aiida_vibroscopy.calculations.numerical_derivatives_utils

Calcfunctions utils for numerical derivatives workchain.

Module Contents

Functions

get_central_derivatives_coefficients(→ list[int])	Return an array with the central derivatives coefficients.
central_derivatives_calculator(step_size, order, ...)	Calculate the central difference derivatives.
compute_susceptibility_derivatives(→ dict)	Return the Raman (1/Angstrom) and the non-linear optical susceptibility (pm/V) tensors.
compute_nac_parameters(→ dict)	Return high frequency dielectric and Born charge tensors using central difference schemes.

aiida_vibroscopy.calculations.numerical_derivatives_utils.get_central_derivatives_coefficients(accuracy: int, order: int) → list[int]

Return an array with the central derivatives coefficients.

Implementation following Math. Comp. 51 (1988), 699-706.

aiida_vibroscopy.calculations.numerical_derivatives_utils.central_derivatives_calculator(step_size: float, order: int, vector_name: str, data_0: aiida.orm.TrajectoryData, **field_data: aiida.orm.TrajectoryData)

Calculate the central difference derivatives.

The accuracy of the central finite difference is determined by the number of keys in data.

Parameters:

• step_size – step size for finite differenciation

• order – order of the derivative

• vector_name – either forces or electronic_dipole_cartesian_axes

• data – trajectory data for a particular direction in space; it is expected to be given with stringed numbers as labels, in the order: \([c_1, c_{-1}, c_2, c_{-2}, \\dots , c_0]\) where \(c_i\) is the coefficient for f(i*step_size)

aiida_vibroscopy.calculations.numerical_derivatives_utils.compute_susceptibility_derivatives(preprocess_data: aiida_phonopy.data.PreProcessData, electric_field: aiida.orm.Float, diagonal_scale: aiida.orm.Float, accuracy_order: aiida.orm.Int, **kwargs) → dict

Return the Raman (1/Angstrom) and the non-linear optical susceptibility (pm/V) tensors.

..note:

• If the numerical accuracy order is greater than 2, arrays at lower orders are given as well.

• Units are 1/Angstrom for Raman tensors, normalized using the UNITCELL volume.

• Units are pm/V for non-linear optical susceptibility

• Raman tensors indecis: (atomic, atomic displacement, electric field, electric field)

Returns:

dictionaries of numerical accuracies with ArrayData having keys: * raman_tensors containing (num_atoms, 3, 3, 3) arrays; * nlo_susceptibility containing (3, 3, 3) arrays; * units as Dict containing the units of the tensors.

aiida_vibroscopy.calculations.numerical_derivatives_utils.compute_nac_parameters(preprocess_data: aiida_phonopy.data.PreProcessData, electric_field: aiida.orm.Float, accuracy_order: aiida.orm.Int, **kwargs) → dict

Return high frequency dielectric and Born charge tensors using central difference schemes.

..note:

• Units are in atomic units, meaning:

  1. Dielectric tensor in vacuum permittivity units.

  2. Born charges in electric charge units.

• Born charges tensors indecis: (atomic, electric field, atomic displacement)

Returns:

dictionary with ArrayData having keys: * born_charges as containing (num_atoms, 3, 3) arrays * dielectric as containing (3, 3) arrays.