Theoretical S1 →S0 Absorption Energies of the Anionic Forms of Oxyluciferin by Variational Monte Carlo and Many-Body Green's Function Theory

The structures of three negatively charged forms (anionic keto-1 and enol-1 and dianionic enol-2) of oxyluciferin (OxyLuc), which are the most probable emitters responsible for the firefly bioluminescence, have been fully relaxed at the variational Monte Carlo (VMC) level. Absorption energies of the S1 ← S0 vertical transition have been computed using different levels of theory, such as TDDFT, CC2, and many-body Green’s function theory (MBGFT). The use of MBGFT, by means of the Bethe–Salpeter (BS) formalism, on VMC structures provides results in excellent agreement with the value (2.26(8) eV) obtained by action spectroscopy experiments for the keto-1 form (2.32 eV). To unravel the role of the quality of the optimized ground-state geometry, BS excitation energies have also been computed on CASSCF geometries, inducing a non-negligible blue shift (0.08 and 0.07 eV for keto-1 and enol-1 forms, respectively) with respect to the VMC ones. Structural effects have been analyzed in terms of over- or undercorrelation along the conjugated bonds of OxyLuc by using different methods for the ground-state optimization. The relative stability of the S1 state for the keto-1 and enol-1 forms depends on the method chosen for the excited-state calculation, thus representing a fundamental caveat for any theoretical study on these systems. Finally, Kohn–Sham HOMO and LUMO orbitals of enol-2 are (nearly) bound only when the dianion is embedded into a solvent (water and toluene in the present work); excited-state calculations are therefore meaningful only in the presence of a dielectric medium which localizes the electronic density. The combination of VMC for the ground-state geometry and BS formalism for the absorption spectra clearly outperforms standard TDDFT and quantum chemistry approaches.