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Focus on the overlap density of wavefunctions in GW approximations.

The quasiparticle energies in a single-shot GW approximation are presented with the focus on the overlap density of wavefunctions. Group theory is employed to classify wavefunctions into irreducible representations and to assess the overlap density. The theoretical inspection assures that a quasiparticle energy depends primarily on spatially overlapped and symmetrically compatible wavefunctions. The numerical inspection indicates that a quasiparticle energy relies largely on all-electron wavefunctions not only in occupied bands but also in high-energy unoccupied bands. These are demonstrated for SrTiO3 and ascertained consistently by the symmetry analysis of the overlap density.