Lattice- and Spin–Orbit-Controlled Band-Edge Ordering in Monolayer MoS₂: A Convergence-Validated SIESTA Reference for Defect and Adsorption Studies

Localized-orbital density functional theory (DFT) is widely used to model defects and molecular adsorption on monolayer MoS₂, but the numerical uncertainty of the pristine reference is rarely quantified at the meV scale that governs band-edge ordering. We establish a convergence-validated SIESTA reference for monolayer 2H-MoS₂ using the PBE functional, a double-ζ polarized basis and PseudoDojo norm-conserving pseudopotentials, including fully relativistic spin–orbit coupling (SOC). Mesh-cutoff and k-point errors are below 0.1 meV atom⁻¹. A refined fixed-cell scan gives a₀ = 3.196 Å and a layer modulus of 81–84 N m⁻¹. Without SOC, the K and Γ valence-band maxima differ by only 8.0 meV, and a 0.13% biaxial expansion reverses their order; the direct-gap deformation rate (≈−0.11 eV per % strain) is close to the measured optical value. Fully relativistic PBE gives a direct K–K gap of 1.613 eV, a valence-band splitting of 150.6 meV and a K-over-Γ margin of 79.7 meV, which makes the direct-gap assignment robust. The reference transfers to a 75-atom supercell within 0.06 meV per formula unit and provides a quantified baseline for defect and adsorption studies of MoS₂ nanosheets.