First, we compare the computational expenses of constructing the overlap matrix by Method #1 versus Method #2. In Fig. , we quantify the performance difference by averaging the speedup over 20 calculations of the overlap matrix at different times using one cpu core. We find that the performance of Method #2 is faster than Method #1 by orders of magnitude, especially for a large number of electronic states. In fact, as shown in Fig. , Method #2 can be ≈ 700 times faster than Method #1 when we construct the overlap matrix for N s = 256 CIS states. Method #1 Method #2 SHARC 0.9 SHARC 0.99