Application of the RPA method in the semi-empirically treated molecular system

Derivative Couplings between Time-Dependent Density Functional Theory Excited States in the Random-Phase Approximation Based on Pseudo-Wavefunctions: Behavior around Conical Intersections

“…The random-phase approximation (RPA) has been an extremely useful tool for calculating excited state properties and the oscillator strength of atoms and molecules since the 1960s. − More recently, the application of RPA in time-dependent density functional theory (TD-DFT/RPA) has played an increasingly important role in the field of theoretical chemistry for several reasons: (i) As a single-reference ab initio method, TD-DFT/RPA is computationally affordable and sometimes retains relatively high accuracy. , (ii) TD-DFT/RPA is a size-consistent method which is able to give pure singlet and triplet states for closed-shell molecules . (iii) In contrast to TD-DFT within the Tamm–Dancoff approximation (TDA), TD-DFT/RPA maintains the Thomas–Reiche–Kuhn sum rule of the oscillator strengths by taking into account the B matrix in the TD-DFT working equation; as such, TD-DFT/RPA gives improved results for transition moment calculations. , For these reasons, despite its well-known triplet instability, , TD-DFT/RPA is one of the most widely used approaches for modeling excited-state electronic structure. − …”