Coverage for eminus/atoms.py: 98.15%

1# SPDX-FileCopyrightText: 2021 The eminus developers

2# SPDX-License-Identifier: Apache-2.0

3"""Atoms class definition."""

5import numbers

7import numpy as np

8from scipy.fft import next_fast_len

9from scipy.linalg import det, eigh, inv, norm

11from . import operators

12from .kpoints import KPoints

13from .logger import create_logger, get_level, log

14from .occupations import Occupations

15from .tools import center_of_mass, cutoff2gridspacing, inertia_tensor

16from .utils import atom2charge, BaseObject, molecule2list

19class Atoms(BaseObject):

20 """Atoms object that holds all system and cell parameters.

22 Args:

23 atom: Atom symbols.

25 A string can be given, e.g., with :code:`CH4` that will be parsed to

26 :code:`["C", "H", "H", "H", "H"]`. When calculating atoms one can directly provide the

27 charge, e.g., with :code:`Li-q3`.

28 pos: Atom positions.

30 Keyword Args:

31 ecut: Cut-off energy.

33 Defaults to 30 Eh (ca. 816 eV).

34 a: Cell size or vacuum size.

36 Floats will create a cubic unit cell. Defaults to a 20 a0 (ca. 10.5 A) cubic cell.

37 Scaled lattice vectors can be given to build a custom cell.

38 spin: Number of unpaired electrons.

40 This is the difference between the number of up and down electrons.

41 charge: Charge of the system.

42 unrestricted: Handling of spin.

44 :code:`False` for restricted, :code:`True` for unrestricted, and :code:`None` for

45 automatic detection.

46 center: Center the system inside the cell.

48 Aligns the geometric center of mass with the center of the call and rotates the system,

49 such that its geometric moment of inertia aligns with the coordinate axes. Can be one of

50 bool, "shift", and "rotate".

51 verbose: Level of output.

53 Can be one of "critical", "error", "warning", "info" (default), or "debug". An integer

54 value can be used as well, where larger numbers mean more output, starting from 0.

55 None will use the global logger verbosity value.

56 """

58 def __init__(

59 self,

60 atom,

61 pos,

62 ecut=30,

63 a=20,

64 spin=None,

65 charge=0,

66 unrestricted=None,

67 center=False,

68 verbose=None,

69 ):

70 """Initialize the Atoms object."""

71 # Set the input parameters (the ordering is important)

72 self._log = create_logger(self) #: Logger object.

73 self.verbose = verbose #: Verbosity level.

74 self.occ = Occupations() #: Occupations object.

75 self.atom = atom #: Atom symbols.

76 self.pos = pos #: Atom positions.

77 self.a = a #: Cell/Vacuum size.

78 self.ecut = ecut #: Cut-off energy.

79 self.center = center #: Enables centering the system in the cell.

80 self.charge = charge #: System charge.

81 self.spin = spin #: Number of unpaired electrons.

82 self.unrestricted = unrestricted #: Enables unrestricted spin handling.

83 self.kpts = KPoints("sc", self.a) #: KPoints object.

85 # Initialize other attributes

86 self.occ.fill() #: Fill states from the given input.

87 self.is_built = False #: Determines the Atoms object build status.

88 self.clear()

90 # ### Class properties ###

92 @property

93 def atom(self):

94 """Atom symbols."""

95 return self._atom

97 @atom.setter

98 def atom(self, value):

99 # Quick option to set the charge for single atoms

100 if isinstance(value, str) and "-q" in value:

101 atom, Z = value.split("-q")

102 self._atom = [atom]

103 self._Natoms = 1

104 self.Z = int(Z)

105 else:

106 # If a string, i.e., chemical formula is given convert it to a list of chemical symbols

107 if isinstance(value, str):

108 self._atom = molecule2list(value)

109 else:

110 self._atom = value

111 # Get the number of atoms and determine the charges

112 self._Natoms = len(self._atom)

113 self.Z = None

114

115 @property

116 def pos(self):

117 """Atom positions."""

