Beyond TD-DFT: Assessing the Bethe-Salpeter Equation within the GW Approximation for Absorption Properties

Time-dependent density functional theory (TD-DFT) has been the "go-to" computational approach for predicting optical absorption properties, balancing computational efficiency and reasonable accuracy. However, the Bethe-Salpeter equation within the GW approximation (GW/BSE) is rapidly emerging as a powerful alternative to overcoming key limitations of TD-DFT. This letter presents a comprehensive evaluation of one-photon and two-photon absorption (1PA and 2PA) properties across a chemically diverse set of fluorophores, comparing TD-DFT with the eigenvalue self-consistent GW (evGW/BSE) and single-shot G₀W₀/BSE approaches, within the resolution-of-identity approximation, relative to resolution-of-identity second-order approximate coupled-cluster (RI-CC2). While TD-DFT maintains its dominance for 1PA, both evGW/BSE and G₀W₀/BSE exhibit superiority for 2PA, offering lower absolute errors and stronger agreement with qualitative trends. A persistent challenge in TD-DFT is the trade-off between quantitative accuracy and capturing structure-property trends, with no single functional reliably achieving both. In contrast, the tested GW/BSE approaches overcome this limitation, offering reliable values alongside a robust linear correlation. These findings further demonstrate evGW/BSE and G₀W₀/BSE as promising frameworks for modeling optical properties including 2PA.