case, the fine-grained level method (mixed-precision diagonalization) surprisingly performed better than the coarse-grained level method (single-precision sweep). The deeper reason is that when dealing with the Cr 2 system, the diagonalization process is difficult to converge for the single-precision sweep method. To further investigate this phenomenon, we tested three different settings of the mixed-precision scheme, which are: (1) only the coarse-grained level method is applied; (2) only the fine-grained level method is applied; (3) both of these methods are applied. We also conducted a full double-precision test as a baseline and a full single-precision test as a contrast. Two different types of the system were chosen for this test. Besides the Cr 2 system, we also choose the benzene molecule as an example for those systems with no transition metal element. Both of these systems are using 6-31G basis set with the active space of (24e,24o). The bond dimension of Cr 2 is 2000 and benzene is 3000.