dft.occupations

Spin and orbital occupation models for DFT.

import mlx_atomistic.dft.occupations

Classes

`FermiDiracOccupations`

class FermiDiracOccupations
    def __init__(electron_count: float, temperature: float = 0.01, spin_mode: SpinMode = 'unpolarized', tolerance: float = 1e-10, max_iterations: int = 100)

Fermi-Dirac occupations with electron-count conservation.

Parameters

Name	Type	Default
`electron_count`	`float`
`temperature`	`float`	`0.01`
`spin_mode`	`SpinMode`	`'unpolarized'`
`tolerance`	`float`	`1e-10`
`max_iterations`	`int`	`100`

Methods

`resolve`

def resolve(eigenvalues: Sequence[float] | mx.array) -> OccupationResult

Return Fermi-Dirac occupations for sorted or unsorted eigenvalues.

Parameters

Name	Type	Default	Description
`eigenvalues`	`Sequence[float] \| mx.array`

Returns

OccupationResult

`FixedOccupations`

class FixedOccupations
    def __init__(occupations: Sequence[float], *, spin_mode: SpinMode = 'unpolarized')

Explicit fixed orbital occupations.

Parameters

Name	Type	Default	Description
`occupations`	`Sequence[float]`
`spin_mode`	`SpinMode`	`'unpolarized'`

Methods

`resolve`

def resolve(_eigenvalues: Sequence[float] | mx.array | None = None) -> OccupationResult

Return fixed occupations.

Parameters

Name	Type	Default	Description
`_eigenvalues`	`Sequence[float] \| mx.array \| None`	`None`

Returns

OccupationResult

`OccupationResult`

class OccupationResult
    def __init__(occupations: mx.array, electron_count: float, chemical_potential: float | None = None, temperature: float | None = None, spin_mode: SpinMode = 'unpolarized')

Orbital occupations and chemical-potential diagnostics.

Parameters

Name	Type	Default
`occupations`	`mx.array`
`electron_count`	`float`
`chemical_potential`	`float \| None`	`None`
`temperature`	`float \| None`	`None`
`spin_mode`	`SpinMode`	`'unpolarized'`

Methods

`to_dict`

def to_dict() -> dict

Return a JSON-safe occupation summary.

Returns

dict

Functions

`magnetization_density`

def magnetization_density(up_density: mx.array, down_density: mx.array) -> mx.array

Return m(r) = ρ↑(r) - ρ↓(r).

Parameters

Name	Type	Default	Description
`up_density`	`mx.array`
`down_density`	`mx.array`

Returns

mx.array

`spin_density_from_orbitals`

def spin_density_from_orbitals(up_orbitals: mx.array, down_orbitals: mx.array, grid: RealSpaceGrid, *, up_occupations: Sequence[float], down_occupations: Sequence[float]) -> tuple[mx.array, mx.array]

Build collinear spin densities ρ↑ and ρ↓.

Parameters

Name	Type	Default	Description
`up_orbitals`	`mx.array`
`down_orbitals`	`mx.array`
`grid`	`RealSpaceGrid`
`up_occupations`	`Sequence[float]`
`down_occupations`	`Sequence[float]`

Returns

tuple[mx.array, mx.array]