This study re-examines the influence of quadrupole deformation \(\beta _2\) on optimum fusion orientations and, for the first time in this context, investigates the role of hexadecapole deformation \(\beta _4\) using a microscopic framework. Employing the Skyrme energy density formalism (SEDF) within the semiclassical extended Thomas–Fermi (ETF) approach, we analyse hot-compact and cold-elongated configurations in the fusion of silicon isotopes. While earlier studies based on phenomenological models, such as the Prox77 proximity potential, suggested that optimum orientations depend solely on the sign of \(\beta _2\) and are unaffected by higher-order deformations, our findings show otherwise. We demonstrate that \(\beta _4\) can induce significant deviations, up to 40 \(^\circ\) , in optimum hot-compact orientations. In contrast, cold-elongated configurations remain unchanged. Moreover, we find that optimum orientations depend on both the sign and the magnitude of \(\beta _2\) , particularly when \(\beta _2\) is large. Our results reveal that higher-order multipole deformations are essential for a precise description of orientation-dependent fusion dynamics.
