Vibrationally Resolved Optical Spectra of Point Defects from Particle-Particle Random Phase Approximation

Accurate prediction of vibrationally resolved optical spectra is crucial for understanding and designing solid-state point defects. In this work, we extend the particle-particle random phase approximation (ppRPA) framework by implementing analytic nuclear gradients and transition dipole moments, enabling the calculation of vibrationally resolved absorption spectra. As a particle-nonconserving excitation theory, ppRPA accesses the ground and excited states of an N-electron system from a (N ± 2)-electron reference, allowing for a natural inclusion of double excitations and strong correlation effects. We apply the newly developed ppRPA gradient and transition dipole formalism to the negatively charged nitrogen-vacancy center in diamond (NV⁻ center) to compute its optical spectra with vibronic resolution using Huang–Rhys theory. This work demonstrates ppRPA as a promising and systematically improvable approach for modeling excited-state properties of solid-state defect systems.