The GW Self-Screening Error and its Correction Using a Local Density-Functional

In electronic structure theory, the self-screening error is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. In the GW approach to many-electron theory, the self-screening introduces error into the electron density, energy and ionization potential. We illustrate this self-screening error in a straightforward way for model systems using orbital-dependent potentials. We propose a simple, computationally inexpensive correction to any GW calculation (including fully self-consistent GW) to remove this error. Our correction is a spatially local potential, added to the self-energy, that depends on the local electron density, obtained via a series of one-dimensional one-electron finite training systems. We then test our correction for other one-dimensional systems where we have access to the exact many-electron density and energy, and show that our correction removes the unwanted effects of self-screening on the electron density and the ionization potential.