dft.periodic_electrostatics

Periodic point-charge electrostatics for full-rank cells.

import mlx_atomistic.dft.periodic_electrostatics

Functions

periodic_ewald_energy

def periodic_ewald_energy(charges: Sequence[float], positions: Sequence[Sequence[float]], cell_lengths: Cell | Sequence[float] | Sequence[Sequence[float]], *, eta: float | None = None, tolerance: float = 1e-10) -> float

Return periodic point-charge Ewald energy with neutralizing background.

Parameters

Name	Type	Default	Description
charges	Sequence[float]		Point charges in atomic units.
positions	Sequence[Sequence[float]]		Cartesian positions in bohr.
cell_lengths	Cell | Sequence[float] | Sequence[Sequence[float]]		A periodic Cell, three orthorhombic lengths, or a full row-vector cell matrix in bohr.
eta	float | None	None	Optional Ewald splitting parameter in inverse bohr. Defaults to a cell-scaled value.
tolerance	float	1e-10	Real/reciprocal truncation target. Defaults to 1e-10.

Returns

• float — Ewald energy in Hartree.

periodic_ewald_forces

def periodic_ewald_forces(charges: Sequence[float], positions: Sequence[Sequence[float]], cell_lengths: Cell | Sequence[float] | Sequence[Sequence[float]], *, displacement: float = 0.0001, eta: float | None = None, tolerance: float = 1e-10, method: str = 'analytic') -> np.ndarray

Return forces for the periodic Ewald ion-ion energy.

Parameters

Name	Type	Default	Description
charges	Sequence[float]		Point charges in atomic units.
positions	Sequence[Sequence[float]]		Cartesian positions in bohr.
cell_lengths	Cell | Sequence[float] | Sequence[Sequence[float]]		A periodic Cell, three orthorhombic lengths, or a full row-vector cell matrix in bohr.
displacement	float	0.0001	Central-difference step used only when method="finite_difference". Defaults to 1e-4.
eta	float | None	None	Optional Ewald splitting parameter. Defaults to a cell-scaled value.
tolerance	float	1e-10	Ewald truncation target. Defaults to 1e-10.
method	str	'analytic'	"analytic" or the validation-only "finite_difference". Defaults to "analytic".

Returns

• np.ndarray — Force array with shape (n_ions, 3) in Hartree/bohr.

periodic_ewald_stress

def periodic_ewald_stress(charges: Sequence[float], positions: Sequence[Sequence[float]], cell_lengths: Cell | Sequence[float] | Sequence[Sequence[float]], *, eta: float | None = None, tolerance: float = 1e-10) -> np.ndarray

Return compression-positive periodic Ewald stress.

Parameters

Name	Type	Default	Description
charges	Sequence[float]		Point charges in atomic units.
positions	Sequence[Sequence[float]]		Cartesian positions in bohr.
cell_lengths	Cell | Sequence[float] | Sequence[Sequence[float]]		Periodic cell in bohr.
eta	float | None	None	Optional Ewald splitting parameter in inverse bohr.
tolerance	float	1e-10	Real/reciprocal truncation target.

Returns

• np.ndarray — Symmetric stress tensor in Hartree/bohr cubed.