Computational Approach to Investigate Structure-Property Relationship of a series of Carbazole Containing Thermally Activated Delayed Fluorescent Molecules

Donor-acceptor type compounds are an important category of organic materials that show properties suitable for light emission applications. To achieve a full understanding of the mechanism of thermally activated delayed fluorescence (TADF) process, we studied the structure-property relationship for a series of carbazole based TADF emitters, 2CzPN, 4CzPN, 4CzIPN, 4CzBN and 5CzBN. We applied density functional theory to investigate kinetic and electronic properties. We find that the energetic position of triplet excited state of these emitters depends on their molecular structure. Our findings emphasize that to enable reverse intersystem crossing and eventually TADF, strong spin orbit coupling and minimal energy difference between singlet and triplet states $ΔE_{ST}$ must be obtained simultaneously. We also find that the reverse intersystem crossing rates $k_{RISC}$ values are higher where $ΔE_{ST}$ values are closer to reorganization energy. Furthermore, a small change in the absorption peak of optical absorption spectra with and without spin orbit coupling (SOC) is observed for each emitter. This result is extremely beneficial for the design of new TADF molecules, and we believe that our work contributes to the progress of future development of high-performance organic molecular light-emitting devices.

💡 Research Summary

In this work, the authors performed a comprehensive computational investigation of five carbazole‑based thermally activated delayed fluorescence (TADF) emitters—2CzPN, 4CzPN, 4CzIPN, 4CzBN and 5CzBN—to elucidate the structure‑property relationships governing their photophysical performance. Geometry optimizations were carried out with Gaussian 16 using the B3LYP functional and the DEF2‑SVP basis set, revealing that all molecules adopt highly twisted donor‑acceptor conformations with dihedral angles between 118° and 127°. This twist leads to a clear spatial separation of the highest occupied molecular orbital (HOMO), localized on the carbazole donor units, and the lowest unoccupied molecular orbital (LUMO), localized on the benzonitrile or dicyanobenzene acceptor cores. The calculated HOMO‑LUMO gaps range from 3.09 eV (4CzBN) to 3.48 eV (4CzPN), indicating that the electronic structures are conducive to small singlet‑triplet energy gaps (ΔE_ST) essential for efficient reverse intersystem crossing (RISC).

Excited‑state calculations were performed with ORCA using time‑dependent DFT (TD‑DFT) at the ZORA‑DEF2‑TZVP level, including solvent effects (methyl chloride). The authors obtained the energies of the lowest singlet (S₁, S₂) and triplet (T₁, T₂, T₃) states and evaluated spin‑orbit coupling matrix elements (SOCME) between S₁ and T₁. 4CzIPN exhibits the smallest ΔE_ST (0.12 eV) and a moderate SOCME (0.22 cm⁻¹), while 5CzBN shows the largest SOCME (0.99 cm⁻¹) due to the higher number of nitrogen atoms. The presence of multiple triplet states below S₁ for the four‑carbazole derivatives (4CzBN, 4CzIPN, 4CzPN) versus a single or three triplet states for 2CzPN and 5CzBN underscores a clear structure‑dependent excited‑state landscape.

RISC rate constants (k_RISC) were estimated using the Marcus‑Hush formalism, which incorporates the SOCME, the reorganization energy (λ), and the thermal energy at 300 K. Two λ values (0.1 eV and 0.2 eV) were considered, reflecting typical ranges for purely organic molecules. The calculations reveal that k_RISC is maximized when ΔE_ST is comparable to λ. Accordingly, 4CzIPN shows the highest k_RISC (1.38 × 10⁵ s⁻¹) for λ = 0.1 eV, whereas for λ = 0.2 eV, 4CzPN, 5CzBN and 2CzPN display relatively larger rates because their ΔE_ST values (0.18–0.26 eV) match the larger reorganization energy. The authors also examined temperature dependence, finding that 4CzIPN’s k_RISC strongly increases with temperature, consistent with Marcus theory, while 2CzPN shows negligible temperature sensitivity, indicating non‑TADF behavior.

A key structural insight emerges from comparing donor‑acceptor (D‑A) versus donor‑acceptor‑donor (D‑A‑D) architectures. The D‑A‑D molecules (4CzIPN, 4CzBN, 5CzBN) consistently exhibit larger dihedral angles, stronger HOMO‑LUMO separation, and higher RISC rates than the D‑A counterparts (2CzPN, 4CzPN). This aligns with previous experimental observations that orthogonal D‑A arrangements facilitate small ΔE_ST and enhance spin‑orbit mixing.

In conclusion, the study identifies three synergistic criteria for designing high‑performance TADF emitters: (i) strong spin‑orbit coupling (achieved by incorporating heavier atoms such as nitrogen), (ii) a narrow singlet‑triplet gap, and (iii) a reorganization energy that closely matches ΔE_ST. Meeting all three simultaneously yields rapid RISC, which is essential for near‑unity internal quantum efficiencies in OLEDs. The computational framework presented provides a predictive tool for rationally engineering next‑generation organic light‑emitting materials.