Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond

We investigated the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first-principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and, subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects into first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.