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from typing import Tuple
import numpy as np
from ase.units import Bohr, Ha
from ase.data import covalent_radii
from ase.neighborlist import NeighborList
class LippincottStuttman:
# atomic polarizability values from:
# Lippincott and Stutman J. Phys. Chem. 68 (1964) 2926-2940
# DOI: 10.1021/j100792a033
# see also:
# Marinov and Zotov Phys. Rev. B 55 (1997) 2938-2944
# DOI: 10.1103/PhysRevB.55.2938
# unit: Angstrom^3
atomic_polarizability = {
'B': 1.358,
'C': 0.978,
'N': 0.743,
'O': 0.592,
'Al': 3.918,
'Si': 2.988,
}
# reduced electronegativity Table I
reduced_eletronegativity = {
'B': 0.538,
'C': 0.846,
'N': 0.927,
'O': 1.0,
'Al': 0.533,
'Si': 0.583,
}
def __call__(self, el1: str, el2: str,
length: float) -> Tuple[float, float]:
"""Bond polarizability
Parameters
----------
el1: element string
el2: element string
length: float
Returns
-------
alphal: float
Parallel component
alphap: float
Perpendicular component
"""
alpha1 = self.atomic_polarizability[el1]
alpha2 = self.atomic_polarizability[el2]
ren1 = self.reduced_eletronegativity[el1]
ren2 = self.reduced_eletronegativity[el2]
sigma = 1.
if el1 != el2:
sigma = np.exp(- (ren1 - ren2)**2 / 4)
# parallel component
alphal = sigma * length**4 / (4**4 * alpha1 * alpha2)**(1. / 6)
# XXX consider fractional covalency ?
# prependicular component
alphap = ((ren1**2 * alpha1 + ren2**2 * alpha2)
/ (ren1**2 + ren2**2))
# XXX consider fractional covalency ?
return alphal, alphap
class Linearized:
def __init__(self):
self._data = {
# L. Wirtz, M. Lazzeri, F. Mauri, A. Rubio,
# Phys. Rev. B 2005, 71, 241402.
# R0 al al' ap ap'
'CC': (1.53, 1.69, 7.43, 0.71, 0.37),
'BN': (1.56, 1.58, 4.22, 0.42, 0.90),
}
def __call__(self, el1: str, el2: str,
length: float) -> Tuple[float, float]:
"""Bond polarizability
Parameters
----------
el1: element string
el2: element string
length: float
Returns
-------
alphal: float
Parallel component
alphap: float
Perpendicular component
"""
if el1 > el2:
bond = el2 + el1
else:
bond = el1 + el2
assert bond in self._data
length0, al, ald, ap, apd = self._data[bond]
return al + ald * (length - length0), ap + apd * (length - length0)
class BondPolarizability:
def __init__(self, model=LippincottStuttman()):
self.model = model
def __call__(self, *args, **kwargs):
"""Shorthand for calculate"""
return self.calculate(*args, **kwargs)
def calculate(self, atoms, radiicut=1.5):
"""Sum up the bond polarizability from all bonds
Parameters
----------
atoms: Atoms object
radiicut: float
Bonds are counted up to
radiicut * (sum of covalent radii of the pairs)
Default: 1.5
Returns
-------
polarizability tensor with unit (e^2 Angstrom^2 / eV).
Multiply with Bohr * Ha to get (Angstrom^3)
"""
radii = np.array([covalent_radii[z]
for z in atoms.numbers])
nl = NeighborList(radii * 1.5, skin=0,
self_interaction=False)
nl.update(atoms)
pos_ac = atoms.get_positions()
alpha = 0
for ia, atom in enumerate(atoms):
indices, offsets = nl.get_neighbors(ia)
pos_ac = atoms.get_positions() - atoms.get_positions()[ia]
for ib, offset in zip(indices, offsets):
weight = 1
if offset.any(): # this comes from a periodic image
weight = 0.5 # count half the bond only
dist_c = pos_ac[ib] + np.dot(offset, atoms.get_cell())
dist = np.linalg.norm(dist_c)
al, ap = self.model(atom.symbol, atoms[ib].symbol, dist)
eye3 = np.eye(3) / 3
alpha += weight * (al + 2 * ap) * eye3
alpha += weight * (al - ap) * (
np.outer(dist_c, dist_c) / dist**2 - eye3)
return alpha / Bohr / Ha
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