Widening of the fundamental gap in cluster GW for metal-molecular interfaces

The GW approximation is very promising for an accurate first-principles description of charged excitations in single-molecule-metal interfaces. In the cluster approach for electronic transport across molecules, the infinite metal (with an adsorbed molecule) is replaced by a finite cluster whose volume should be incrementally increased to test the approach to the thermodynamic limit. Here we show that in GW, the approach to the thermodynamic limit will be much slower than in Kohn-Sham density-functional theory (DFT) because of the Coulomb interaction. To demonstrate this statement, we investigate spectral gaps in an ensemble of disordered sodium clusters in Kohn-Sham DFT, quasiparticle eigenvalue-self-consistent GW and Hartree-Fock. The fundamental gaps (i.e. difference between the lowest unoccupied and highest occupied level) in GW scale as N^-1/3 on average, where N is the number of atoms. We demonstrate that this slow decrease artificially depletes the density of states at the Fermi level when the cluster is used to simulate a semi-infinite electrode. Therefore, the GW method cannot be taken as an out-of-the-box improvement of the DFT in cluster geometries, unless careful convergence checks are performed.