The first quest is to find a possible way to fix the convergence issue in the diagonalization process. A potential approach is to implement some other diagonalization methods such as the Jacobi-Davidson method within single precision. Maybe the Jacobi-Davidson method has less issues than the Lanczos method. Moreover, maybe one can use the mixed-precision approach to solve the convergence problem. Although, in this work, the mixed-precision approach was only applied to achieve a better computational performance, the mix-precision approach can also be applied to achieve a better convergence. This approach has already been used by other numerical methods. Thence, we think a higher precision may be able to help dealing with the convergence issue for those systems with transition metal elements.