The <i>GW</i>-Method for Quantum Chemistry Applications: Theory and Implementation

The GW-technology corrects the Kohn-Sham (KS) single particle energies and single particle states for artifacts of the exchange-correlation (XC) functional of the underlying density functional theory (DFT) calculation. We present the formalism and implementation of GW adapted for standard quantum chemistry packages. Our implementation is tested using a typical set of molecules. We find that already after the first iteration of the self-consistency cycle, G0W0, the deviations of quasi-particle energies from experimental ionization potentials and electron affinities can be reduced by an order of magnitude against those of KS-DFT using GGA or hybrid functionals. Also, we confirm that even on this level of approximation there is a considerably diminished dependency of the G0W0-results on the XC-functional of the underlying DFT.