in the Brillouin zone.

        The dynamical matrix at arbitrary q-vectors is obtained by Fourier
        transforming the real-space matrix. In case of negative eigenvalues
        (squared frequency), the corresponding negative frequency is returned.

        Parameters
        ----------
        path_kc: ndarray
            List of k-point coordinates (in units of the reciprocal lattice
            vectors) specifying the path in the Brillouin zone for which the
            dynamical matrix will be calculated.
        modes: bool
            Returns both frequencies and modes (mass scaled) when True.
        acoustic: bool
            Restore the acoustic sum-rule in the calculated force constants.
            
        """

        for k_c in path_kc:
            assert np.all(np.asarray(k_c) <= 1.0), \
                   "Scaled coordinates must be given"

        # Assemble the dynanical matrix from calculated force constants
        self.dyn.assemble(acoustic=acoustic)
        # Get the dynamical matrix in real-space
        DR_lmn, R_clmn = self.dyn.real_space()

        # Reshape for the evaluation of the fourier sums
        shape = DR_lmn.shape
        DR_m = DR_lmn.reshape((-1,) + shape[-2:])
        R_cm = R_clmn.reshape((3, -1))

        # Lists for frequencies and modes along path
        omega_kn = []
        u_kn =  []
        # Number of atoms included
        N = len(self.dyn.get_indices())
        
        # Mass prefactor for the normal modes
        m_inv_av = self.dyn.get_mass_array()
        
        for q_c in path_kc:

            # Evaluate fourier transform 
            phase_m = np.exp(-2.j * pi * np.dot(q_c, R_cm))
            # Dynamical matrix in unit of Ha / Bohr**2 / amu
            D_q = np.sum(phase_m[:, np.newaxis, np.newaxis] * DR_m, axis=0)

            if modes:
                omega2_n, u_avn = la.eigh(D_q, UPLO='L')
                # Sort eigenmodes according to eigenvalues (see below) and
                # multiply with mass prefactor
                u_nav = u_avn[:, omega2_n.argsort()].T.copy() * m_inv_av
                # Multiply with mass prefactor
                u_kn.append(u_nav.reshape((3*N, -1, 3)))
            else:
                omega2_n = la.eigvalsh(D_q, UPLO='L')

            # Sort eigenvalues in increasing order
            omega2_n.sort()
            # Use dtype=complex to handle negative eigenvalues
            omega_n = np.sqrt(omega2_n.astype(complex))

            # Take care of imaginary frequencies
            if not np.all(omega2_n >= 0.):
                indices = np.where(omega2_n < 0)[0]
                print ("WARNING, %i imaginary frequencies at "
                       "q = (% 5.2f, % 5.2f, % 5.2f) ; (omega_q =% 5.3e*i)"
                       % (len(indices), q_c[0], q_c[1], q_c[2],
                          omega_n[indices][0].imag))
                
                omega_n[indices] = -1 * np.sqrt(np.abs(omega2_n[indices].real))

            omega_kn.append(omega_n.real)

        # Conversion factor from sqrt(Ha / Bohr**2 / amu) -> eV
        s = units.Hartree**0.5 * units._hbar * 1.e10 / \
            (units._e * units._amu)**(0.5) / units.Bohr
        # Convert to eV and Ang
        omega_kn = s * np.asarray(omega_kn)
        if modes:
            u_kn = np.asarray(u_kn) * units.Bohr
            return omega_kn, u_kn
        
        return omega_kn

    def write_modes(self, q_c, branches=0, kT=units.kB*300, repeat=(1, 1, 1),
                    nimages=30, acoustic=True):
        """Write mode to trajectory file.

        The classical equipartioning theorem states that each normal mode has
        an average energy::
        
            <E> = 1/2 * k_B * T = 1/2 * omega^2 * Q^2

                =>

              Q = sqrt(k_B*T) / omega

        at temperature T. Here, Q denotes the normal coordinate of the mode.
        
        Parameters
        ----------
        q_c: ndarray
            q-vector of the modes.
        branches: int or list
            Branch index of calculated modes.
        kT: float
            Temperature in units of eV. Determines the amplitude of the atomic
            displacements in the modes.
        repeat: tuple
            Repeat atoms (l, m, n) times in the directions of the lattice
            vectors. Displacements of atoms in repeated cells carry a Bloch
            phase factor given by the q-vector and the cell lattice vector R_m.
        nimages: int
            Number of images in an oscillation.
            
