All-electron $GW$ methods implemented in molecular orbital space: Ionization energy and electron affinity of conjugated molecules

An efficient all-electron $G^0{W}^0$ method and a quasiparticle self-consistent $GW$ (QSGW) method for molecules are proposed in the molecular-orbital space with the full random-phase approximation. The convergence with the basis set is examined. As an application, the ionization energy and electron affinity of a series of conjugated molecules (up to 32 atoms) are calculated and compared to the experiment. The QSGW result improves the $G^0{W}^0$ result and both of them are in significantly better agreement with experimental data than those from Hartree-Fock (HF) and hybrid density-functional calculations, especially for electron affinity. The nearly correct energy gap and suppressed self-interaction error by the HF exchange make our method a good candidate for investigating electronic and transport properties of molecular systems.

Figure 1

Dependence of the $-{\epsilon }_{\mathrm{HOMO}}$ of the He atom (upper panel) and Be atom (lower panel) on the size of the basis set used in the HF and $G^0{W}^0$calculations. The experimental result of IE is shown by the horizontal dashed line.

Figure 2

Comparison between the calculated results and experimental data of the IE and EA of the ten conjugated molecules in Table .