Accurate and efficient prediction of double excitation energies using the particle-particle random phase approximation

Double excitations are crucial to understanding numerous chemical, physical, and biological processes, but accurately predicting them remains a challenge. In this work, we explore the particle-particle random phase approximation (ppRPA) as an efficient and accurate approach for computing double excitation energies. We benchmark ppRPA using various exchange-correlation functionals for 21 molecular systems and two point defect systems. Our results show that ppRPA with functionals containing appropriate amounts of exact exchange provides accuracy comparable to high-level wave function methods such as CCSDT and CASPT2, with significantly reduced computational cost. Furthermore, we demonstrate the use of ppRPA starting from an excited (N - 2)-electron state calculated by Delta SCF for the first time, as well as its application to double excitations in bulk periodic systems. These findings suggest that ppRPA is a promising tool for the efficient calculation of double and partial double excitation energies in both molecular and bulk systems.