        """

        if isinstance(branches, int):
            branch_n = [branches]
        else:
            branch_n = list(branches)

        # Calculate modes
        omega_n, u_n = self.band_structure([q_c], modes=True, acoustic=acoustic)
        
        # Repeat atoms
        atoms = self.atoms * repeat
        pos_mav = atoms.positions.copy()
        # Total number of unit cells
        M = np.prod(repeat)
            
        # Corresponding lattice vectors R_m
        R_cm = np.indices(repeat[::-1]).reshape(3, -1)[::-1]
        # Bloch phase
        phase_m = np.exp(2.j * pi * np.dot(q_c, R_cm))
        phase_ma = phase_m.repeat(len(self.atoms))

     
        for n in branch_n:

            omega = omega_n[0, n]
            u_av = u_n[0, n] # .reshape((-1, 3))
            # Mean displacement at high T ?
            u_av *= sqrt(kT / abs(omega))
            
            mode_av = np.zeros((len(self.atoms), 3), dtype=self.dtype)
            indices = self.dyn.get_indices()
            mode_av[indices] = u_av
            mode_mav = (np.vstack([mode_av]*M) * phase_ma[:, np.newaxis]).real

            traj = PickleTrajectory('%s.mode.%d.traj' % (self.name, n), 'w')

            for x in np.linspace(0, 2*pi, nimages, endpoint=False):
                # XXX Is it correct to take out the sine component here ?
                atoms.set_positions(pos_mav + sin(x) * mode_mav)
                traj.write(atoms)
                
            traj.close()
Exemplo n.º 4
0
class PhononCalculator:
    """This class defines the interface for phonon calculations."""
    def __init__(self,
                 calc,
                 gamma=True,
                 symmetry=False,
                 e_ph=False,
                 communicator=serial_comm):
        """Inititialize class with a list of atoms.

        The atoms object must contain a converged ground-state calculation.

        The set of q-vectors in which the dynamical matrix will be calculated
        is determined from the ``symmetry`` kwarg. For now, only time-reversal
        symmetry is used to generate the irrecducible BZ.

        Add a little note on parallelization strategy here.

        Parameters
        ----------
        calc: str or Calculator
            Calculator containing a ground-state calculation.
        gamma: bool
            Gamma-point calculation with respect to the q-vector of the
            dynamical matrix. When ``False``, the Monkhorst-Pack grid from the
            ground-state calculation is used.
        symmetry: bool
            Use symmetries to reduce the q-vectors of the dynamcial matrix
            (None, False or True). The different options are equivalent to the
            old style options in a ground-state calculation (see usesymm).
        e_ph: bool
            Save the derivative of the effective potential.
        communicator: Communicator
            Communicator for parallelization over k-points and real-space
            domain.
        """

        # XXX
        assert symmetry in [None, False], "Spatial symmetries not allowed yet"

        if isinstance(calc, str):
            self.calc = GPAW(calc, communicator=serial_comm, txt=None)
        else:
            self.calc = calc

        cell_cv = self.calc.atoms.get_cell()
        setups = self.calc.wfs.setups
        # XXX - no clue how to get magmom - ignore it for the moment
        # m_av = magmom_av.round(decimals=3)  # round off
        # id_a = zip(setups.id_a, *m_av.T)
        id_a = setups.id_a

        if symmetry is None:
            self.symmetry = Symmetry(id_a,
                                     cell_cv,
                                     point_group=False,
                                     time_reversal=False)
        else:
            self.symmetry = Symmetry(id_a,
                                     cell_cv,
                                     point_group=False,
                                     time_reversal=True)

        # Make sure localized functions are initialized
        self.calc.set_positions()
        # Note that this under some circumstances (e.g. when called twice)
        # allocates a new array for the P_ani coefficients !!

        # Store useful objects
        self.atoms = self.calc.get_atoms()
        # Get rid of ``calc`` attribute
        self.atoms.calc = None

        # Boundary conditions
        pbc_c = self.calc.atoms.get_pbc()

        if np.all(pbc_c == False):
            self.gamma = True
            self.dtype = float
            kpts = None
            # Multigrid Poisson solver
            poisson_solver = PoissonSolver()
        else:
            if gamma:
                self.gamma = True
                self.dtype = float
                kpts = None
            else:
                self.gamma = False
                self.dtype = complex
                # Get k-points from ground-state calculation
                kpts = self.calc.input_parameters.kpts

