"""
functions for working with optical properties from vasprun.xml
"""
from math import pi
import numpy as np
from scipy.constants import physical_constants, speed_of_light # type: ignore
import matplotlib.pyplot as plt # type: ignore
eV_to_recip_cm = 1.0 / (
physical_constants["Planck constant in eV s"][0] * speed_of_light * 1e2
)
[docs]def matrix_eigvals(matrix):
"""Calculate the eigenvalues of a matrix.
Args:
matrix (np.array): The matrix to diagonalise.
Returns:
(np.array): Array of the matrix eigenvalues.
"""
eigvals, eigvecs = np.linalg.eig(matrix)
return eigvals
[docs]def to_matrix(xx, yy, zz, xy, yz, xz):
"""Convert a list of matrix components to a symmetric 3x3 matrix.
Inputs should be in the order xx, yy, zz, xy, yz, xz.
Args:
xx (float): xx component of the matrix.
yy (float): yy component of the matrix.
zz (float): zz component of the matrix.
xy (float): xy component of the matrix.
yz (float): yz component of the matrix.
xz (float): xz component of the matrix.
Returns:
(np.array): The matrix, as a 3x3 numpy array.
"""
matrix = np.array([[xx, xy, xz], [xy, yy, yz], [xz, yz, zz]])
return matrix
[docs]def plot_dielectric_functions(dielectric, ax=None):
real_dielectric = parse_dielectric_data(dielectric[1])
imag_dielectric = parse_dielectric_data(dielectric[2])
if ax is None:
fig, ax = plt.subplots(1, 1, figsize=(6.0, 3.0))
else:
fig = None
ax.plot(
dielectric[0], np.mean(real_dielectric, axis=1), "-", zorder=2
) # better to pass in v.dielectric
ax.plot(dielectric[0], np.mean(imag_dielectric, axis=1), "-", zorder=2)
ax.set_xlim([0, 8])
ax.set_ylim([0, 5])
return fig
[docs]def parse_dielectric_data(data):
"""Convert a set of 2D vasprun formatted dielectric data to
the eigenvalues of each corresponding 3x3 symmetric numpy matrices.
Args:
data (list): length N list of dielectric data. Each entry should be
a list of ``[xx, yy, zz, xy, xz, yz ]`` dielectric
tensor elements.
Returns:
(np.array): a Nx3 numpy array. Each row contains the eigenvalues
for the corresponding row in `data`.
"""
return np.array([matrix_eigvals(to_matrix(*e)) for e in data])
[docs]def absorption_coefficient(dielectric):
"""Calculate the optical absorption coefficient from an input set of
pymatgen vasprun dielectric constant data.
Args:
dielectric (list): A list containing the dielectric response function
in the pymatgen vasprun format.
| element 0: list of energies
| element 1: real dielectric tensors, in ``[xx, yy, zz, xy, xz, yz]`` format.
| element 2: imaginary dielectric tensors, in ``[xx, yy, zz, xy, xz, yz]`` format.
Returns:
(np.array): absorption coefficient using eV as frequency units (cm^-1).
Notes:
The absorption coefficient is calculated as
.. math:: \\alpha = \\frac{2\\sqrt{2} \\pi}{\\lambda} \\sqrt{-\\epsilon_1+\\sqrt{\\epsilon_1^2+\\epsilon_2^2}}
"""
energies_in_eV = np.array(dielectric[0])
real_dielectric = parse_dielectric_data(dielectric[1])
imag_dielectric = parse_dielectric_data(dielectric[2])
epsilon_1 = np.mean(real_dielectric, axis=1)
epsilon_2 = np.mean(imag_dielectric, axis=1)
return (
2.0
* np.sqrt(2.0)
* pi
* eV_to_recip_cm
* energies_in_eV
* np.sqrt(-epsilon_1 + np.sqrt(epsilon_1**2 + epsilon_2**2))
)