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Understanding the dynamics of photophysical processes in Ln complexes remains challenging due to the intricate nature involving the metallic center, where sensitization (antenna effect) plays a pivotal role. Current studies have often overlooked the vibronic coupling within the antenna effect, leading to incomplete insights into excited-state dynamics. To address these shortcomings, we introduce a novel theoretical and computational approach that leverages the impact of the vibrational modes of the S and T states in this effect through the correlation function formalism, offering a comprehensive view of intersystem crossing (ISC).

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Nonadiabatic quantum-classical mapping approaches have significantly gained in popularity over the past several decades because they have acceptable accuracy while remaining numerically tractable even for large system sizes. In the recent few years, several novel mapping approaches have been developed that display higher accuracy than the traditional Ehrenfest method, linearized semiclassical initial value representation (LSC-IVR), and Poisson bracket mapping equation (PBME) approaches. While various benchmarks have already demonstrated the advantages and limitations of those methods, unified theoretical justifications of their short-time accuracy are still demanded.

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