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DFT Metallic Validation

This document is the completed scientific specification and evidence summary for Phase 1 of the DFT roadmap. It closes one material-level metallic validation without expanding the runtime beyond the existing unpolarized PBE/GTH and Fermi-Dirac capability.

Objective

Section titled “Objective”

Promote fcc Aluminum from an execution smoke test to a source-bound metallic equation-of-state validation. The accepted workload must exercise a global chemical potential, fractional occupations, electronic entropy, and the Helmholtz free energy F = E - TS over a converged weighted k-point mesh.

The work must also make the dense metallic mesh practical. It may add general k-point construction and explicit symmetry-reduction utilities, but it must not add a reference engine, automatic space-group detection, a C++ extension, or a new dependency.

Source Contract

Section titled “Source Contract”

The primary source is the Materials Cloud ACWF verification dataset, record yf0rj-w3r97, DOI 10.24435/materialscloud:s4-3h. The downloaded archive has MD5 6bd97a883b439507d0be4638c1bc7514. Only the compact Aluminum values and their provenance are committed; the source archive remains external.

The exact source records are:

  • Al-FCC.xsf, SHA-256 c4446a6d46475e4cca8067169330284c17c031b97477010b2a433bbf85be25ac;
  • results-unaries-verification-PBE-v1-AE-average.json, SHA-256 d7844caa127eae860fe5087ead42f80d1b6b5eb952a686ff4b912ddaed7db48b;
  • results-unaries-verification-PBE-v1-cp2k_TZV2P.json, SHA-256 3a787c7197cc50e003b38494c4b489b72eeb553e8ca0da3a4505ed08f96e9b6e.

The all-electron FLEUR/WIEN2k average is the primary scientific target:

  • equilibrium volume: 16.49535905981626 A^3/atom;
  • conventional fcc lattice: 4.040861093109186 A;
  • bulk modulus: 0.4837908557795412 eV/A^3;
  • bulk derivative: 4.623179033235038.

CP2K Quickstep is the same-pseudopotential-family diagnostic. Its TZV2P-MOLOPT-PBE-GTH-q3 basis uses Al GTH-PBE-q3 and gives:

  • equilibrium volume: 16.437017660642258 A^3/atom;
  • conventional fcc lattice: 4.036091509687826 A;
  • bulk modulus: 0.48951774655729935 eV/A^3;
  • bulk derivative: 4.514335571200874.

Against the all-electron target, that CP2K fit has a project Delta factor of 0.9954359681 meV/atom and passes the existing excellent thresholds. Absolute energies are not comparable because CP2K uses a Gaussian orbital basis while the MLX runtime uses plane waves.

The historical protocol is reconstructed from the ACWF 1.0 release line. The v1.0.1 tag resolves to commit c08c3f2f7babcb78c7b0a1ddaa28f2fb1d0d8d39 and records PBE, a 0.06 A^-1 maximum k-point spacing, Fermi-Dirac smearing at 710.5 K, 20 additional molecular orbitals, and Al GTH-PBE-q3. This reconstruction is protocol evidence, not a substitute for the source result files above.

Local Protocol

Section titled “Local Protocol”

The source primitive cell is represented locally as the equivalent four-atom conventional cubic cell because the current DFT grid is orthorhombic. The seven volumes are the source lattice scaled by volume factors 0.94, 0.96, 0.98, 1.00, 1.02, 1.04, 1.06 around 4.040422065345 A.

The locked physics is:

  • unpolarized PBE-PW92;
  • Al GTH-PBE-q3, extracted and fingerprinted from the CP2K database;
  • 12 valence electrons per conventional cell;
  • Fermi-Dirac width 0.00225 Ha, equivalent to the ACWF electronic temperature within the recorded precision;
  • the stationary Helmholtz free energy as the EOS energy;
  • a Gamma-centered mesh with maximum conventional-cell reciprocal spacing no greater than 0.06 A^-1.

A numerical CP2K GPW grid cutoff is not transferable to a plane-wave kinetic cutoff. The local cutoff, FFT shape, band capacity, and k-point density are therefore admitted by representation-appropriate convergence gates rather than by copying unlike numeric inputs.

Efficient K-Point Contract

Section titled “Efficient K-Point Contract”

The runtime will retain explicit weighted KPointMesh as the integration contract and add two composable utilities:

  1. a Gamma-centered regular grid, distinct from the existing even half-shifted MonkhorstPackGrid;
  2. deterministic reduction by caller-supplied reciprocal-space symmetry operations.

