The influence of spin–orbit coupling, Duschinsky rotation and displacement vector on the rate of intersystem crossing of benzophenone and its fused analog fluorenone: a time dependent correlation function based approach

Abstract

To understand the effect of structural rigidity or flexibility on the intersystem crossing rate, herein we have adopted time dependent correlation function based approach, an exact method for harmonic oscillator...

Expanding the Knowledge of the Selective-Sensing Mechanism of Nitro Compounds by Luminescent Terbium Metal–Organic Frameworks through Multiconfigurational ab Initio Calculations

“… , In terms of the population of the T 1 electronic state, the radiative deactivation channel of the S 1 electronic state via the fluorescence mechanism is an unfavorable process . In this way, in comparison to a radiative deactivation processes such as fluorescence, an efficient antenna requires a quick ISC channel S 1 → T 1 . , Thus, the calculated rate constants for the fluorescence and ISC process are crucial to support the hypothesis of the efficient T 1 state population via the ISC channel. , In this sense, the analysis of the BTTA antenna excited state dynamic parameters indicates that the rate of nonradiative ISC channels S 1 → T 1 is 3.22 × 10 8 s –1 . This result shows that the k ISC (S 1 → T 1 ) value is 1 order of magnitude bigger than the k F rate, k F (S 1 → S 0 ) = 7.72 × 10 7 s –1 ; see Figure .…”

“…76,80 Thus, the calculated rate constants for the fluorescence and ISC process are crucial to support the hypothesis of the efficient T 1 state population via the ISC channel. 84,85 In this sense, the analysis of the BTTA antenna excited state dynamic parameters indicates that the rate of nonradiative ISC channels S 1 → T 1 is 3.22 × 10 8 s −1 . This result shows that the k ISC (S 1 → T 1 ) value is 1 order of magnitude bigger than the k F rate, k F (S 1 → S 0 ) = 7.72 × 10 7 s −1 ; see Figure 2.…”

Demystifying the Origin of Vibrational Coherence Transfer Between the S1 and T1 States of the Pt-pop Complex

“…Etinski, Tatchen, and Marian have derived three distinct formulas for the evaluation of the intersystem crossing rate constant ( k ISC ). Recently, Karak and Chakrabarti simplified their TDCF method considering only the direct SOC in the evaluation of k ISC . However, it is worth noting that if the direct SOC between the singlet and the triplet states is very small, it is necessary to go beyond the Franck–Condon regime, i.e., to include spin-vibronic contributions to the ISC rate in order to obtain meaningful results.…”

“…The expression for b is where Q denotes the dimensionless normal coordinates, and q 0 is the coordinate of the equilibrium geometry of the initial state. In addition, J and D indicate the Duschinsky rotation matrix − and displacement vector, respectively, which are connected through the relation Q T = JQ S + D , where Q S and Q T are the dimensionless normal coordinates of the singlet and triplet electronic states, respectively. Z = ∑ i e – βE i is the vibrational partition function of the initial electronic state and , where E i , T , and k represent the energy of the i th vibrational level, temperature, and Boltzmann constant, respectively.…”

“…In our present approach, after separating eqs and into real and imaginary parts, we have considered only the real part for the calculation of k ISC since the imaginary part is an odd function of time. The separation of the k ISC DSO part at the finite temperature region has already been presented by Karak and Chakrabarti, whereas the details of the simplified equation we arrive at after separation of k ISC SV is provided in the Supporting Information. Moreover, the derivative coupling term is evaluated numerically using a finite vector differentiation technique, the corresponding formula given as In the above equation, Q represents dimensionless coordinates of the respective normal mode, and δ denotes the displacement from the equilibrium geometry ( q 0 ) along a particular direction of Q .…”