Because of algorithmic similarity with MP2 calculation, the “resolution of the identity” approximation can also be used in CIS(D). In fact, RI-CIS(D) is orders of magnitudes more efficient than previously explained CIS(D) algorithms for effectively all molecules with more than a few atoms. Like in MP2, this is achieved by reducing the prefactor of the computational load. In fact, the overall cost still scales with the fifth power of the system size.
Presently in Q-Chem, RI approximation is supported for closed-shell restricted CIS(D) and open-shell unrestricted UCIS(D) energy calculations. The theta diagnostic is not implemented for RI-CIS(D).