Coupled localized electron spins hosted by defects in semiconductors implement quantum bits with the potential to revolutionize nanoscale sensors and quantum information processing. The present understanding of optical means of spin state manipulation and read-out calls for quantitative theoretical description of the active states, built-up from correlated electrons in a bath of extended electron states. Hitherto we propose a first-principles scheme based on many body perturbation theory and configuration interaction and address two room temperature point defect qubits, the nitrogen vacancy in diamond and the divacancy in silicon carbide. We provide a complete quantitative description of the electronic structure and analyze the crossings and local minima of the energy surface of triplet and singlet states. Our numerical results not only extend the knowledge of the spin-dependent optical cycle of these defects, but also demonstrate the potential of our method for quantitative theoretical studies of point defect qubits.