dft.xc

Exchange-correlation functionals for the spin-unpolarized DFT prototype.

import mlx_atomistic.dft.xc

Classes

DiracExchange

class DiracExchange
    def __init__(name: str = 'dirac-exchange')

Unpolarized Dirac LDA exchange.

Parameters

Name	Type	Default	Description
name	str	'dirac-exchange'

Methods

evaluate

def evaluate(density: mx.array, grid: RealSpaceGrid | None = None, *, density_floor: float = 1e-12) -> XCResult

Evaluate the Dirac LDA exchange energy density, potential, and total energy.

Parameters

Name	Type	Default	Description
density	mx.array		Electron density rho sampled on the grid.
grid	RealSpaceGrid | None	None	Real-space grid providing the integration weight dv; None uses unit weight. Defaults to None.
density_floor	float	1e-12	Lower clamp applied to the density for numerical stability. Defaults to 1e-12.

Returns

• XCResult — An XCResult with the energy density, potential, and total energy.

ExchangeCorrelationFunctional

class ExchangeCorrelationFunctional(Protocol)

Protocol for local exchange-correlation functionals.

Methods

evaluate

def evaluate(density: mx.array, grid: RealSpaceGrid | None = None, *, density_floor: float = 1e-12) -> XCResult

Evaluate energy density, total energy, and potential for ρ.

Parameters

Name	Type	Default	Description
density	mx.array
grid	RealSpaceGrid | None	None
density_floor	float	1e-12

Returns

• XCResult

LDACorrelationPZ81

class LDACorrelationPZ81
    def __init__(name: str = 'lda-correlation-pz81', a: float = 0.0311, b: float = -0.048, c: float = 0.002, d: float = -0.0116, gamma: float = -0.1423, beta1: float = 1.0529, beta2: float = 0.3334)

Perdew-Zunger 1981 unpolarized LDA correlation parameterization.

Parameters

Name	Type	Default	Description
name	str	'lda-correlation-pz81'
a	float	0.0311
b	float	-0.048
c	float	0.002
d	float	-0.0116
gamma	float	-0.1423
beta1	float	1.0529
beta2	float	0.3334

Methods

evaluate

def evaluate(density: mx.array, grid: RealSpaceGrid | None = None, *, density_floor: float = 1e-12) -> XCResult

Evaluate the PZ81 LDA correlation energy density, potential, and total energy.

Parameters

Name	Type	Default	Description
density	mx.array		Electron density rho sampled on the grid.
grid	RealSpaceGrid | None	None	Real-space grid providing the integration weight dv; None uses unit weight. Defaults to None.
density_floor	float	1e-12	Lower clamp applied to the density for numerical stability. Defaults to 1e-12.

Returns

• XCResult — An XCResult with the energy density, potential, and total energy.

LDAExchangeCorrelation

class LDAExchangeCorrelation
    def __init__(exchange: ExchangeCorrelationFunctional = DiracExchange(), correlation: ExchangeCorrelationFunctional = LDACorrelationPZ81(), name: str = 'lda-xc-pz81')

Combined Dirac exchange plus PZ81 LDA correlation.

Parameters

Name	Type	Default	Description
exchange	ExchangeCorrelationFunctional	DiracExchange()
correlation	ExchangeCorrelationFunctional	LDACorrelationPZ81()
name	str	'lda-xc-pz81'

Methods

evaluate

def evaluate(density: mx.array, grid: RealSpaceGrid | None = None, *, density_floor: float = 1e-12) -> XCResult

Evaluate the combined LDA exchange-correlation (Dirac + PZ81).

Parameters

Name	Type	Default	Description
density	mx.array		Electron density rho sampled on the grid.
grid	RealSpaceGrid | None	None	Real-space grid providing the integration weight dv; None uses unit weight. Defaults to None.
density_floor	float	1e-12	Lower clamp applied to the density for numerical stability. Defaults to 1e-12.

Returns

• XCResult — An XCResult with the energy density, potential, and total energy.

XCResult

class XCResult
    def __init__(name: str, energy_density: mx.array, potential: mx.array, total_energy: mx.array)

Exchange-correlation energy density, total energy, and potential.

Parameters

Name	Type	Default	Description
name	str
energy_density	mx.array
potential	mx.array
total_energy	mx.array