Convergence of Surface States on Al(001) Slabs: Implications for Optoelectronic Modeling

Density functional theory (DFT) calculations of metallic surfaces routinely employ periodic slab models in which spurious coupling between top and bottom surfaces artificially splits surface states, yet the thickness required to eliminate this artifact remains poorly characterized. Here, we systematically investigate convergence of surface states at the Γ¯ point of Al(001) slabs as a function of slab thickness (11–81 atomic layers) and relaxation depth (3–11 layers). The splitting and energy position of the surface states are largely insensitive to the relaxation depth, but depend strongly on the slab thickness. At Γ¯, for symmetric relaxation, the splitting decays exponentially with slab thickness, requiring at least 55 layers to fall below 10 meV; for asymmetric relaxation, a persistent splitting of ∼35 meV does not vanish even in the thick-slab limit. We interpret this behavior using a two-state coupling model. For practical comparison with experimental binding energies, the midpoint energy Emid of a symmetric 31-layer slab offers a computationally efficient alternative to full decoupling for the Γ¯ surface states. For asymmetric slabs, however, the lower-energy branch Elow, corresponding to the relaxed surface, should be used instead of midpoint averaging. These results establish validated convergence criteria for Al(001) and provide a methodological framework transferable to other metallic optoelectronic materials.