PCM-ROKS for the Description of Charge-Transfer States in Solution: Singlet–Triplet Gaps with Chemical Accuracy from Open-Shell Kohn–Sham Reaction-Field Calculations

Abstract

The adiabatic energy gap between the lowest singlet and triplet excited states ΔE ST is a central property of thermally activated delayed fluorescence (TADF) emitters. Since these states are dominated by a charge-transfer character, causing strong orbital-relaxation and environmental effects, an accurate prediction of ΔE ST is very challenging, even with modern quantum-chemical excited-state methods. Addressing this major challenge, we present an approach that combines spin-unrestricted (UKS) and restricted open-shell Kohn–Sham (ROKS) self-consistent field calculations with a polarizable-continuum model and range-separated hybrid functionals. Tests on a new representative benchmark set of 27 TADF emitters with accurately known ΔE ST values termed STGABS27 reveal a robust and unprecedented performance with a mean absolute deviation of only 0.025 eV (∼0.5 kcal/mol) and few deviations greater than 0.05 eV (∼1 kcal/mol), even in electronically challenging cases. Requiring only two geometry optimizations per molecule at the ROKS/UKS level in a compact double-ζ basis, the approach is computationally efficient and can routinely be applied to molecules with more than 100 atoms.

Effective models for TADF: the role of the medium polarizability

“…The dielectric properties of the matrix, its polarity and polarizability affect in different ways LE and CT states, leading to qualitatively different TADF properties in different media and making the comparison with theoretical gas-phase results unreliable. 15,16,[20][21][22][23][24][25][26] The rigidity and viscosity of the medium also play a role, affecting in turn the molecular conformation and flexibility. 25 Different theoretical approaches have been exploited to account for environmental effects in TADF processes.…”

“…25 Different theoretical approaches have been exploited to account for environmental effects in TADF processes. 15,16,[23][24][25][26] They can be classified in two broad families. Continuum models (typically conductor-like screening model (COSMO) and polarizable continuum model (PCM)) describe the environment as a continuum dielectric medium, then loosing all information about the atomistic nature of the matrix, its rigidity and viscosity, but leading to a simple and economic picture for dielectric effects.…”

Eliminating the Reverse ISC Bottleneck of TADF Through Excited State Engineering and Environment‐Tuning Toward State Resonance Leading to Mono‐Exponential Sub‐µs Decay. High OLED External Quantum Efficiency Confirms Efficient Exciton Harvesting

“…Although this approach can only model one state at a time (state-specific) and thus, does not provide transition properties or vertical energies of other states, it is by far more accurate and reliable than typical TD-DFT based approaches. [26,40] Inspection of the state energies given in Table 1 shows good agreement between experiment and theory. Both methods confirm that the energy separation between the 1,3 CT(DA) charge transfer states and the 3 LE(F) state varies strongly from the gas phase environment with ε = 1.0 to toluene (ε = 2.38) and further to chloroform (ε = 4.8).…”

“…Note that these energies are obtained with a state-specific spin-unrestricted Kohn-Sham/polarizable continuum model (UKS/PCM) approach tailored to the description of CT states in solution (see refs. [26,40] for details). Although this approach can only model one state at a time (state-specific) and thus, does not provide transition properties or vertical energies of other states, it is by far more accurate and reliable than typical TD-DFT based approaches.…”

“…To explore the low-lying excited states in more detail, we employ Grimme's PBEh-3c composite method [41] as implemented in the Q-Chem 5.4 software [42] and use time-dependent density functional theory in the Tamm-Dancoff approximation (TDA-DFT) [43] for vertical transition energies and (unrestricted) UKS/PCM to optimize the ground and excited states with full equilibration of the solvent-field (see refs. [26,40] for a detailed discussion and tests).…”