Description:

Focus on internal, result-identical optimizations to make the QEq core faster without changing outputs or user-facing behavior. We will eliminate redundant work in matrix assembly, reuse allocations, and keep parallelism simple via Rayon/faer defaults. No approximations or configurable “fast” modes in this issue—strict numerical equivalence is required.

Tasks:

• Matrix Build Refactor (Lossless)

  • Precompute geometry-dependent terms (distances/J_ij) and build a base matrix once; per-iteration only patch hydrogen diagonals.
  • Reuse matrix/vector buffers (workspace) across iterations to avoid repeated allocations.

• Parallel-Friendly Fill (Deterministic)

  • Use Rayon global pool for the O(N²) fill in a race-free, deterministic manner; provide a clean serial fallback if Rayon is disabled.
  • Keep faer defaults; note how to disable global parallelism for users who need it (docs comment only, no behavior change).

• Validation

  • Confirm strict equality (within ULP) vs current outputs on regression cases.
  • Add/adjust tests for symmetry, total charge conservation, and unchanged results in strict mode.
  • Add a lightweight benchmark (criterion or timing harness) for N≈10/100/500 to document speedups.