Читать книгу Handbook of Aggregation-Induced Emission, Volume 1 - Группа авторов - Страница 31

The radiative decay rate constant (k_r) and nonradiative decay rate constant (k_nr = k_ic + k_isc) are decisive parameters for the luminescence quantum efficiency, where k_ic and k_isc are nonradiative internal conversion (IC) and intersystem crossing (ISC) rate constants, respectively. In most organic molecules, k_isc can be neglected owing to the small spin−orbit coupling for the π → π* electronic transition; therefore, k_nr ≈ k_ic.

The k_r was computed by integrating over the whole emission spectrum:

(2.1)

(2.2)

where P_iν is the Boltzmann distribution function of the initial state at a certain temperature, Θ is the nuclear vibrational wave function, and is the electric transition dipole moment between two electronic states.

Based on the FGR, the nonradiative IC constant can be written as [23]:

(2.3)

where E_iv(E_fu) reflects the electronic and vibrational energies of the initial (final) state, and represents the non‐Born–Oppenheimer coupling.

Based on the Franck–Condon principle, applying Fourier transform of the δ‐function, Equation 2.3 can be written as [24, 25]:

(2.4)

where is the nonadiabatic electronic coupling and ρ_IC(t, T) is the thermal vibration correlation function (TVCF) [10–12]

(2.5)

As shown in Equation 2.4, k_IC is mainly ruled by three factors: nonadiabatic electronic coupling, transition energy, and the vibronic relaxation energy. Based on the electronic structure information obtained from first‐principle calculations, the radiative and nonradiative rate constants were calculated by solving Equations 2.1 and 2.3 through the TVCF rate theory in the MOMAP program [26]. The difference between the PESs of two electronic states is considered by Q_i = SQ_f + D, where S is the Duschinsky rotation matrix and D is the displacement vector, that is, Duschinsky rotation effect (DRE) [13, 14].