Why the lowest electronic excitations of rhodamines are overestimated by time-dependent density functional theory

Rhodamines are widely used as laser dyes and fluorescent probes due to their excellent photophysical and photochemical properties. Previous theoretical studies have shown that the lowest excitation energies of rhodamines are overestimated systematically by time-dependent density functional theory (TDDFT). In this study, we first perform a TDDFT benchmark study with 21 exchange-correlation functionals (XCFs) on a series of rhodamines and assess the performance of different types of functional in predicting the lowest excitation energies of rhodamines. Statistical results reveal that the fraction of Hartree-Fock exchange (HFX) included in the XCF is a key parameter. Pure functionals without HFX offer the best performance, with the mean absolute error (MAE) of approximately 0.1 eV. However, they provide a wrong order of the lowest n pi* and pi pi* states and suffer from charge-transfer contamination problem for rhodamine dyes (RDs) in zwitterionic form. Among the other tested functionals, popular global hybrid functional B3LYP delivers the smallest MAE of 0.36 eV. We then perform calculations with second-order algebraic diagrammatic construction and extended multiconfiguration quasi-degenerate perturbation theory at second-order of PT expansion methods. Remarkably accurate results are obtained. We confirm that the reason for the overestimation of the lowest excitation energies of RDs by TDDFT method should be similar to that of cyanine dyes, and that double excitations contribute to this systematic deviation.