Spin-forbidden transitions of a conjugated polymer repeat unit

Explanation of TR-EPR experiments

Time-resolved electron paramagnetic resonance (TR-EPR) is an important experimental probe of the dynamics of excited triplet states that are often involved in molecular and biomolecular photo-excited exciton transport processes. A surprising experimental observation in an organic molecule with low spin-orbit (SOC) coupling (the repeat unit of a PCDTBT polymer) is that similar triplet (TR-EPR) signals are detected when the molecule is photo-excited in the absorbing and non-absorbing regions of its spectrum [D. L. Meyer, F. Lombeck, S. Huettner, M. Sommer and T. Biskup, J. Phys. Chem. Lett. 8, 1677 (2017)].

In a recently published JCP article, Mavrommati and Skourtis at the University of Cyprus explained this paradox by performing relativistic and non-relativistic quantum-chemical computations using ADF, coupled with theoretical models. The authors computed the population transfer to the triplet states from the singlet ground state (via direct excitation) and from the photo-excited singlet state (via intersystem crossing (ISC)). Their results demonstrate that, due to the low ISC rates, the intensities of the TR-EPR spectra are almost exclusively determined by the initial triplet populations formed upon direct photo-excitation inside and below the absorption band.

The article describes relativistic TD-DFT computations of the vertical singlet-to-singlet and singlet-to-triplet transition energies and the related oscillator strengths and molar extinction coefficients (by means of the scalar relativistic ZORA Hamiltonian where the SOC is applied as a perturbation). The absorption coefficients are used to estimate the initial number of photo-excited molecules in the singlet and triplet states. ISC rates between the photo-excited singlet state (S₁^SOC) and the triplets (T_n^SOC, n=1,2) are calculated utilizing quantum nonadiabatic rate theory with ab-initio values for the energy and coupling ISC-rate parameters. In particular, geometry optimizations and normal-mode calculations of the singlet and triplet excited states are used in the FCF auxiliary program to extract the reorganization energies of all normal modes (needed for the computation of all Frank-Condon factors). The other ISC-rate parameters are the minimum Born-Oppenheimer energies of the initial and final excited states (obtained from the geometry optimizations) and the electronic couplings between these states (obtained from the SOC computations). In addition, the quality of the excited-state-energy calculations (with respect to DFT functional choice) is tested by examining the charge-transfer characteristics of the lowest-lying excited states of the molecule using the diagnostic overlap quantity Λ and the hole-electron distance Δr [M. J. G. Peach, P. Benfield, T. Helgaker and D. Tozer, J. Chem. Phys. 128, 044118 (2008) and C. A Guido, P. Cortona, B. Mennucci and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)].

For SOC integral calculations see also the advanced tutorials:
Optimizing TADF emission
Phosphorescent lifetimes of OLED emitters

For the ISC reorganization energies see also:
Vibrational progression of an OLED emitter
Manual: Vibrationally resolved spectra

Example input files are available.

S. A. Mavrommati and S. S. Skourtis, “Initial-state preparation effects in time-resolved electron paramagnetic resonance experiments”, J. Chem. Phys. 152, 044304 (2020).