Derivative couplings between time-dependent density functional theory excited states in the random-phase approximation based on pseudo-wavefunctions: Behavior around conical intersections

In this paper, we present a formalism for derivative couplings between time-dependent density functional theory (TD-DFT) excited states within the random-phase approximation (RPA) using analytic gradient theory. Our formalism is based on a pseudo-wavefunction approach in a companion paper (DOI 10.1021/jp505767b), and can be checked against finite-difference overlaps. Our approach recovers the correct properties of derivative couplings around a conical intersection (CI), which is a crucial prerequisite for any derivative coupling expression. As an example, we study the test case of protonated formaldimine (CH₂NH2₊).