No primary-source ³¹P hyperfine data in Si; only DFT methodology tutorials — E8 Intelligence Research

FINDING: Search returned no primary-source results on ³¹P hyperfine coupling in Si; only generic DFT/DFTB methodology tutorials and one TD-DFTB exchange-correction paper. | MATH: No hyperfine constants, no A-tensor values, no donor binding energies present in the corpus. | CONNECTION: None supported by evidence. | DEPTH: 1 --- **Assessment of the actual content retrieved:** **1. Key mathematical insight** None specific to ³¹P:Si. The corpus contains only: - DFTB (Density Functional Tight Binding) pedagogy — parameterization via two-center integrals, not first-principles hyperfine. - TD-DFTB long-range correction (arXiv:1503.01714v2): adds exact HF exchange switched on at large r to the ground-state Hamiltonian and linear-response coupling matrix. **2. Equations/constants present** - TD-DFTB correction: H → H + f(r)·Σ_exchange (range-separation function f(r) → 1 at large r). - No Fermi contact term A = (2μ₀/3) g_e μ_B g_N μ_N |ψ(0)|² appears anywhere in the retrieved material. - No Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com