Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

Abstract

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S 1 → S 0 transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob’s ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 106–1016 s–1 compared with an experimental rate of the order 107 s–1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

Charge Transfer-Mediated Multi-exciton Mechanisms in Weakly Coupled Perylene Dimers

“…The transition dipole moments across all optimized geometries show that, of the three optimized singlet geometries, only the S 1 state is optically bright, with an average moment of ∼2.87 au found on all geometries. This is slightly smaller than those moments found for perylene in previous works 102 but still larger than expected with respect to experiment. 102,223,224 From these results, we calculate transition dipole moments of μ D = 2.907 au (moment at the S 1 geometry) and μ A = 2.745 au (moment at the S 0 geometry), respectively.…”

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations

“…We employed a set of seven XCFs, representative of the typically selected hybrids in simulations of organic compounds, namely, B3LYP, PBE0, , BH&HLYP, CAM-B3LYP, ωB97, ωB97X, and ωB97X-D . Note that, to our knowledge, no previous systematic XCF benchmarks are available for k r , but for the specific case of perylene …”

“…60 We employed a set of seven XCFs, representative of the typically selected hybrids in simulations of organic compounds, namely, B3LYP, 61 PBE0, 62,63 BH&HLYP, 64 CAM-B3LYP, 65 ωB97, 66 ωB97X, 66 and ωB97X-D. 67 Note that, to our knowledge, no previous systematic XCF benchmarks are available for k r , but for the specific case of perylene. 29 As the experimental data were recorded in aprotic solutions, we used the polarizable continuum model (PCM) 68 to account for solvent−solute interactions at all stages of the electronic structure calculations. For the TD(A)-DFT calculations, the linear-response PCM model was used.…”

“…The current results are, however, more in line with a recent study. 29 Statistical results for the entire cleaned set can be found in Table 3 and Figure 7. If it was previously reported that the inclusion of the HT terms can lead to anomalies when dealing with (very) bright transitions, 46 this problem should be avoided here since the maximum value of the oscillator strength in our set of chromophores is 0.15.…”

“…, k r is very robust with respect to the details of the selected broadening. Another recent study focused on benchmarking non-adiabatic couplings for the internal conversion rates of perylene also reports k r determined with two atomic basis sets and a large panel of XCFs . For that rigid molecule, it was found that all hybrid functionals deliver rather similar radiative rates and that the HT effects (on k r ) are small.…”