118 return self._pos

119

120 @pos.setter

121 def pos(self, value):

122 # We need atom positions as a two-dimensional array

123 self._pos = np.atleast_2d(value)

124 if self.Natoms != len(self._pos):

125 msg = (

126 f"Mismatch between number of atoms ({self.Natoms}) and number of "

127 f"coordinates ({len(self._pos)})."

128 )

129 raise ValueError(msg)

130 # The structure factor changes when changing pos

131 self.is_built = False

132

133 @property

134 def ecut(self):

135 """Cut-off energy."""

136 return self._ecut

137

138 @ecut.setter

139 def ecut(self, value):

140 self._ecut = value

141 # Calculate the sampling from the cut-off energy

142 s = np.int64(norm(self.a, axis=1) / cutoff2gridspacing(value))

143 # Multiply by two and add one to match PWDFT.jl

144 s = 2 * s + 1

145 # Calculate a fast length to optimize the FFT calculations

146 self.s = [next_fast_len(i) for i in s]

147 # The cell discretization changes when changing s or ecut

148 self.is_built = False

149

150 @property

151 def a(self):

152 """Cell/Vacuum size."""

153 return self._a

154

155 @a.setter

156 def a(self, value):

157 # Build a cubic cell if a number or 1d-array is given

158 if np.asarray(value).ndim <= 1:

159 self._a = value * np.eye(3)

160 # Otherwise scaled cell vectors are given

161 else:

162 self._a = np.asarray(value)

163 # Update ecut and s if it has been set before

164 if hasattr(self, "ecut"):

165 self.ecut = self.ecut

166 # Calculate the unit cell volume

167 self._Omega = abs(det(self._a))

168 if hasattr(self, "kpts"):

169 self.kpts.a = self._a

170 # The cell changes when changing a

171 self.is_built = False

172

173 @property

174 def spin(self):

175 """Number of unpaired electrons."""

176 return self.occ.spin

177

178 @spin.setter

179 def spin(self, value):

180 self.occ.spin = value

181

182 @property

183 def charge(self):

184 """System charge."""

185 return self.occ.charge

186

187 @charge.setter

188 def charge(self, value):

189 self.occ.charge = value

190

191 @property

192 def unrestricted(self):

193 """Enables unrestricted spin handling."""

194 return self.occ.Nspin == 2

195

196 @unrestricted.setter

197 def unrestricted(self, value):

198 if value is None:

199 self.occ.Nspin = value

200 else:

201 self.occ.Nspin = value + 1

202

203 @property

204 def center(self):

205 """Enables centering the system in the cell."""

206 return self._center

207

208 @center.setter

209 def center(self, value):

210 if isinstance(value, str):

211 self._center = value.lower()

212 if self._center not in {"rotate", "shift", "recentered"}:

213 log.error(f"{self._center} is not a recognized center method.")

214 else:

215 self._center = value

216 # Do nothing when recentering

217 if self._center == "recentered":

218 return

219 # Center system such that the geometric inertia tensor will be diagonal

220 # Rotate before shifting!

221 if self._center is True or self._center == "rotate":

222 I = inertia_tensor(self.pos)

223 _, eigvecs = eigh(I)

224 self.pos = (inv(eigvecs) @ self.pos.T).T

225 # Shift system such that its geometric center of mass is in the center of the cell

226 if self._center is True or self._center == "shift":

227 com = center_of_mass(self.pos)

228 self.pos = self.pos - (com - np.sum(self.a, axis=0) / 2)

229 # The structure factor changes when changing pos

230 self.is_built = False

231

232 @property

233 def verbose(self):

234 """Verbosity level."""

235 return self._verbose

236

237 @verbose.setter

238 def verbose(self, value):

239 # If no verbosity is given use the global verbosity level

240 if value is None:

241 value = log.verbose

242 self._verbose = get_level(value)

243 self._log.verbose = self._verbose

244

245 # ### Class properties with a setter outside of the init method ###

246

247 @property

248 def f(self):

249 """Occupation numbers per state."""

250 return self.occ.f

251

252 @f.setter

253 def f(self, value):

254 # Pass through to the Occupations object

255 self.occ.f = value

256

257 @property

258 def s(self):

259 """Real-space sampling of the cell."""