            # FFT Poisson solver
            poisson_solver = FFTPoissonSolver(dtype=self.dtype)

        # K-point descriptor for the q-vectors of the dynamical matrix
        # Note, no explicit parallelization here.
        self.kd = KPointDescriptor(kpts, 1)
        self.kd.set_symmetry(self.atoms, self.symmetry)
        self.kd.set_communicator(serial_comm)

        # Number of occupied bands
        nvalence = self.calc.wfs.nvalence
        nbands = nvalence // 2 + nvalence % 2
        assert nbands <= self.calc.wfs.bd.nbands

        # Extract other useful objects
        # Ground-state k-point descriptor - used for the k-points in the
        # ResponseCalculator
        # XXX replace communicators when ready to parallelize
        kd_gs = self.calc.wfs.kd
        gd = self.calc.density.gd
        kpt_u = self.calc.wfs.kpt_u
        setups = self.calc.wfs.setups
        dtype_gs = self.calc.wfs.dtype

        # WaveFunctions
        wfs = WaveFunctions(nbands, kpt_u, setups, kd_gs, gd, dtype=dtype_gs)

        # Linear response calculator
        self.response_calc = ResponseCalculator(self.calc,
                                                wfs,
                                                dtype=self.dtype)

        # Phonon perturbation
        self.perturbation = PhononPerturbation(self.calc,
                                               self.kd,
                                               poisson_solver,
                                               dtype=self.dtype)

        # Dynamical matrix
        self.dyn = DynamicalMatrix(self.atoms, self.kd, dtype=self.dtype)

        # Electron-phonon couplings
        if e_ph:
            self.e_ph = ElectronPhononCoupling(self.atoms,
                                               gd,
                                               self.kd,
                                               dtype=self.dtype)
        else:
            self.e_ph = None

        # Initialization flag
        self.initialized = False

        # Parallel communicator for parallelization over kpts and domain
        self.comm = communicator

    def initialize(self):
        """Initialize response calculator and perturbation."""

        # Get scaled atomic positions
        spos_ac = self.atoms.get_scaled_positions()

        self.perturbation.initialize(spos_ac)
        self.response_calc.initialize(spos_ac)

        self.initialized = True

    def __getstate__(self):
        """Method used when pickling.

        Bound method attributes cannot be pickled and must therefore be deleted
        before an instance is dumped to file.

        """

        # Get state of object and take care of troublesome attributes
        state = dict(self.__dict__)
        state['kd'].__dict__['comm'] = serial_comm
        state.pop('calc')
        state.pop('perturbation')
        state.pop('response_calc')

        return state

    def run(self, qpts_q=None, clean=False, name=None, path=None):
        """Run calculation for atomic displacements and update matrix.

        Parameters
        ----------
        qpts: List
            List of q-points indices for which the dynamical matrix will be
            calculated (only temporary).

        """

        if not self.initialized:
            self.initialize()

        if self.gamma:
            qpts_q = [0]
        elif qpts_q is None:
            qpts_q = range(self.kd.nibzkpts)
        else:
            assert isinstance(qpts_q, list)

        # Update name and path attributes
        self.set_name_and_path(name=name, path=path)
        # Get string template for filenames
        filename_str = self.get_filename_string()

        # Delay the ranks belonging to the same k-point/domain decomposition
        # equally
        time.sleep(rank // self.comm.size)

        # XXX Make a single ground_state_contributions member function
        # Ground-state contributions to the force constants
        self.dyn.density_ground_state(self.calc)
        # self.dyn.wfs_ground_state(self.calc, self.response_calc)

        # Calculate linear response wrt q-vectors and displacements of atoms
        for q in qpts_q:

            if not self.gamma:
                self.perturbation.set_q(q)

            # First-order contributions to the force constants
            for a in self.dyn.indices:
                for v in [0, 1, 2]:

                    # Check if the calculation has already been done
                    filename = filename_str % (q, a, v)
                    # Wait for all sub-ranks to enter
                    self.comm.barrier()

                    if os.path.isfile(os.path.join(self.path, filename)):
                        continue

                    if self.comm.rank == 0:
                        fd = open(os.path.join(self.path, filename), 'w')

                    # Wait for all sub-ranks here
                    self.comm.barrier()

                    components = ['x', 'y', 'z']
                    symbols = self.atoms.get_chemical_symbols()
                    print("q-vector index: %i" % q)
                    print("Atom index: %i" % a)
                    print("Atomic symbol: %s" % symbols[a])
                    print("Component: %s" % components[v])

                    # Set atom and cartesian component of perturbation
                    self.perturbation.set_av(a, v)
                    # Calculate linear response
                    self.response_calc(self.perturbation)