The reducer validates finite reduced coordinates, integer unimodular operations, mesh closure, unique transformed matches, and equal weights within each orbit. It retains the full orbit mapping used by SCF density reconstruction and never infers that a symmetry is valid for a Hamiltonian. Workload schema v2 persists that mapping so reloading a mesh cannot silently degrade it to scalar weight aggregation.

For conventional fcc Aluminum, the 48 signed permutation operations of the cubic point group reduce the source-density 27 x 27 x 27 Gamma-centered mesh from 19,683 explicit points to 560 weighted representatives, a 97.2% lane reduction. The odd mesh keeps the maximum reciprocal spacing below 0.06 A^-1 at every EOS volume. A full-mesh path remains available as the correctness oracle.

Acceptance Criteria

Section titled “Acceptance Criteria”

Numerical admission requires every retained point to pass:

  • converged SCF and finite free energy, internal energy, entropy, and chemical potential;
  • electron-count error no greater than 1e-4 per cell;
  • maximum orbital residual no greater than 1e-6;
  • maximum orthonormality error no greater than 1e-4;
  • maximum occupation of the highest computed band no greater than 1e-6;
  • consistency of F = E - TS within 5e-6 Ha.

Cutoff and k-point admission reuse the existing EOS convergence thresholds: maximum curve change 1 meV/atom, lattice change 0.1%, bulk-modulus change 3%, and bulk-derivative change 10%. The final seven-point fit must pass the existing verified material thresholds: Delta no greater than 3 meV/atom, lattice error 0.5%, bulk-modulus error 10%, and bulk-derivative error 15%. Thresholds are fixed before the production run and are not relaxed afterward.

The symmetry path must reproduce a full-grid invariant quadrature exactly and a bounded full-versus-reduced SCF within the established numerical gates. The final report records complete wall time, peak memory, explicit point count, representative count, and work counters. Existing fixed-occupation and time-reversal tests must not regress.

Accepted Result

Section titled “Accepted Result”

The admitted profile is c15-k15-b11: a 15 Ha plane-wave cutoff, 36 x 36 x 36 FFT grid, 15 x 15 x 15 Gamma-centered k-point mesh reduced to 120 weighted representatives, 11 bands, and the locked 0.00225 Ha Fermi-Dirac width. The band-capacity gate was evaluated on the denser locked 27 x 27 x 27 mesh at the largest EOS volume. Ten bands failed because the highest occupation was 2.93e-6; 11 bands passed at 1.30e-18.

The selected seven-volume fit gives:

  • conventional fcc lattice: 4.039885108 A;
  • bulk modulus: 76.630636 GPa;
  • bulk derivative: 4.583841965;
  • Delta factor against the all-electron reference: 0.229587 meV/atom.

The corresponding relative errors are 0.0242% for the lattice, 1.14% for the bulk modulus, and 0.851% for the bulk derivative. All locked numerical, convergence, and scientific gates pass. A bounded 4 x 4 x 4 full-grid oracle and its ten-representative symmetry reduction differ by 8.45e-6 Ha/atom, below the fixed 5e-5 Ha/atom gate.

On an Apple M5 Max connected to AC power with Low Power Mode disabled, the accepted seven-point curve took 48.03 s complete wall time. Individual points took 6.37-7.62 s; maximum process physical memory was 3.06 GB. These measurements are current-verified for this workload and power state, not a cross-device performance claim. Raw reports remain under gitignored results/.

Delivery Plan

Section titled “Delivery Plan”
  1. Commit the compact, hash-guarded Aluminum reference bundle and portable workload preparation contract.
  2. Add and test Gamma-centered meshes and explicit reciprocal-symmetry reduction without changing existing MonkhorstPackGrid behavior.
  3. Add a bounded Aluminum point runner and fail-early admission ladder for band capacity, cutoff, k-point density, and the seven-volume EOS.
  4. Run the ladder on Metal, retain only generated evidence under results/, and promote the smallest profile that passes every locked gate.
  5. Commit the accepted scientific summary, runtime measurement, known boundary, and roadmap status; keep raw calculations gitignored.

All five delivery steps are complete.

Out Of Scope

Section titled “Out Of Scope”

This phase does not add spin polarization, general cells, stress, ionic relaxation, projected observables, new exchange-correlation functionals, automatic crystal-symmetry discovery, or broad Aluminum chemistry. Those claims remain governed by later roadmap phases.