Modeling <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> factors, hyperfine interaction, and optical properties of semiconductor quantum dots: Atomistic and eight-band <mml:math xmlns:mml="http://www.w3.org/19

We present a detailed comparative study of two important theoretical approaches: atomistic ${sp}^{3}{d}^{5}{s}^{*}$ tight-binding and continuum eight-band $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ methods, for modeling the spin and optical properties of quantum dots (QDs). Our investigation spans key physical observables, including single-particle energy levels, $g$ factors, exciton radiative lifetimes, and hyperfine-induced Overhauser field fluctuations. We perform our calculations for self-assembled InGaAs/GaAs QD systems as representative case studies. While both methods yield qualitatively consistent trends, quantitative discrepancies arise due to the different treatment of atomistic details, strain effects, and confinement. We introduce targeted corrections to the eight-band $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ framework, including a modified deformation potential scheme and adjusted remote-band contributions. Furthermore, we validate the eight-band implementation of hyperfine interactions by benchmarking it against the tight-binding model, showing reasonable convergence for both electrons and holes.