We then apply this formula to test its effectiveness in controlling truncation error in large systems. To do this, we extend the size of the water clusters to include up to 60 water molecules. The 6-31G* basis set is used to reduce computational workload, although the largest system still contains more than 1000 atomic orbitals and approximately 7000 auxiliary orbitals. All of the water clusters calculated have relatively spherical conformations, which is an example of a 3-dimensional dense system. The constant k is set to 40. Table presents the relationship between the number of water molecules and the truncation error, expressed in kcal/mol, while Figure shows the transformation time of the ERI as a function of the number of basis functions. The figure compares the time cost of the untruncated (exact) scheme with that of the truncated (t > 0) scheme. As shown in Table and Figure , using the truncated scheme significantly reduces the time required for the ERI transformation. Despite the number of basis functions and auxiliary functions tripling from 360 to 1080, the truncation error remains within 0.01 kcal/mol. It is worth mentioning that although this truncation scheme would make the theory not size consistent, the consistency error would remain small even for large systems by using an appropriate truncation threshold as exemplified above.