                    # Calculate row of the matrix of force constants
                    self.dyn.calculate_row(self.perturbation,
                                           self.response_calc)

                    # Write force constants to file
                    if self.comm.rank == 0:
                        self.dyn.write(fd, q, a, v)
                        fd.close()

                    # Store effective potential derivative
                    if self.e_ph is not None:
                        v1_eff_G = self.perturbation.v1_G + \
                            self.response_calc.vHXC1_G
                        self.e_ph.v1_eff_qavG.append(v1_eff_G)

                    # Wait for the file-writing rank here
                    self.comm.barrier()

        # XXX
        # Check that all files are valid and collect in a single file
        # Remove the files
        if clean:
            self.clean()

    def get_atoms(self):
        """Return atoms."""

        return self.atoms

    def get_dynamical_matrix(self):
        """Return reference to ``dyn`` attribute."""

        return self.dyn

    def get_filename_string(self):
        """Return string template for force constant filenames."""

        name_str = (self.name + '.' +
                    'q_%%0%ii_' % len(str(self.kd.nibzkpts)) +
                    'a_%%0%ii_' % len(str(len(self.atoms))) + 'v_%i' + '.pckl')

        return name_str

    def set_atoms(self, atoms):
        """Set atoms to be included in the calculation.

        Parameters
        ----------
        atoms: list
            Can be either a list of strings, ints or ...
        """

        assert isinstance(atoms, list)

        if isinstance(atoms[0], str):
            assert np.all([isinstance(atom, str) for atom in atoms])
            sym_a = self.atoms.get_chemical_symbols()
            # List for atomic indices
            indices = []
            for type in atoms:
                indices.extend(
                    [a for a, atom in enumerate(sym_a) if atom == type])
        else:
            assert np.all([isinstance(atom, int) for atom in atoms])
            indices = atoms

        self.dyn.set_indices(indices)

    def set_name_and_path(self, name=None, path=None):
        """Set name and path of the force constant files.

        name: str
            Base name for the files which the elements of the matrix of force
            constants will be written to.
        path: str
            Path specifying the directory where the files will be dumped.
        """

        if name is None:
            self.name = 'phonon.' + self.atoms.get_chemical_formula()
        else:
            self.name = name
        # self.name += '.nibzkpts_%i' % self.kd.nibzkpts

        if path is None:
            self.path = '.'
        else:
            self.path = path

        # Set corresponding attributes in the ``dyn`` attribute
        filename_str = self.get_filename_string()
        self.dyn.set_name_and_path(filename_str, self.path)

    def clean(self):
        """Delete generated files."""

        filename_str = self.get_filename_string()

        for q in range(self.kd.nibzkpts):
            for a in range(len(self.atoms)):
                for v in [0, 1, 2]:
                    filename = filename_str % (q, a, v)
                    if os.path.isfile(os.path.join(self.path, filename)):
                        os.remove(filename)

    def band_structure(self, path_kc, modes=False, acoustic=True):
        """Calculate phonon dispersion along a path in the Brillouin zone.

        The dynamical matrix at arbitrary q-vectors is obtained by Fourier
        transforming the real-space matrix. In case of negative eigenvalues
        (squared frequency), the corresponding negative frequency is returned.

        Parameters
        ----------
        path_kc: ndarray
            List of k-point coordinates (in units of the reciprocal lattice
            vectors) specifying the path in the Brillouin zone for which the
            dynamical matrix will be calculated.
        modes: bool
            Returns both frequencies and modes (mass scaled) when True.
        acoustic: bool
            Restore the acoustic sum-rule in the calculated force constants.
        """

        for k_c in path_kc:
            assert np.all(np.asarray(k_c) <= 1.0), \
                "Scaled coordinates must be given"

        # Assemble the dynanical matrix from calculated force constants
        self.dyn.assemble(acoustic=acoustic)
        # Get the dynamical matrix in real-space
        DR_lmn, R_clmn = self.dyn.real_space()

        # Reshape for the evaluation of the fourier sums
        shape = DR_lmn.shape
        DR_m = DR_lmn.reshape((-1, ) + shape[-2:])
        R_cm = R_clmn.reshape((3, -1))

        # Lists for frequencies and modes along path
        omega_kn = []
        u_kn = []
        # Number of atoms included
        N = len(self.dyn.get_indices())

        # Mass prefactor for the normal modes
        m_inv_av = self.dyn.get_mass_array()

        for q_c in path_kc:

