# Source code for gpaw.nlopt.linear

```import numpy as np
from ase.units import Bohr, _hbar, _e, _me, _eps0

from gpaw.mpi import world

[docs]def get_chi_tensor(
freqs=[1.0], eta=0.05,
ftol=1e-4, Etol=1e-6, eshift=0.0,
band_n=None, mml_name='mml.npz', out_name=None):
"""
Calculate full linear susceptibility tensor for nonmagnetic semiconductors.

Input:
freqs           Excitation frequency array (a numpy array or list)
eta             Broadening, a number or an array (default 0.05 eV)
Etol, ftol      Tol. in energy and fermi to consider degeneracy
eshift          Bandgap correction
band_n          List of bands in the sum (default 0 to nb)
out_name        If it is given: output filename
mml_name        The momentum filename (default 'mml.npz')
Output:
chi_vvl         The output tensor (3, 3, nw)
chi.npy         If specified: array containing the spectrum and freqs

"""

freqs = np.array(freqs)
nw = len(freqs)
w_lc = freqs + 1j * eta

if k_info:
tmp = list(k_info.values())[0]
nb = len(tmp[1])
if band_n is None:
band_n = list(range(nb))

# Initialize the outputs
sum_vvl = np.zeros((3, 3, nw), complex)

# Do the calculations
for _, (we, f_n, E_n, p_vnn) in k_info.items():
tmp = np.zeros((3, 3, nw), complex)
for v1 in range(3):
for v2 in range(v1, 3):
sum_l = calc_chi(
w_lc, f_n, E_n, p_vnn, [v1, v2],
band_n, ftol, Etol, eshift=eshift)
tmp[v1, v2] = sum_l
tmp[v2, v1] = sum_l
# Add it to previous with a weight
sum_vvl += tmp * we

world.sum(sum_vvl)

# Make the output in SI unit
dim_sigma = 1j * _e**2 * _hbar / (_me**2 * (2 * np.pi)**3)
dim_chi = 1j * _hbar / (_eps0 * _e)
dim_sum = (_hbar / (Bohr * 1e-10))**2 / \
(_e**2 * (Bohr * 1e-10)**3)
dim_SI = dim_sigma * dim_chi * dim_sum
chi_vvl = dim_SI * sum_vvl

# Save it to the file
if world.rank == 0 and out_name is not None:
tmp = chi_vvl.reshape(9, nw)
lin = np.vstack((freqs, tmp))
np.save(out_name, lin)

return chi_vvl

def calc_chi(
w_l, f_n, E_n, p_vnn, pol_v,
band_n=None, ftol=1e-4, Etol=1e-6, eshift=0):
"""
Loop over bands for computing the response

Input:
w_l             Complex frequency array
f_n             Fermi levels
E_n             Energies
p_vnn           Momentum matrix elements
pol_v           Tensor element
band_n          Band list
Etol, ftol      Tol. in energy and fermi to consider degeneracy
eshift          Bandgap correction
Output:
sum_l           Output sum value (array with length of w_l)
"""

# Initialize variables
nb = len(f_n)
if band_n is None:
band_n = list(range(nb))
sum_l = np.zeros(w_l.size, complex)

# Loop over bands
for nni in band_n:
for mmi in band_n:
# Use TRS to reduce
if mmi <= nni:
continue
fnm = f_n[nni] - f_n[mmi]
Emn = E_n[mmi] - E_n[nni] + fnm * eshift
if np.abs(fnm) < ftol or np.abs(Emn) < Etol:
continue
# *2 for real, /2 for TRS, *2 for m<n
sum_l += 2 * fnm * np.real(
p_vnn[pol_v[0], nni, mmi] * p_vnn[pol_v[1], mmi, nni]) \
/ (Emn * (w_l**2 - Emn**2))

return sum_l
```