In the gradient descent method, convergence is achieved when the magnitude of the forces, |∇E|, falls below a predefined threshold, indicating that the atoms are near their equilibrium positions. To improve convergence efficiency, advanced implementations often include dynamic adjustments of the step size α to balance between stability and rapid convergence . For systems with many degrees of freedom, the potential energy surface (PES) can exhibit local minima, and the algorithm is designed to avoid being trapped in these through careful initialization and adaptive corrections. The total potential energy is evaluated using density functional theory (DFT), and the forces (equation 2) are derived as the negative gradient of this energy, F=-∇E.