ElectricFieldGradients¶

class ElectricFieldGradients(configuration, atom_indices=None)¶

Class for calculating and representing the electric field gradients at the atomic nuclei.

Parameters:

configuration (BulkConfiguration) – Configuration with a calculator that supports EFG calculations.
atom_indices (All | list of ints.) – The indices of the atoms for which to calculate the electric field gradient.
Default: All i.e. all atoms in the configuration.

atomIndices()¶

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

evaluate()¶

Get the electric field gradient tensors for each atom.

Returns:: A list of electric field gradient tensors.
Return type:: list

evaluatePrincipalAxis()¶

Determine the principel axis (eigenvectors and eigenvalues of the EFG tensor) for each atom.

Returns:: The principel axis for each atom.
Return type:: two ndarray

evaluatePrincipelAxisComponents()¶

Determine the principel axis components for each atom.

Returns:: The principel axis components and asymmetry parameter for each atom.
Return type:: tuple of 2 lists

evaluateQuadrupoleCouplingConstants(quadrupole_moments=None)¶

Determine the quadrupole coupling constants for each atom.

Parameters:: quadrupole_moments (list | None | Automatic) – List of quadrupole moments for each atom in units of Barns. If Automatic, the quadrupole moment is taken from Pekka Pyykkö (2018): Year-2017 nuclear quadrupole moments, Molecular Physics, DOI: 10.1080/00268976.2018.1426131 select non zero quadrupole moment for isotope of highest abbundance.
Default: 1 Barn = 1.e-28*m^2
Returns:: The quadrupole coupling constants and asymmetry parameter for each atom.
Return type:: tuple of 2 lists

metatext()¶

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

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()

quadrupoleMoments(atom_index, quadrupole_moments=None)¶

Returns the quadrupole moment of the atom index in the configuration.

Parameters:

atom_index (int) – The atom index in the configuration.
quadrupole_moments (None | Automatic) – If Automatic, the quadrupole moment is taken from Pekka Pyykkö (2018): Year-2017 nuclear quadrupole moments, Molecular Physics, DOI: 10.1080/00268976.2018.1426131 select non zero quadrupole moment for isotope of highest abbundance.
Default: 1 Barn = 1.e-28*m^2.

Returns:

The quadrupole moment of the atom index in the configuration.

Return type:

PhysicalQuantity

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.

Usage Examples¶

Calculate the electric field gradient of silicon, save it to a file, and print out the quadrupole coupling constant:

# Set up silicon crystal.
bulk_configuration = BulkConfiguration(
    bravais_lattice=FaceCenteredCubic(5.4306 * Angstrom),
    elements=[Silicon, Silicon],
    cartesian_coordinates=[[ 0.     , 0.     , 0.],
                           [ 1.35765, 1.35765, 1.35765]] * Angstrom
    )
# Setup calculator.
numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(6, 6, 6),
    )
# Setup PAW data set.
basis_set = [
    PAWPBEGPAW.Silicon,
    ]

# Setup plane wave calculator.
calculator = PlaneWaveCalculator(
    basis_set=basis_set,
    numerical_accuracy_parameters=numerical_accuracy_parameters,
    )
bulk_configuration.setCalculator(calculator)
bulk_configuration.update()

# Electric Field Gradients.
efg_analysis = ElectricFieldGradients(
    configuration=bulk_configuration,
    atom_indices=All,
    )

nlsave('si_efg.hdf5', efg_analysis)

# Print out the quadrupole coupling constant.
print('Quadrupole coupling constants')
print(efg_analysis.evaluateQuadrupoleCouplingConstants())

si_efg.py

Notes¶

The quadrupole coupling constant is defined as

\[C_{q} = \frac{ e V_{zz} q}{h},\]

where \(e\) is the absolute value of the electron charge, \(h\) the plank constant and \(q\) is the nuclear quadrupolar momentum.

\(V_{zz}\) is the largest eigenvalue of the diagonalized traceless electric field gradient tensor at the nucleus:

\[V_{ij}(\mathbf{r}) = \int d\mathbf{r}' \frac{\rho(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|^{3}} \left[ \delta_{ij} - 3 \frac{(\mathbf{r}_{i} - \mathbf{r}_{i}')(\mathbf{r}_{j} - \mathbf{r}_{j}')}{|\mathbf{r} - \mathbf{r}'|^{2}} \right],\]

where \(\rho(\mathbf{r})\) is the charge neutral nuclear and all electron density. \(i, j\) denote Cartesian coordinates