Why Does the Optimal Tuning Method of the Range Separation Parameter of a Long-Range Corrected Density Functional Fail in Intramolecular Charge Transfer Excitation Calculations?

We performed intra- and intermolecular charge transfer (CT) excitation energy calculations of (a) conjugated carbon chain [H2N-(CH=CH)(n)-X] and (b) its equidistant H2NH center dot center dot center dot HX (n = 2 similar to 8) with various electron acceptors (X = NH2, OH, Cl, CHO, CN, and NO2) using EOM-CCSD, time-dependent (TD) Hartree-Fock (HF) and various density functional theory (DFT) functionals, such as BLYP, B3LYP, long-range corrected (LC) DFT, and LC-DFT with an optimally tuned (OT) range separation parameter (mu) using Koopman's theorem to investigate the effect of the electron-withdrawing (or -donating) strength of end-capped functional group (X) and CT distance (R) on intra- and intermolecular CT excitation energies. As the electron-withdrawing strength of X increases, both intra- and intermolecular CT excitation energies tend to decrease, since energy gaps between orbitals corresponding to CT excitations (e.g., HOMO and LUMO) decrease. However, the effect of the electron-withdrawing group on intramolecular CT excitation energy is negligible (at most 0.5 eV). OT-LC-DFT shows accurate intermolecular CT excitation energy, but worse results in intramolecular CT excitation energy than LC-DFT with the default mu value (0.47). Therefore, we conclude that the optimal tuning method is not effective in predicting intramolecular CT excitation energy. While intermolecular CT excitation energy has excitonic binding energy with asymptotic behavior to CT distance that is not affected by the choice of range separation parameter, intramolecular CT excitation energy is affected by orbital relaxation energy, which strongly depends on the choice of range separation parameter, which makes the OT method of range separation parameter ineffective in predicting intramolecular CT excitation energy as well as local excitation with high accuracy.