Quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction with G W / BSE

We present a quantum embedding theory called dynamical configuration interaction (DCI) that combines wave function and Green's function theories. DCI captures static correlation in a correlated subspace with configuration interaction and couples to high-energy, dynamic correlation outside the subspace with many-body perturbation theory based on Green's functions. DCI takes the strengths of both theories to balance static and dynamic correlation in a single, fully ab initio embedding concept. The theory adds dynamic correlation around a fixed active space of orbitals with efficient $\mathcal{O}({N}^{5})$ scaling, while maintaining a multireference treatment of the active space. We show that treating high-energy correlation up to the $GW$ and Bethe-Salpeter equation level is sufficient even for challenging multireference problems. Our theory treats ground and excited states on equal footing, and we compute the dissociation curve of ${\mathrm{N}}_{2}$, the vertical excitation energies of small molecules, and the ionization spectrum of benzene in excellent agreement with high-level quantum chemistry methods and experiment.