260 return self._s

261

262 @s.setter

263 def s(self, value):

264 # Choose the same sampling for every direction if an integer is given

265 if isinstance(value, numbers.Integral):

266 value = value * np.ones(3, dtype=int)

267 self._s = np.asarray(value)

268 self._Ns = int(np.prod(self._s))

269 # The cell discretization changes when changing s

270 self.is_built = False

271

272 @property

273 def Z(self):

274 """Valence charge per atom."""

275 return self._Z

276

277 @Z.setter

278 def Z(self, value):

279 # Assume same charges for all atoms if an integer is given

280 if isinstance(value, numbers.Integral):

281 value = value * np.ones(self.Natoms, dtype=int)

282 elif isinstance(value, dict):

283 value = [value[ia] for ia in self.atom]

284 # Get the valence charges from the GTH files

285 elif value is None or isinstance(value, str):

286 value = atom2charge(self.atom, value)

287 self._Z = np.asarray(value)

288 if self.Natoms != len(self._Z):

289 msg = (

290 f"Mismatch between number of atoms ({self.Natoms}) and number of "

291 f"charges ({len(self._Z)})."

292 )

293 raise ValueError(msg)

294 # Get the number of calculated electrons and pass it to occ

295 self.occ.Nelec = np.sum(self._Z) - self.charge

296 if self.occ.Nspin and self.occ.bands < self.occ.Nelec * self.occ.Nspin // 2:

297 log.warning("The number of bands is too small, reset to the minimally needed amount.")

298 self.occ.bands = 0

299

300 # ### Read-only properties ###

301

302 @property

303 def Natoms(self):

304 """Number of atoms."""

305 return self._Natoms

306

307 @property

308 def Ns(self):

309 """Number of real-space grid points."""

310 return self._Ns

311

312 @property

313 def Omega(self):

314 """Unit cell volume."""

315 return self._Omega

316

317 @property

318 def r(self):

319 """Real-space sampling points."""

320 return self._r

321

322 @property

323 def active(self):

324 """Mask for active G-vectors."""

325 return self._active

326

327 @property

328 def G(self):

329 """G-vectors."""

330 return self._G

331

332 @property

333 def G2(self):

334 """Squared magnitudes of G-vectors."""

335 return self._G2

336

337 @property

338 def G2c(self):

339 """Truncated squared magnitudes of G-vectors."""

340 return self._G2c

341

342 @property

343 def Gk2(self):

344 """Squared magnitudes of G+k-vectors."""

345 return self._Gk2

346

347 @property

348 def Gk2c(self):

349 """Truncated squared magnitudes of G+k-vectors."""

350 return self._Gk2c

351

352 @property

353 def Sf(self):

354 """Structure factor per atom."""

355 return self._Sf

356

357 @property

358 def dV(self):

359 """Volume element to multiply when integrating field properties."""

360 return self.Omega / self._Ns

361

362 @property

363 def _atoms(self):

364 """Return the Atoms object itself."""

365 # This way we can access the object from Atoms and SCF classes with the same code

366 return self

367

368 # ### Class methods ###

369

370 def build(self):

371 """Build all parameters of the Atoms object."""

372 self.kpts.build()

373 self._sample_unit_cell()

374 self.occ.wk = self.kpts.wk # Pass the weights of k-points to the Occupations object

375 self.occ.fill()

376 self.is_built = True

377 return self

378

379 kernel = build

380

381 def recenter(self, center=None):

382 """Recenter the system inside the cell.

383

384 Keyword Args:

385 center: Point to center the system around.

386 """

387 com = center_of_mass(self.pos)

388 if center is None:

389 self.pos = self.pos - (com - np.sum(self.a, axis=0) / 2)

390 else:

391 center = np.asarray(center)

392 self.pos = self.pos - (com - center)

393 if self.Sf is not None:

394 # Recalculate the structure factor since it depends on the atom positions

395 self._Sf = np.exp(1j * self.G @ self.pos.T).T

396 self._center = "recentered"

397 return self

398

399 def set_k(self, k, wk=None):

400 """Interface to set custom k-points.

401

402 Args:

403 k: k-point coordinates.

