Spin-Flip TDDFT for Photochemistry

This chapter provides an overview of computational methods based on "spin-flip" (SF) modifications to time-dependent density functional theory (TDDFT), with specific focus on photochemical problems that require exploration of excited-state potential energy surfaces and which may access crossing regions (conical intersections or seams) between those surfaces. Although TDDFT is a widely-used method for computing vertical excitation energies and electronic absorption spectra, it suffers from certain pathologies in the description of conical intersections whenever the ground state is involved. These issues are resolved in SF-TDDFT, albeit at the expense of greater spin contamination that sometimes becomes problematic, and which has motivated the development of spin-complete extensions of TDDFT that produce spin-pure (or nearly spin pure) eigenstates. Following a general introduction to conical intersections and the theoretical description of photochemical phenomena, the formalism of SF-TDDFT is reviewed along with an overview of applications in which SF-TDDFT has been combined with trajectory surface hopping to simulate photochemical reactions. From a theoretical point of view, this work emphasizes how recent modifications to TDDFT, which were originally designed to overcome the aforementioned problems, have the effect of rendering the theory more and more ``wave function-like'', blurring the distinction between TDDFT and limited configuration interaction models.