This study presents a refined approach to computing the electronic structure of indium antimonide (InSb) using advanced ab initio techniques with the In and Sb $4d^{10}$ semicore electrons included in the valence states. These states are modeled using fully relativistic projector augmented waves (PAW) and optimized norm-conserving Vanderbilt (ONCV) pseudopotentials. However, standard Kohn-Sham density-functional theory (DFT) calculations with these pseudopotentials often produce nonphysical band inversions and incorrect band gaps at the $\mathrm{\Gamma }$ point because of $5p\text{−}4d$ repulsion and self-interaction errors (SIE). To resolve these issues, we apply a combination of hybrid Heyd-Scuseria-Ernzerhof (HSE) exchange-correlation (XC) functionals, many-body perturbation theory (MBPT) via quasiparticle $G_0{W}_0$, and $\mathrm{DFT}+U$, significantly improving the accuracy of the band structure over previous studies. A Bayesian optimization framework is used to refine key parameters, including the inverse screening length $\left(\mathit{\mu }\right)$ and Hartree-Fock (HF) exchange fraction $\left(\mathit{\alpha }\right)$ in HSE-based XC functionals, as well as the Hubbard $\mathit{U}$ parameters in $\mathrm{DFT}+U$, leading to significantly improved band structure predictions. This approach yields highly precise band gaps, bulk moduli, effective masses, Luttinger parameters, valence bandwidth, and $4d$ band positions, achieving unprecedented agreement with experimental data. The resulting model resolves a long-standing incomplete description of InSb's electronic band structure and provides a transferable computational framework for accurate electronic structure predictions across diverse material systems, offering valuable insights for future electronic, optoelectronic, and quantum applications.

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• Electronic structure
• Electronic structure of atoms & molecules
• First-principles calculations
• Optimization problems
• Optoelectronics
• Spin-orbit coupling
• Semiconductors
• Ab initio calculations
• Band structure methods
• Bayesian methods
• DFT+U
• GW method
• Hybrid functionals