404

405 Keyword Args:

406 wk: k-point weights.

407 """

408 self.kpts.build()

409 self.kpts._k = np.atleast_2d(k)

410 if wk is None:

411 self.kpts._wk = np.ones(len(self.kpts._k)) / len(self.kpts._k)

412 else:

413 self.kpts._wk = np.asarray(wk)

414 self.kpts._Nk = len(self.kpts._wk)

415 self.kpts._kmesh = None

416 self.occ.wk = self.kpts.wk

417 self._sample_unit_cell()

418 return self

419

420 def clear(self):

421 """Initialize or clear parameters that will be built out of the inputs."""

422 self._r = None # Sample points in cell

423 self._active = None # Mask for active G-vectors

424 self._G = None # G-vectors

425 self._G2 = None # Squared magnitudes of G-vectors

426 self._G2c = None # Truncated squared magnitudes of G-vectors

427 self._Gk2 = None # Squared magnitudes of G+k-vectors

428 self._Gk2c = None # Truncated squared magnitudes of G+k-vectors

429 self._Sf = None # Structure factor

430 self.is_built = False # Flag to determine if the object was built or not

431 return self

432

433 def _get_index_matrices(self):

434 """Build index matrices M and N to build the real and reciprocal space samplings.

435

436 The matrices are using C ordering (the last index is the fastest).

437

438 Returns:

439 Index matrices.

440 """

441 # Build index matrix M

442 # ms = np.arange(self._Ns)

443 # m1 = np.floor(ms / (self.s[2] * self.s[1])) % self.s[0]

444 # m2 = np.floor(ms / self.s[2]) % self.s[1]

445 # m3 = ms % self.s[2]

446 # M = np.column_stack((m1, m2, m3))

447 M = np.indices(self.s).transpose((1, 2, 3, 0)).reshape((-1, 3))

448 # Build index matrix N

449 N = M - (self.s / 2 < M) * self.s

450 return M, N

451

452 def _sample_unit_cell(self):

453 """Build the real-space sampling and all G-vector parameters."""

454 # Calculate index matrices

455 M, N = self._get_index_matrices()

456 # Build the real-space sampling

457 self._r = M @ inv(np.diag(self.s)) @ self.a

458 # Build G-vectors

459 self._G = 2 * np.pi * N @ inv(self.a.T)

460 # Calculate squared magnitudes of G-vectors

461 self._G2 = norm(self.G, axis=1) ** 2

462 # Calculate the G2 restriction

463 self._active = [

464 np.nonzero(2 * self.ecut >= norm(self.G + self.kpts.k[ik], axis=1) ** 2)

465 for ik in range(self.kpts.Nk)

466 ]

467 self._G2c = self._G2[np.nonzero(2 * self.ecut >= self._G2)]

468 # Calculate G+k-vectors

469 self._Gk2 = np.asarray(

470 [norm(self.G + self.kpts.k[ik], axis=1) ** 2 for ik in range(self.kpts.Nk)]

471 )

472 self._Gk2c = [self.Gk2[ik][self._active[ik]] for ik in range(self.kpts.Nk)]

473 # Calculate the structure factor per atom

474 self._Sf = np.exp(1j * self.G @ self.pos.T).T

475

476 # Create the grid used for the non-wave function fields and append it to the end

477 self._active.append(np.nonzero(2 * self.ecut >= self._G2))

478 self._Gk2 = np.vstack((self._Gk2, self._G2))

479 self._Gk2c.append(self._G2c)

480

481 O = operators.O

482 L = operators.L

483 Linv = operators.Linv

484 K = operators.K

485 T = operators.T

486 I = operators.I

487 J = operators.J

488 Idag = operators.Idag

489 Jdag = operators.Jdag

490

491 def __repr__(self):

492 """Print the parameters stored in the Atoms object."""

493 out = "Atom Valence Position"

494 for i in range(self.Natoms):

495 out += (

496 f"\n{self.atom[i]:>3} {self.Z[i]:>6} "

497 f"{self.pos[i, 0]:10.5f} {self.pos[i, 1]:10.5f} {self.pos[i, 2]:10.5f}"

498 )

499 return out