Spin–Vibronic Coupling From Higher-Lying Triplets is Crucial for Intersystem Crossing and Room-Temperature Phosphorescence

Abstract

Achieving highly efficient purely organic room-temperature phosphorescence (RTP) remains a formidable challenge due to inherently weak spin–orbit coupling and slow intersystem crossing (ISC) between the singlet and triplet manifolds. To address this limitation, the involvement of higher-lying triplet states (T_n)—either through direct ISC (S₁→T_n→T₁) or indirect nonadiabatic spin–vibronic coupling (NA-SVC) enhanced ISC (T_n mediates S₁→T₁ without being populated)—has emerged as a powerful strategy to facilitate triplet harvesting. However, it remains unclear exactly how T_n participates in these two distinct pathways, and under which conditions one pathway dominates over the other. To address these questions, we develop a theoretical framework integrating the time-dependent generating function (TD-GF) algorithm with the multilayer energy-based fragment (MLEBF) method, enabling evaluation of NA-SVC contributions to ISC rate constants in the crystalline phase at the full quantum mechanical (QM) level. This computational protocol is applied to elucidate the competing ISC pathways in a series of carbazole derivatives (BeCbz, AcCbz, and PhCbz) in solution and crystalline phases. Quantitative evaluations reveal that the superior RTP performance of BeCbz is decisively governed by a direct, T₂-mediated S₁→T₂→T₁ pathway. Moreover, the significant NA-SVC enhancement drives an ultrafast S₁→T₂ ISC that effectively outcompetes fluorescence. In contrast, AcCbz primarily utilizes a direct spin–orbit coupling (DSO)-dominated S₁→T₁ pathway, whereas PhCbz exhibits solely fluorescence due to severely hindered ISC channels. Overall, this study demonstrates that explicit full QM modeling of environmental effects and NA-SVC is of great importance, providing a rigorous predictive tool for the rational design of high-performance organic phosphors.

Keywords

excited stated calculations / intersystem crossing / room-temperature phosphorescence / spin–vibronic coupling

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