Charge-Transfer States and Their Description

Work with Andreas Dreuw, John Herbert, Lukas Kunze, and Thomas Froitzheim

These projects emerged from my Master's and PhD theses, in which I studied a charged molecule's photochemical reactivity (light-triggered CO2-release) in solution. However, this left me frustrated: Virtually no software could carry out excited-state calculations in the presence of a solvent, particularly for long solvent-equilibrated states. In general, you want to be able to describe equilibrium and non-equilibrium regimes of solvation (>> 1 ps and << 1 ps, respectively). While the environment can strongly influence polar molecules' absorption, emission, and photochemistry, it becomes decisive as soon as charge-transfer states are involved. To have an accurate model for CT states and to overcome this limitation, I decided to develop and implement a versatile state-specific polarizable-continuum-solvation model (SS-PCM) for excited states, which became the major project of my PhD (here and here).

I interfaced the SS-PCM not only with ADC (Algebraic-Diagrammatic Construction, a wavefunction-based excited-state method) developed in the group of Andreas Dreuw, but also to TD-DFT and some functionality also for EOM-CCSD, all of which are available in the Q-Chem software. For testing purposes, I applied it to various interesting systems, often with charge-transfer states such as nitrobenzene derivatives and dimethylamino-benzonitrile (DMABN), whose solvatochromism was accurately predicted (MAD <0.05 eV). I even entered an actual lab and recorded some missing experimental reference data. These projects pushed me towards organic light-emitting diode (OLED) materials and, specifically, thermally-activated delayed fluorescence (TADF), where change-transfer (CT) states and the molecular environment play important roles.

Eventually, I employed the ADC/SS-PCM approach as a reference to test another - more efficient - SCF-based approach for the description of CT states (here) to be able to treat much larger molecules. Later, in a project with PhD student Lukas Kunze, we combined the maximum-overlap method (MOM) and restricted open-shell Kohn-Sham (ROKS) with state-of-the-art density functionals (optimally-tuned range-separated hybrids) with a PCM solvation model. A key aspect of this approach is that CT states are technically obtained as the Kohn-Sham ground state, which avoids many pitfalls of TDDFT and the available solvation models like LR-PCM. The most recent publication impressively demonstrates this by accurately recovering experimental singlet-triplet energy splittings with sub-kcal/mol precision (MAD 0.02-0.05 eV depending on the functional and method).

Next, we tried to formulate TD-DFT-based approach that yields similarly accurate singlet-triplet gaps for STAGBS27, though with mixed success: no physically sound TD-DFT prediction gets even close to ROKS/PCM, no matter which solvent models and/or (optimal)-tuning protocols are applied. Combining proper solvent models like SS-PCM equilibrium solvation and optimally-tuned range-separated functionals yields an okay agreement with the experiment (MAD of about 0.10 eV instead of 0.02 eV for ROKS/PCM, but with many large deviations, see below). Still, it is not nearly as good as ROKS/PCM. Further, lowering the error requires making physically questionable choices and relying heavily on error compensation. For example, with ground-state geometries and functionals with a very low amount of Fock Exchange (about 10%), the MAD moves into 0.05 eV territory. Still, excitation/emission energies are much too low (by as much as 1 eV).

Currently, we are testing high-level approaches like ADC(2)/SS-PCM, DFT-MRCI, and delta-SCF combined with post-HF correlation treatments on the STGABS27 set. The first results nicely agree with ROKS/PCM, specifically for SCS-ADC(2)/SS-PCM: This method reproduces even the outliers observed with ROKS/PCM and generally agrees to within 0.02 eV. The same holds for delta-CCSD/PCM, which is only possible for the smallest systems.