Charge-Transfer States and ΔDFT

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

These projects emerged from my Master’s and PhD theses, during which I investigated the photochemical reactivity of charged molecules in solution—for example, the light‑triggered release of CO₂. One major frustration was that virtually no software could perform excited‑state calculations in the presence of a solvent, particularly for long solvent‑equilibrated states (≫1 ps versus ≪1 ps). In many systems, the environment strongly influences the absorption, emission, and photochemistry of polar molecules; this influence becomes decisive when charge‑transfer (CT) states are involved. To overcome these challenges and achieve an accurate model for CT states, I developed and implemented a versatile state‑specific polarizable‑continuum solvation model (SS‑PCM) for excited states (here and here).

I interfaced the SS‑PCM not only with ADC—a wavefunction‑based excited‑state method developed in Andreas Dreuw’s group—but also with TD‑DFT and even some EOM‑CCSD functionality available in Q‑Chem. For testing purposes, I applied the method to a variety of interesting systems—often those with pronounced CT character such as nitrobenzene derivatives and dimethylamino‑benzonitrile (DMABN)—and the predicted solvatochromism agreed with experiment to within a mean absolute deviation of less than 0.05 eV. I even visited a laboratory to record some missing experimental reference data. These projects naturally pushed me toward the field of organic light‑emitting diode (OLED) materials and, in particular, toward thermally activated delayed fluorescence (TADF), where CT states and the molecular environment play crucial roles.

Later in Bonn, in a project with PhD student Lukas Kunze, we combined the maximum‑overlap method (MOM) with restricted open‑shell Kohn–Sham (ROKS) theory using state‑of‑the‑art density functionals (optimally tuned range‑separated hybrids) together with a PCM solvation model. A key advantage of this approach is that CT states are obtained essentially as the Kohn–Sham ground state, thereby avoiding many of the pitfalls of TD‑DFT and of available solvation models like LR‑PCM. Our most recent publication impressively demonstrates that experimental singlet–triplet energy splittings can be recovered with sub‑kcal/mol precision (MAD 0.02–0.05 eV, depending on the functional and method).

Next, we tried to formulate a 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 the performance of ROKS/PCM, no matter which solvent models or (optimal) tuning protocols are applied. Combining proper solvent models like SS‑PCM equilibrium solvation with optimally tuned range‑separated functionals produces only an okay agreement with experiment (MAD of about 0.10 eV instead of 0.02 eV for ROKS/PCM, albeit with many large deviations). Further lowering the error requires making physically questionable choices and relying heavily on error compensation. For example, using ground‑state geometries together with functionals that have an extremely low amount of Fock exchange (about 10%) reduces the MAD to around 0.05 eV, yet the excitation and emission energies are then too low—by as much as 1 eV.

Currently, we are testing high‑level approaches such as ADC(2)/SS‑PCM, DFT‑MRCI, and delta‑SCF combined with post‑HF correlation treatments on the STGABS27 set. The first results agree nicely with those from ROKS/PCM; specifically, SCS‑ADC(2)/SS‑PCM reproduces even the outliers observed with ROKS/PCM and generally agrees with experimental values to within 0.02 eV. A similar performance is observed for delta‑CCSD/PCM, although this level of theory is feasible only for the smallest systems. In our latest work, we extended the scope of the ΔUKS approach by applying a recently refined variant—ΔUKS combined with FX200‑wPBE and a polarizable continuum model (PCM)—to systems with inverted singlet–triplet gaps (INVEST) as well as to multi‑resonant TADF (MR‑TADF) emitters. In these studies, the ΔUKS/FX200‑wPBE/PCM methodology not only captures the subtle balance between orbital relaxation and dynamic spin polarization but also reproduces experimental energy splittings with chemical accuracy. The approach’s inherent efficiency and robust error‑cancellation allow us to reliably describe even those systems where standard TD‑DFT fails due to the absence of double excitations.

Moreover, the versatility of this SCF‑based method is underscored by its performance across different families of organic emitters. Whether dealing with INVEST molecules—where the inversion of the singlet and triplet states challenges conventional theoretical methods—or with MR‑TADF emitters that demand a delicate treatment of short‑range charge‑transfer character, the ΔUKS/FX200‑wPBE/PCM strategy proves remarkably general. This opens up new avenues not only for detailed studies of excitonic properties in advanced OLED materials but also for high‑throughput computational screenings aimed at designing next‑generation organic electronic devices.