Conical intersections and double excitations in time-dependent density functional theory

There is a clear need for computationally inexpensive electronic structure theory methods which can model excited state potential energy surfaces. Time-dependent density functional theory (TDDFT) has emerged as one of the most promising contenders in this context. Many previous tests have concentrated on vertical excitation energies, which can be compared to experimental absorption maxima. Here, we focus attention on more global aspects of the resulting potential energy surfaces, especially conical intersections which play a key role in photochemical mechanisms. We introduce a new method for minimal energy conical intersection (MECI) searches which does not require knowledge of the non-adiabatic coupling vector. Using this new method, we compute MECI geometries with multi-state complete active space perturbation theory (MS-CASPT2) and TDDFT. We show that TDDFT in the linear response and adiabatic approximations can predict MECI geometries and energetics quite accurately, but that there are a number of qualitative deficiencies which need to be addressed before TDDFT can be used routinely in photochemical problems.