Either Accurate Singlet–Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters

The energy gap between the lowest singlet and triplet
excited states
(ΔEST) is a key property of thermally
activated delayed fluorescence (TADF) emitters, where these states
are dominated by charge-transfer (CT) character. Despite its well-known
shortcomings concerning CT states, time-dependent density functional
theory (TD-DFT) is widely used to predict this gap and study TADF.
Moreover, polar CT states exhibit a strong interaction with their
molecular environment, which further complicates their computational
description. Addressing these two major challenges, this work studies
the performance of Tamm–Dancoff-approximated TD-DFT (TDA-DFT)
on the recent STGABS27 benchmark set,1 exploring different
strategies to include orbital and structural relaxation, as well as
dielectric embedding. The results show that the best-performing strategy
is to calculate ΔEST at the ground-state
structure using functionals with a surprisingly small amount of Fock
exchange of ≈10% and without a (complete) solvent model. However,
as this approach heavily relies on error cancellation to mimic dielectric
relaxation, it is not robust and exhibits large systematic deviations
in excited state energies, state characters, and structures. More
rigorous approaches, including state-specific solvation, do not share
these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude
that for the description of CT states in dielectric environments,
none of the tested TDA-DFT methods is competitive with the recently
presented ROKS/PCM approach regarding robustness, accuracy, and computational
efficiency.

最低单重态与三重态激发态间的能级差（ΔEST）是热激活延迟荧光（Thermally Activated Delayed Fluorescence，TADF）发光体的核心属性，这类激发态以电荷转移（Charge Transfer，CT）特性为主导。尽管含时密度泛函理论（Time-Dependent Density Functional Theory，TD-DFT）在处理电荷转移态时存在公认的局限性，但其仍被广泛用于该能级差的预测与热激活延迟荧光材料的研究。此外，极性电荷转移态与其分子环境存在强相互作用，进一步增加了其计算描述的复杂度。针对这两大挑战，本研究在最新的STGABS27基准数据集1上评估了塔姆-唐可夫近似含时密度泛函理论（Tamm–Dancoff-approximated Time-Dependent Density Functional Theory，TDA-DFT）的性能，探索了包含轨道弛豫、结构弛豫以及介电嵌入的多种策略。研究结果表明，表现最优的策略是在基态结构下，采用福克交换（Fock exchange）占比约10%的低交换泛函，且无需（完整）溶剂模型来计算ΔEST。然而，由于该方法严重依赖误差抵消（Error cancellation）以模拟介电弛豫，其鲁棒性较差，且在激发态能量、态特性以及结构方面存在显著的系统性偏差。更为严谨的方法（包括态特异性溶剂化模型）虽无此类系统性偏差，但其预测的ΔEST值却呈现出更大的统计误差。因此我们得出结论：对于介电环境中的电荷转移态描述，所有测试过的TDA-DFT方法在鲁棒性、准确性与计算效率方面，均无法与近期提出的ROKS/PCM方法相媲美。