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An efficient all-electron G$^0$W$^0$ method and a quasiparticleselfconsistent GW (QSGW) method for molecules are proposed in the molecularorbital space with the full random phase approximation. The convergence withbasis set is examined. As an application, the ionization energy ($I$) andelectron affinity ($A$) of a series of conjugated molecules (up to 32 atoms)are calculated and compared to experiment. The QSGW result improves theG$^0$W$^0$ result and both of them are in significantly better agreement withexperimental data than those from Hartree-Fock (HF) and hybrid densityfunctional calculations, especially for $A$. The nearly correct energy gap andsuppressed self-interaction error by the HF exchange make our method a goodcandidate for investigating electronic and transport properties of molecularsystems.

All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules