"""
.. module:: Charge_charge
:synopsis: Generate the charge_charge interaction matrix.
.. moduleauthor:: D. Wang <dwang5@zoho.com>
"""
import numpy as np
from netCDF4 import Dataset
import time
from math import atan
from scipy import special
import os
import sys
sys.path.insert(0, os.path.abspath('../src'))
from supercell import Supercell
from ewald_cc import cc_set_parameters, cc_sum_over_k
[docs]class Charge_charge(Supercell):
"""
Charge_charge inherits the *Supercell* class, it first initializes the supercell it works on.
:param n1: Number of unit cells along the first Bravais vector of 'lattice'.
:param n2: Number of unit cells along the second Bravais vector of 'lattice'.
:param nz: Number of unit cells along the third Bravais vector of "lattice'.
:param lattice: The lattice of the **unit cell**, not the supercell.
"""
def __init__(self, n1, n2, nz, lattice):
Supercell.__init__(self, n1, n2, nz, lattice)
self.ccij = np.zeros(self.nsites)
self.charge_matrix_calculated = False
def write_charge_matrix(self, fn):
if self.charge_matrix_calculated == False:
print("Calculate the matrix first ...")
self.generate_charge_matrix()
self.dipole_matrix_calculated = True
ccm = Dataset(fn, "w", format="NETCDF4")
ia = ccm.createDimension("ia", None)
# ias = ccm.createVariable("ia",np.int32,("ia"))
# The actual 2-d varable.
matrix = ccm.createVariable('matrix', np.float64, 'ia')
ccm.description = 'Charge matrix: interaction matrix'
ccm.history = 'Created at ' + time.ctime(time.time())
matrix[:] = self.ccij[:]
ccm.close()
def generate_charge_matrix(self):
pi = 4.0 * atan(1.0)
pi2 = pi * 2.0
NN = 10
tol = 1.0e-12
eta = sqrt(-log(tol))
gcut = 2.0 * eta ** 2
gcut2 = gcut ** 2
eta4 = 1.0 / (4 * eta ** 2)
am = np.zeros(3)
for i in range(3):
for k in range(3):
am[i] += self.a[i, k] ** 2
am[i] = sqrt(am[i])
mg1 = int(gcut * am[0] / pi2) + 1
mg2 = int(gcut * am[1] / pi2) + 1
mg3 = int(gcut * am[2] / pi2) + 1
print('Gcut: ', gcut, ' mg1, mg2, mg3: ', mg1, mg2, mg3)
# Set parameters to be used in the PYBIND11 C++ computation.
cc_set_parameters(self.b, mg1, mg2, mg3, gcut2, eta4)
c = 4.0 * pi / self.celvol
residue = 2.0 * eta / sqrt(pi)
pos0 = np.zeros(3)
pos0 = self.ixa[0] * self.lattice[0, :] \
+ self.iya[0] * self.lattice[1, :] \
+ self.iza[0] * self.lattice[2, :]
for ia in range(self.nsites):
# Note how the three dimensional (dx,dy,dz) is mapped
# into a single array, which is important for correct
# later use of the generated matrix.
print('site: ', ia)
pos = np.zeros(3)
pos = self.ixa[ia] * self.lattice[0, :] \
+ self.iya[ia] * self.lattice[1, :] \
+ self.iza[ia] * self.lattice[2, :]
rx = pos[0]
ry = pos[1]
rz = pos[2]
# print('Summing over k space')
krslt = cc_sum_over_k(rx - pos0[0], ry - pos0[1], rz - pos0[2])
self.ccij[ia] = krslt * c
for ir1 in range(-NN, NN + 1):
for ir2 in range(-NN, NN + 1):
for ir3 in range(-NN, NN + 1):
if (ir1 == 0 and ir2 == 0 and ir3 == 0): continue
Rpos = np.zeros(3)
Rpos = ir1 * self.a[0, :] + ir2 * self.a[1, :] + ir3 * self.a[2, :]
Rix = Rpos[0]
Riy = Rpos[1]
Riz = Rpos[2]
x = (rx - Rix)
y = (ry - Riy)
z = (rz - Riz)
r = sqrt(x ** 2 + y ** 2 + z ** 2)
# self.ccij[ia] += 1.0/r * special.erfc(r*eta)
if (ia == 0):
self.ccij[ia] -= residue
else:
dum0 = sqrt(rx * rx + ry * ry + rz * rz)
self.ccij[ia] += 1.0 / dum0 * special.erfc(dum0 * eta)
self.ccij[:] = 0.5 * self.ccij[:]