from typing import Union
import numpy as np
from ase.units import fs
from ase import Atoms
from numpy.typing import NDArray
from .tools import inv
from ..units import Dalton_to_dmu
class DynasorAtoms:
"""Dynasor's representation of a structure."""
def __init__(self, atoms: Atoms):
"""Initialized using an ASE Atoms object"""
self._atoms = atoms
@property
def pos(self) -> NDArray[float]:
"""Cartesian positions."""
return self._atoms.positions.copy()
@property
def positions(self) -> NDArray[float]:
"""Cartesian positions."""
return self.pos
@property
def spos(self) -> NDArray[float]:
"""Reduced (or scaled) positions of atoms."""
return self._atoms.get_scaled_positions()
@property
def scaled_positions(self) -> NDArray[float]:
"""Reduced (or scaled) positions of atoms."""
return self.spos
@property
def cell(self) -> NDArray[float]:
"""Cell of atoms with cell vectors as rows."""
return self._atoms.cell.array.copy()
@property
def inv_cell(self) -> NDArray[float]:
"""The inverse cell transpose so the inverse cell vectors are rows, no 2pi."""
return np.linalg.inv(self._atoms.cell.array).T
@property
def numbers(self) -> NDArray[int]:
"""Chemical number for each atom, e.g., 1 for H, 2 for He etc."""
return self._atoms.numbers.copy()
@property
def masses(self) -> NDArray[float]:
"""Masses of atoms in dmu."""
return self._atoms.get_masses() / fs ** 2 # In eVfs²/Ų
@property
def volume(self) -> float:
"""Volume of cell."""
return self._atoms.get_volume()
@property
def n_atoms(self) -> int:
"""Number of atoms."""
return len(self._atoms)
@property
def symbols(self) -> list[str]:
"""List of chemical symbol for each element."""
return list(self._atoms.symbols)
def to_ase(self) -> Atoms:
"""Converts the internal Atoms to ASE :class:`Atoms`."""
return Atoms(cell=self.cell, numbers=self.numbers, positions=self.positions, pbc=True)
def __repr__(self) -> str:
return str(self)
[docs]
class Prim(DynasorAtoms):
def __str__(self):
strings = [f"""Primitive cell:
Number of atoms: {self.n_atoms}
Volume: {self.volume:.3f}
Atomic species present: {set(self.symbols)}
Atomic numbers present: {set([int(n) for n in self.numbers])}
Cell:
[[{self.cell[0, 0]:<20}, {self.cell[0, 1]:<20}, {self.cell[0, 2]:<20}],
[{self.cell[1, 0]:<20}, {self.cell[1, 1]:<20}, {self.cell[1, 2]:<20}],
[{self.cell[2, 0]:<20}, {self.cell[2, 1]:<20}, {self.cell[2, 2]:<20}]]
"""]
strings.append(f"{'Ind':<5}{'Sym':<5}{'Num':<5}{'Mass (Da)':<10}{'x':<10}{'y':<10}{'z':<10}"
f"{'a':<10}{'b':<10}{'c':<10}")
atom_s = []
for i, p, sp, m, n, s in zip(
range(self.n_atoms), self.positions, self.spos, self.masses / Dalton_to_dmu,
self.numbers, [a.symbol for a in self.to_ase()]):
atom_s.append(f'{i:<5}{s:<5}{n:<5}{m:<10.2f}{p[0]:<10.3f}{p[1]:<10.3f}{p[2]:<10.3f}'
f'{sp[0]:<10.3f}{sp[1]:<10.3f}{sp[2]:<10.3f}')
strings = strings + atom_s
string = '\n'.join(strings)
return string
[docs]
class Supercell(DynasorAtoms):
"""The supercell takes care of some mappings between the primitive and repeated structure.
In particular the P-matrix connecting the cells as well as the offset-index of each atom is
calculated.
Note that the positions cannot be revovered as `offset x cell + basis` since the atoms get
wrapped.
Parameters
----------
supercell
Some ideal repetition of the primitive structure and possible wrapping.
prim
Primitive structure.
"""
def __init__(self, supercell: Union[Atoms, DynasorAtoms], prim: Union[Atoms, DynasorAtoms]):
self.prim = Prim(prim.copy())
super().__init__(supercell)
# determine P-matrix relating supercell to primitive cell
from dynasor.tools.structures import get_P_matrix
self._P = get_P_matrix(self.prim.cell, self.cell) # P C = S
self._P_inv = inv(self.P)
# find the index and offsets for supercell using primitive as base unit
from dynasor.tools.structures import get_offset_index
self._offsets, self._indices = get_offset_index(prim, supercell, wrap=True)
@property
def P(self) -> NDArray[float]:
"""P-matrix is defined as dot(P, prim.cell) = supercell.cell"""
return self._P.copy()
@property
def P_inv(self) -> NDArray[float]:
"""Inverse of `P`."""
return self._P_inv.copy()
@property
def offsets(self) -> NDArray[float]:
"""The offset of each atom."""
return self._offsets.copy()
@property
def indices(self) -> NDArray[int]:
"""The basis index of each atom"""
return self._indices.copy()
@property
def n_cells(self) -> int:
"""Number of unit cells"""
return self.n_atoms // self.prim.n_atoms
def __str__(self):
string = f"""Supercell:
Number of atoms: {self.n_atoms}
Volume: {self.volume:.3f}
Number of unit cells: {self.n_cells}
Cell:
[[{self.cell[0, 0]:<20}, {self.cell[0, 1]:<20}, {self.cell[0, 2]:<20}],
[{self.cell[1, 0]:<20}, {self.cell[1, 1]:<20}, {self.cell[1, 2]:<20}],
[{self.cell[2, 0]:<20}, {self.cell[2, 1]:<20}, {self.cell[2, 2]:<20}]]
P-matrix:
[[{self.P[0, 0]:<20}, {self.P[0, 1]:<20}, {self.P[0, 2]:<20}],
[{self.P[1, 0]:<20}, {self.P[1, 1]:<20}, {self.P[1, 2]:<20}],
[{self.P[2, 0]:<20}, {self.P[2, 1]:<20}, {self.P[2, 2]:<20}]]
{self.prim}
"""
return string
