Diatomic molecule as a testbed for combining DMFT with electronic structure methods such as GW and DFT

We implemented a combination of DMFT and $GW$ in its fully self-consistent way, one shot $GW$ approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods perform on a H₂ molecule as compared to more established methods such as LDA+DMFT. We found that most flavors of GW+DMFT break down in a strongly correlated regime due to causality violation. Among GW+DMFT methods, only the self-consistent quasiparticle GW+DMFT with static double-counting, and a method with causal double-counting, correctly recover the atomic limit at large H-atom separation. While some flavors of GW+DMFT improve the single-electron spectra as compared to LDA+DMFT, the total energy is best predicted by LDA+DMFT, for which the exact double-counting is known, and is static.