Impact of Structure on Excitation Energies and S1-T1 Energy Gaps of Asymmetrical Systems of Interest for Inverted Singlet-Triplet Gaps

Abstract

Computational investigations of Inverted Singlet-Triplet (INVEST) emitters often rely on ADC(2) and TD-DFT excitation energies (EEs) obtained with the vertical approximation. Here, we first considered several cyclazine derivatives and examine the sensitivity of vertical EEs (VEEs) as well as singlet-triplet gaps, ΔE_S1T1 gaps, to the level at which the ground state (S₀) structure was optimized. For cyclazine, VEEs and vertical gaps from ADC(2) or TD-DFT are spread over a narrow range (< 0.064 eV) whether the S₀ structure is optimized with various DFT, CCSD, and RI-MP2 methods. However, for asymmetric cyclazines, depending on the protocol for optimizing S₀ structures, not only are VEEs spread over a substantially wider range (up to 0.75 eV) but so are vertical ΔE_S1T1 gaps (up to 0.30 eV), leading to cases where, with different S₀ structures, one obtains positive vertical ΔE_S1T1 gaps or significantly negative gaps. We relate this behavior to the introduction of significant asymmetry and bond-length variations in the cyclazine derivatives, formed by ligand functionalization or modification of the cyclazine core. On a more positive note, adiabatic EEs (AEEs) and adiabatic ΔE_S1T1 gaps display significantly lower sensitivity (7–30× less) to the geometry optimization protocols than their vertical analogs. Crucially, for cyclazine, the M06-HF functional with 100% non-local exchange provides the closest S₀ geometry to available CCSD(T) data. We show that this effect exists also for other frameworks (e.g., azulene, pentaazaphenalene, and non-alternant polycyclic hydrocarbons) that have been considered for the INVEST property, with VEEs spread over a broader range of up to 1.19 eV and vertical ΔE_S1T1 gaps over a range of 0.62 eV. For INVEST emitters, it is therefore extremely important to judiciously choose the computational protocol for optimizing ground state geometries, in computing VEEs and vertical ΔE_S1T1 gaps.