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The physics of electronic energy level alignment at interfaces formed betweenmolecules and metals can in general be accurately captured by the \emph{abinitio} $GW$ approach. However, the computational cost of such $GW$calculations for typical interfaces is significant, given their large systemsize and chemical complexity. In the past, approximate self-energy corrections,such as those constructed from image-charge models together with gas-phasemolecular level corrections, have been used to compute level alignment withgood accuracy. However, these approaches often neglect dynamical effects of thepolarizability and require the definition of an image plane. In this work, wepropose a new approximation to enable more efficient $GW$-quality calculationsof interfaces, where we greatly simplify the calculation of the non-interactingpolarizability, a primary bottleneck for large heterogeneous systems. This isachieved by first computing the non-interacting polarizability of eachindividual component of the interface, e.g., the molecule and the metal,without the use of large supercells; and then using folding and spatialtruncation techniques to efficiently combine these quantities. Overall thisapproach significantly reduces the computational cost for conventional $GW$calculations of level alignment without sacrificing the accuracy. Moreover,this approach captures both dynamical and nonlocal polarization effects withoutthe need to invoke a classical image-charge expression or to define an imageplane. We demonstrate our approach by considering a model system of benzene atrelatively low coverage on aluminum (111) surface. Although developed for suchinterfaces, the method can be readily extended to other heterogeneousinterfaces.

Accelerating $GW$-Based Energy Level Alignment Calculations for Molecule-Metal Interfaces Using a Substrate Screening Approach