            # Evaluate fourier transform
            phase_m = np.exp(-2.j * pi * np.dot(q_c, R_cm))
            # Dynamical matrix in unit of Ha / Bohr**2 / amu
            D_q = np.sum(phase_m[:, np.newaxis, np.newaxis] * DR_m, axis=0)

            if modes:
                omega2_n, u_avn = la.eigh(D_q, UPLO='L')
                # Sort eigenmodes according to eigenvalues (see below) and
                # multiply with mass prefactor
                u_nav = u_avn[:, omega2_n.argsort()].T.copy() * m_inv_av
                # Multiply with mass prefactor
                u_kn.append(u_nav.reshape((3 * N, -1, 3)))
            else:
                omega2_n = la.eigvalsh(D_q, UPLO='L')

            # Sort eigenvalues in increasing order
            omega2_n.sort()
            # Use dtype=complex to handle negative eigenvalues
            omega_n = np.sqrt(omega2_n.astype(complex))

            # Take care of imaginary frequencies
            if not np.all(omega2_n >= 0.):
                indices = np.where(omega2_n < 0)[0]
                print(("WARNING, %i imaginary frequencies at "
                       "q = (% 5.2f, % 5.2f, % 5.2f) ; (omega_q =% 5.3e*i)" %
                       (len(indices), q_c[0], q_c[1], q_c[2],
                        omega_n[indices][0].imag)))

                omega_n[indices] = -1 * np.sqrt(np.abs(omega2_n[indices].real))

            omega_kn.append(omega_n.real)

        # Conversion factor from sqrt(Ha / Bohr**2 / amu) -> eV
        s = units.Hartree**0.5 * units._hbar * 1.e10 / \
            (units._e * units._amu)**(0.5) / units.Bohr
        # Convert to eV and Ang
        omega_kn = s * np.asarray(omega_kn)
        if modes:
            u_kn = np.asarray(u_kn) * units.Bohr
            return omega_kn, u_kn

        return omega_kn

    def write_modes(self,
                    q_c,
                    branches=0,
                    kT=units.kB * 300,
                    repeat=(1, 1, 1),
                    nimages=30,
                    acoustic=True):
        """Write mode to trajectory file.

        The classical equipartioning theorem states that each normal mode has
        an average energy::

            <E> = 1/2 * k_B * T = 1/2 * omega^2 * Q^2

                =>

              Q = sqrt(k_B*T) / omega

        at temperature T. Here, Q denotes the normal coordinate of the mode.

        Parameters
        ----------
        q_c: ndarray
            q-vector of the modes.
        branches: int or list
            Branch index of calculated modes.
        kT: float
            Temperature in units of eV. Determines the amplitude of the atomic
            displacements in the modes.
        repeat: tuple
            Repeat atoms (l, m, n) times in the directions of the lattice
            vectors. Displacements of atoms in repeated cells carry a Bloch
            phase factor given by the q-vector and the cell lattice vector R_m.
        nimages: int
            Number of images in an oscillation.

        """

        if isinstance(branches, int):
            branch_n = [branches]
        else:
            branch_n = list(branches)

        # Calculate modes
        omega_n, u_n = self.band_structure([q_c],
                                           modes=True,
                                           acoustic=acoustic)

        # Repeat atoms
        atoms = self.atoms * repeat
        pos_mav = atoms.positions.copy()
        # Total number of unit cells
        M = np.prod(repeat)

        # Corresponding lattice vectors R_m
        R_cm = np.indices(repeat[::-1]).reshape(3, -1)[::-1]
        # Bloch phase
        phase_m = np.exp(2.j * pi * np.dot(q_c, R_cm))
        phase_ma = phase_m.repeat(len(self.atoms))

        for n in branch_n:
            omega = omega_n[0, n]
            u_av = u_n[0, n]  # .reshape((-1, 3))
            # Mean displacement at high T ?
            u_av *= sqrt(kT / abs(omega))

            mode_av = np.zeros((len(self.atoms), 3), dtype=self.dtype)
            indices = self.dyn.get_indices()
            mode_av[indices] = u_av
            mode_mav = (np.vstack([mode_av] * M) *
                        phase_ma[:, np.newaxis]).real

            traj = Trajectory('%s.mode.%d.traj' % (self.name, n), 'w')

            for x in np.linspace(0, 2 * pi, nimages, endpoint=False):
                # XXX Is it correct to take out the sine component here ?
                atoms.set_positions(pos_mav + sin(x) * mode_mav)
                traj.write(atoms)

            traj.close()