Excitation Energies from the Single-Particle Green's Function with the GW Approximation.

Quasi-particle energies are important in predicting molecular ionization energies and bulk band structures. The state-of-the-art method for quasi-particle energy calculations, particularly for bulk systems, is the GW approximation. For excited state calculations, one needs to go beyond the GW approximation. The Bethe-Salpeter equation (BSE) is the commonly used approach for bulk-system excited state calculations beyond the GW approximation, which is accurate but computationally cumbersome. In this Article, we develop a new method to extract excitation energies directly from the quasi-particle energies based on the GW approximation. Starting from the ( N - 1)-electron system, we are able to calculate molecular excitation energies with orbital energies at the GW level for HOMO excitations. Our calculations demonstrate that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. Our method is shown to outperform the time-dependent density functional theory (TDDFT) and are comparable with higher level excited state calculations, including the equation-of-motion couple cluster (EOM-CC) theory and the BSE, but with less computational effort. This new approach provides an efficient alternative to the BSE method for accurate excited state calculations.