Predicting Excitation Energies of Twisted Intramolecular Charge-Transfer States with the Time-Dependent Density Functional Theory: Comparison with Experimental Measurements in the Gas Phase and Solvents Ranging from Hexanes to Acetonitrile

Electronically excited states characterized by intramolecular charge transfer play an essential role in many biological processes and optical devices. The ability to make quantitative ab initio predictions of the relative energetics involved is a challenging yet desirable goal, especially for large molecules in solution. In this work, we present a data set of 61 experimental measurements of absorption and emission processes, both in the gas phase and in solvents representing a broad range of polarities, which involve intramolecular charge transfer mediated by a nonzero, “twisted” dihedral angle between one or more donor and acceptor subunits. Among a variety of density functionals investigated within the framework of linear-response theory, the “optimally tuned” LRC-ωPBE functional, which utilizes a system-specific yet nonempirical procedure to specify the range-separation parameter, emerges as the preferred choice. For the entire set of excitation energies, involving changes in dipole moment ranging from 4 to >20 Debye, the mean signed and absolute errors are 0.02 and 0.18 eV, respectively (compared, e.g., to −0.30 and 0.30 for PBE0, 0.44 and 0.47 for LRC-ωPBEh, 0.83 and 0.83 for ωB97X-V). We analyze the performance of polarizable continuum solvation models available in Q-Chem that partition the solvent response into fast and slow time scales, and clear trends emerge when measurements corresponding to the four small 4-(dimethylamino)­benzonitrile (DMABN)-like molecules and a charged species are excluded. We make the case that the large errors found only for small molecules in the gas phase and weak solvents cannot be expected to improve via the optimal tuning procedure, which enforces a condition that is exact only in the well-separated donor–acceptor limit, and present empirical evidence implicating the outsized importance for small donor–acceptor systems of relaxation effects that cannot be accounted for by the linear-response time-dependent density functional theory within the adiabatic approximation. Finally, we demonstrate the utility of the optimally tuned density functional approach by targeting the charge-transfer states of a large biomimetic model system for light-harvesting structures in Photosystem II.

以分子内电荷转移 (intramolecular charge transfer) 为特征的电子激发态，在诸多生物过程与光电器件中发挥着至关重要的作用。对相关相对能量开展定量从头算（ab initio）预测，是一项极具挑战性却又极具价值的目标，对于溶液中的大分子而言更是如此。本研究构建了包含61组实验测量数据的数据集，涵盖气相与多种极性范围溶剂中的吸收与发射过程，这些过程涉及由一个或多个供体与受体亚基间非零的“扭转”二面角介导的分子内电荷转移。在线性响应理论 (linear-response theory) 框架下考察的多种密度泛函 (density functionals) 中，采用体系专属而非经验性流程来指定长程分离参数 (range-separation parameter) 的“优化调谐”LRC-ωPBE泛函脱颖而出，成为最优选择。针对全部激发能数据集（涉及偶极矩变化范围为4至>20德拜 (Debye)），其平均符号误差与平均绝对误差分别为0.02 eV与0.18 eV（例如，对比PBE0的-0.30 eV与0.30 eV、LRC-ωPBEh的0.44 eV与0.47 eV、ωB97X-V的0.83 eV与0.83 eV）。我们分析了Q-Chem中可将溶剂响应划分为快、慢时间尺度的可极化连续介质溶剂化模型 (polarizable continuum solvation models) 的性能，当排除4个类4-(二甲氨基)苯甲腈 (4-(dimethylamino)benzonitrile, DMABN) 小分子与1个带电物种的测量数据后，清晰的性能趋势得以显现。我们指出，仅在气相与弱极性溶剂中的小分子上观测到的较大误差，无法通过优化调谐流程得到改善——该流程仅在供体与受体充分分离的极限下才满足严格的精确条件——同时我们提供了经验证据，表明对于小型供体-受体体系，那些无法被绝热近似下的线性响应含时密度泛函理论所解释的弛豫效应，具有超乎寻常的重要性。最后，我们以光系统II (Photosystem II) 捕光结构的大型仿生模型体系的电荷转移态为研究对象，验证了优化调谐密度泛函方法的实用性。