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mlx-atomistic

DFT Foundations

This first DFT slice is a small spin-unpolarized Γ-point plane-wave prototype. It is meant to make the numerical building blocks inspectable before we try to make them chemically broad or highly optimized.

What It Models

Section titled “What It Models”

The prototype works with one total electron density ρ(r). For closed-shell systems, each spatial orbital is doubly occupied:

ρ(r) = 2Σᵢ |ψᵢ(r)|²

Odd or fractional electron counts are allowed for toy examples, but the code does not yet model separate ρ↑(r) and ρ↓(r) spin densities.

Units

Section titled “Units”

DFT internals use atomic units:

ℏ = 1
m_e = 1
e = 1
4πε₀ = 1

Coordinates and cell lengths are in bohr, energies are in hartree, and the electron density integrates to electron count over the cell.

Numerical Pieces

Section titled “Numerical Pieces”
  • RealSpaceGrid stores an orthorhombic periodic grid.
  • ReciprocalGrid stores FFT-compatible G vectors and |G|².
  • normalize_orbitals(...) enforces ∫ |ψᵢ(r)|² dr = 1.
  • density_from_orbitals(...) builds ρ(r) from occupied orbitals.
  • LocalGaussianPseudopotential provides a toy local external potential.
  • hartree_potential(...) solves the periodic Poisson equation in reciprocal space, with the G = 0 term set to zero.
  • DiracExchange, LDACorrelationPZ81, and LDAExchangeCorrelation expose the first exchange-correlation layer.
  • run_scf(...) iterates density, effective potential, and orbitals with linear or Pulay DIIS density mixing.

Programmatic toy systems are available as toy_one_electron_dft_example() and toy_closed_shell_dft_example() from mlx_atomistic.examples.

Current Limits

Section titled “Current Limits”

This is not production DFT. It intentionally excludes k-points, spin polarization, real pseudopotential formats, correlation functionals, forces, geometry optimization, and custom Metal kernels.

The current value is correctness and observability: density normalization, energy decomposition, SCF residuals, FFT behavior, local Gaussian force checks, and small benchmark evidence. Future DFT milestones can add real pseudopotentials, spin, k-points, forces suitable for geometry updates, and then custom Metal kernels once the hot paths are measured.