Configuration Interaction-Corrected Tamm–Dancoff Approximation: A Time-Dependent Density Functional Method with the Correct Dimensionality of Conical Intersections

Linear response (LR) Kohn-Sham (KS) time-dependent density functional theory (TDDFT), or KS-LR, has been widely used to study electronically excited states of molecules and is the method of choice for large and complex systems. The Tamm-Dancoff approximation to TDDFT (TDDFT-TDA or KS-TDA) gives results similar to KS-LR and alleviates the instability problem of TDDFT near state intersections. However, KS-LR and KS-TDA share a debilitating feature; conical intersections of the reference state and a response state occur in F - 1 instead of the correct F - 2 dimensions, where F is the number of internal degrees of freedom. Here, we propose a new method, named the configuration interaction-corrected Tamm-Dancoff approximation (CIC-TDA), that eliminates this problem. It calculates the coupling between the reference state and an intersecting response state by interpreting the KS reference-state Slater determinant and linear response as if they were wave functions. Both formal analysis and test results show that CIC-TDA gives similar results to KS-TDA far from a conical intersection, but the intersection occurs with the correct dimensionality. We anticipate that this will allow more realistic application of TDDFT to photochemistry.