Evaluating the Bethe-Salpeter Equation within the GW Approximation (GW/BSE) for Excitation Energies of BODIPYs and Aza-BODIPYs

Ashton Henderson, Rishabh Wattal, and Alex Brown

University of Alberta

Boron-dipyrromethenes (BODIPYs) are a class of fluorescent molecules known for their highly tuneable optical properties and diverse array of applications, ranging from medical imaging to photovoltaics. Due to multireference behaviour, strong electron correlation, and double excitation character, excited states of these systems are characteristically difficult to model computationally, complicating the theoretical design of novel BODIPY derivatives. Time-dependent density functional theory (TD-DFT) is known to consistently overestimate BODIPY excitation energies, producing mean absolute error (MAE) values above 0.3 eV; recent work suggests spin-scaled double hybrids with long-range correction can bring the MAE below 0.1 eV, albeit at significant computational cost. To assess an alternative approach, we turn to the Bethe-Salpeter equation within the GW approximation (GW/BSE), which has recently been gaining traction for its ability to eliminate many common issues of TD-DFT (such as the self-interaction error, unequal treatment of local and charge-transfer excitations, and strong functional dependence) at an equivalent computational cost. Using experimental excitation energies for a set of 17 substituted BODIPYs and aza-BODIPYs, we present a comprehensive benchmark of the GW/BSE method. The assessment includes analysis of basis set convergence with the aug-cc-pV\(n\)Z (\(n =\) D, T, Q) basis set series, comparison of evGW and G\(_{0}\)W\(_{0}\) schemes to evaluate the effect of self-consistency in the GW calculation, and evaluation of the impact of different DFT starting points (PBE, LC-\(\omega\)PBE, and PBE0 with varying levels of exact exchange). Results demonstrate that GW/BSE produces MAE values under 0.2 eV while maintaining strong linear correlations, significantly outperforming TD-DFT and cementing GW/BSE as a valuable tool for the prediction of BODIPY excitation energies and design of future BODIPY derivatives.

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