To address the limitations of the rolling oneand two-probe methods for cavity calculation, we have developed an approach that uses an angle measurement technique (Figure ). This method relies on determining the angle θ formed by the center of mass (COM) of the cage, the probe, and the atom of the cage. For probes that do not overlap with cage atoms, one calculates the average of all angles θ for each cage atom within the threshold distance (automatically calculated as the diameter of the maximum escape sphere from the cavity). If the average angle is greater than 90º the probe is considered to be inside the cage; otherwise, it is considered to be outside of the cavity.