We investigate the role of interatomic forces beyond the nearest neighbors on the thermal transport through an atomic junction with a heavy isotope impurity and in a silicon-germanium-like alloy with atomistic calculations. The thermal conductance of the junction incorporating second-nearest-neighbors forces reaches its minimum when the longitudinal optical phonon resonances in the phonon transmission are minimized. We relate the weakening of the optical phonon resonance with the flattening of the longitudinal optical phonon band of the infinite diatomic lattice with second-nearest-neighbors forces, which is the limit of an extended junction. We emphasize that the bypass of the heavy-atom components in the diatomic lattice by long-range interatomic bonds is crucial for the realization of the minimum in bulk thermal conductivity. We highlight the connection between the minimal thermal conductivity of a SiGe-like alloy with the flattening of the longitudinal optical phonon band of the diatomic lattice due to the second-nearest-neighbors forces, in combination with enhanced anharmonic phonon processes and phonon localizations.