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.