DFT SCF Core

The DFT layer now has a more explicit SCF core while staying intentionally small: spin-unpolarized, Γ-point, orthorhombic cells, and local Gaussian pseudopotentials only.

Exchange-Correlation

DFT does not solve directly for the full many-electron wavefunction. In the Kohn-Sham construction, auxiliary orbitals generate the density ρ(r), and the unknown many-electron physics is approximated by an exchange-correlation functional.

This milestone exposes that as a small API:

• DiracExchange
• LDACorrelationPZ81
• LDAExchangeCorrelation

Each functional returns an energy density, total energy, and potential v_xc. The default SCF path now uses LDA exchange plus PZ81 correlation.

SCF Mixing

SCF iteration repeatedly maps an input density to a new output density. Directly replacing the old density is often unstable, so the code now has two mixers:

• LinearMixer: conservative and predictable.
• PulayDIISMixer: uses residual history to accelerate convergence.

SCFResult records density residual, potential residual, energy delta, convergence status, failure reason, timing totals, and mixer metadata.

Restartable State

run_scf(...) accepts initial_density and initial_orbitals. This is enough for continuation workflows and future geometry steps. A restart density is renormalized to the requested electron count so continuation does not silently change the number of electrons.

Forces

local_pseudopotential_forces(...) computes Hellmann-Feynman-style forces on Gaussian centers from a converged or fixed density. These are diagnostic forces for the toy local pseudopotential model, not production DFT forces and not yet a geometry optimizer.

Performance Evidence

The DFT benchmark now reports per-case timings for Hartree solves, XC evaluation, kinetic application, mixer cost, force evaluation, total SCF time, and a compact FFT probe. This makes the next optimization decision evidence based instead of speculative.