Addressing vibronic phosphorescence and associated excited state dynamics of anti-Kasha molecules: a time-dependent correlation function approach

Abstract

Single-molecule white-light emitters (SMWLEs) based on anti-Kasha dual emission present a promising route to simplified fabrication, but their design is constrained by the complex interplay of electronic and vibronic interactions that control emission from higher triplet states. Here we investigate the origin of vibrationally resolved phosphorescence spectra and the photophysics of the excited states of two molecules, namely, dibenzo[a,c]phenazine (DPPZ) and dibenzo[b,d]thiophen-2-yl (4-chlorophenyl)-methanone (ClBDBT), acting as SMWLEs. In this work, we present the efficacy of the present standalone code for simulating the vibronic phosphorescence spectra and elucidate the anti-Kasha behavior of the studied molecules by examining various nonradiative rate processes. For both molecules, we computed the phosphorescence spectra, intersystem crossing (ISC), and internal conversion (IC) rate constants employing the same theoretical framework of time-dependent correlation functions. In DPPZ, it is observed that, despite the small energy gap between the S₁ and the T₂ states, the vanishingly small spin–orbit coupling matrix element (SOCME) between these states precludes the much expected population transfer to the T₂ states through the direct ISC mechanism. Interestingly, we find that the inclusion of the vibrational spin–orbit (VSO) coupling or the Herzberg–Teller (HT) term facilitates the rate of ISC between the S₁ T₂ pathway significantly compared to that of S₁ T₁, which indeed helps break Kasha's rule. Additionally, the population gain via a fast T₂ T₁ internal conversion opens the channel for T₁ → S₀ phosphorescence as well. On the other hand, a significantly higher direct spin–orbit coupling matrix element between S₁ and T₂ of ClBDBT, compared to S₁–T₁ along with a large T₂–T₁ energy gap, leads to S₁ T₂ as the dominant pathway for population transfer that eventually helps achieve anti-Kasha phosphorescence from T₂. In brief, the present work provides the theoretical origin of the vibrational progression in the phosphorescence spectra and sheds light on the genesis of white light emission from the studied anti-Kasha emitters.