Quantum Vibronic Effects on Emission Energies of Solid-State Spin Defects

While significant computational effort has been made to understand the optical cycles of solid-state spin defects, it remains a challenge to quantify quantum vibronic effects on optical transitions. It was previously shown that including quantum vibronic effects on vertical excitation energies of the nitrogen-vacancy center in diamond results in significant renormalizations of the energy levels computed at fixed atomic positions (on the order of hundreds of meV) [1]. These results were obtained using PyEPFD (https://pyepfd.readthedocs.io/) to stochastically sample phonon modes computed with density functional theory (DFT) and the WEST (https://west-code.org/) code to compute electronic properties with time-dependent DFT (TDDFT). Here we present a study of the quantum vibronic effects on emission in the singlet channel of selected spin defects: the nitrogen-vacancy center in diamond, the neutral divacancy center in silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. Using WEST's TDDFT implementation coupled with PyEPFD's stochastic sampling, we find that including quantum vibronic effects results in a substantial renormalization of the emission energies and a quantifiable dynamic Jahn-Teller splitting of degenerate singlet states. Our results further highlight the importance of considering quantum cibronic effects in first-principles calculations of spin defects.