Failures of TDDFT in describing the lowest intramolecular charge-transfer excitation in para-nitroaniline

We investigate the failure of time-dependent density functional theory (TDDFT) with the CAM-B3LYP exchange-correlation (xc) functional coupled to the polarisable embedding (PE) scheme (PE-CAM-B3LYP) in reproducing the solvatochromic shift of the lowest intense charge-transfer excitation in para-nitroaniline (pNA) in water by comparing with results obtained with the coupled cluster singles and doubles (CCSD) model also coupled to the polarisable embedding scheme (PE-CCSD). We determine the amount of charge separation in the ground and excited charge-transfer state with both methods by calculating the electric dipole moments in the gas phase and for 100 solvent configurations. We find that CAM-B3LYP overestimates the amount of charge separation inherent in the ground state and TDDFT/CAM-B3LYP drastically underestimates this amount in the excited charge-transfer state. As the errors in the solvatochromatic shift are found to be inverse proportional to the change in dipole moment upon excitation, we conclude that the flaws in the description of the solvatochromic shift of this excitation are related to TDDFT itself and how it responds to the solvent effects modelled by the PE scheme. We recommend therefore to benchmark results of TDDFT calculations with CAM-B3LYP for intramolecular charge-transfer excitations in molecular systems similar to pNA against higher level ab initio wave function methods, like, e.g. CCSD, prior to their use. Using the calculated change in dipole moment upon excitation as a measure for charge-transfer character, we furthermore confirm that the difference between excitation energies calculated with TDDFT and with the Tamm-Dancoff approximation (TDA) to TDDFT is indeed correlated with the charge-transfer character of a given electronic transition both in vacuo and in solution. This is supported by a corresponding correlation between the change in dipole moment and the size of the index diagnostic for the investigated CT excitation.