A quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction with GW/BSE

We present a new 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. In the correlated subspace, we use a wave function description to avoid embedding the two-particle vertex, which greatly simplifies the frequency structure of the embedding. DCI takes the strengths of both theories to balance static and dynamic correlation in a single, fully ab-initio embedding concept. We show that treating high-energy correlation up to the $GW$ and Bethe-Salpeter equation level is sufficient even for challenging multi-reference problems. Our theory treats ground and excited states on equal footing, and we compute the dissociation curve of N$_2$, vertical excitation energies of N$_2$ and C$_2$, and the ionization spectrum of benzene in excellent agreement with high level quantum chemistry methods and experiment.