Predicting Excitation Energies of Twisted Intramolecular Charge-Transfer States with 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 solvents representing a broad range of polarities, which involve intramolecular charge-transfer mediated by a non-zero, “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 non-empirical 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). The performance of polarizable continuum solvation models for these charge-transfer excited states is closely examined, and clear trends emerge when measurements corresponding to the four small 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 wellseparated 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 linear-response TDDFT 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.