First-Principles Calculations of Excited-State Decay Rate Constants in Organic Fluorophores

Excellent ratiometric two-photon fluorescent probes for hydrogen sulfide detection based on the fluorescence resonance energy transfer mechanism

“…It was reported that for relatively bright transitions ( k r > 10 7 s −1 ), the HT effects have a small impact (<10%) on the radiative rate and can essentially be neglected for bright fluorophores ( k r > 10 8 s −1 ). 53,66 To calculate the ISC rates, two different ISC channels S 1 → T 1 and S 1 → T 2 were taken into account (Fig. 5).…”

“…In cases where the SOC is extremely low, the vibrationally induced SOCs and/or spin-vibronic SOCs 68 could contribute significantly. 53,69 Therefore, the HT-like vibrational SOCs were included in the ISC rate calculations for the transitions with small SOCs (<5 cm −1 ).…”

“…In addition, molecules with flexible groups, such as methyl groups, are more prone to anharmonic motions. 53 Moreover, when the energy gap between electronic states is large, the highly excited vibrational states are likely to deviate from harmonic oscillator eigenfunctions. Therefore, it is important to systematically investigate the reliability of the harmonic approximation in these substituted derivatives.…”

“…k isc for an S i → T f transition is given by 53 where Ĥ SO is the spin–orbit coupling (SOC) operator.…”

“…k r and k ic rates were calculated using the MOMAP program, 58–60 while the k isc rate was computed using the ORCA 4.2.1 program. 61,62 The Herzberg Teller (HT)-like vibrational SOC 53 was included, and the obtained rate of k isc was the summation of three spin substate contributions. The electron transition characteristics were analyzed using the Multiwfn program.…”