VibrationalMode¶

class VibrationalMode(dynamical_matrix, configuration=None, kpoint_fractional=None, mode_indices=None)¶

Class for calculating the vibrational modes of a configuration.

Parameters:

dynamical_matrix (DynamicalMatrix) – The dynamical matrix to use for the calculation.
configuration (MoleculeConfiguration | BulkConfiguration | DeviceConfiguration) – The configuration for which the vibrational modes should be calculated. If no calculator is attached to the configuration, the calculator from dynamical_matrix is used. Currently, configuration must be the same as the configuration from dynamical_matrix and is therefore not needed.
Default: The configuration from dynamical_matrix
kpoint_fractional (tuple of float) – The kpoint (in fractional reciprocal space coordinates) for which the vibrational modes should be calculated.
Default: The gamma point (0.0, 0.0, 0.0)
mode_indices (list of int) – The indices of the modes (bands) to include.
Default: All modes.

eigenvectors(mode_index=None)¶

Return the vibration eigenvectors, \(u\), for the selected k-point and mode indices.

The eigenvectors are solutions to \(D u = \omega^2 u\), where \(D\) is the dynamical matrix, and \(\omega\) is the frequency. If mode_index is not specified all calculated modes are returned.

Note, the mode u[:,i] is the eigenvector corresponding to mode index modeIndices()[i].

Parameters:: mode_index (int) – Mode index.
Default: All calculated modes.
Returns:: Eigenvectors of the vibrational modes
Return type:: numpy.array

evaluate(mode_index=None)¶

Return the vibrational energies at the selected mode index. If mode_index is not specified all mode energies are returned.

Parameters:: mode_index (int) – Mode index.
Default: All modes.
Returns:: Energies of the vibrational modes.
Return type:: PhysicalQuantity of type energy

kPoint()¶

Returns:: The kpoint (in fractional reciprocal space coordinates).
Return type:: tuple of float

metatext()¶

Returns:: The metatext of the object or None if no metatext is present.
Return type:: str | None

mode(mode_index, temperature=None)¶

Return the vibrational mode with the specified mode_index. The eigenmode, \(v\), is obtained from the eigenvectors, \(u\), as \(v = \frac{u}{\sqrt{M}} s\), where the scaling factor, \(s = \frac{\sqrt{k_B T}}{\omega}\), gives the amplitude of a classical oscillator with frequency \(\omega\).

Parameters:

mode_index (int) – The mode index. Must be contained in the list returned by modeIndices().
temperature (PhysicalQuantity of type temperature) – The temperature used in scaling the amplitude.
Default: 300 * Kelvin

Returns:

(N, 3) complex array

Return type:

PhysicalQuantity of type length

modeIndices()¶

Returns:: The mode indices.
Return type:: list of int

movie(mode_index, mode=None, temperature=None, number_of_frames=None, repeat=None)¶

Method for generating a trajectory showing the vibrations with the specified mode_index.

Parameters:

mode_index (int) – The mode index. Must be contained in the list returned by modeIndices().
mode (PhysicalQuantity of type length) – The mode (N, 3) complex array.
temperature (PhysicalQuantity of type temperature) – The temperature used in scaling the amplitude.
Default: 300 * Kelvin
number_of_frames (int) – The number of frames in the trajectory.
Default: 20
repeat (tuple of integers) – The number of repetitions along A, B, and C axes. For molecules this must be (1, 1, 1); for devices (n, m, 1).
Default: (1, 1, 1)

Returns:

A trajectory.

Return type:

Trajectory

nlprint(stream=None)¶

Print a string containing an ASCII table useful for plotting the AnalysisSpin object.

Parameters:: stream (python stream) – The stream the table should be written to.
Default: NLPrintLogger()

setMetatext(metatext)¶

Set a given metatext string on the object.

Parameters:: metatext (str | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.

uniqueString()¶: Return a unique string representing the state of the object.

wavenumbers(mode_index=None)¶

Return vibrational wavenumbers. If mode_index is not specified all wavenumbers are returned.

Parameters:: mode_index (int) – Mode index.
Default: All modes.
Returns:: Wavenumbers of the vibrational modes
Return type:: PhysicalQuantity of type inverse length

Usage Examples¶

Calculate the vibrational eigenmodes of a methane molecule using the BrennerCalculator:

# -------------------------------------------------------------
# Molecule configuration, CH4
# -------------------------------------------------------------

# Define elements
elements = [Hydrogen, Carbon, Hydrogen, Hydrogen, Hydrogen]

# Define coordinates
cartesian_coordinates = [[ 11.61454603,  11.09244804,   9.99999993],
                         [ 10.67862603,  10.93144595,  10.52879495],
                         [  9.99999997,  11.75542099,  10.3236729 ],
                         [ 10.22904002,  10.00000001,  10.1942581 ],
                         [ 10.87074303,  10.87768505,  11.59731907]]*Angstrom

# Set up configuration
molecule_configuration = MoleculeConfiguration(
    elements=elements,
    cartesian_coordinates=cartesian_coordinates
    )

# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------
calculator = BrennerCalculator()

molecule_configuration.setCalculator(calculator)
molecule_configuration.update()

molecule_configuration = OptimizeGeometry(
        molecule_configuration,
        max_forces=0.001*eV/Ang,
        max_steps=200,
        max_step_length=0.5*Ang,
        trajectory_filename=None,
        optimize_cell=False,
        optimizer_method=LBFGS(),
        )

# -------------------------------------------------------------
# Vibrational modes
# -------------------------------------------------------------
# Compute Hessian by finite difference of forces.
dynamical_matrix = DynamicalMatrix(molecule_configuration, 'ch4.hdf5', object_id='dynamical_matrix')

# Vibrational analysis.
vib_mode = VibrationalMode(dynamical_matrix, mode_indices=range(6,15))
vib_mode.nlprint()

vibrationalmode.py

Notes¶

For a MoleculeConfiguration, the six lowest vibrational modes have zero-frequency. In the above example, these modes are not calculated since mode_indices=range(6,15). The six zero-frequency modes correspond to three rigid translational modes and three rigid rotational modes.
It is important to do a fine structual relaxation before calculating vibrational (or phonon) modes. This may also require specifying a higher density_mesh_cutoff in NumericalAccuracyParameters.