3.2 Optimized geometries of the triplet excited states

In Ln(III) complexes the so-called “antenna effect” defines their luminescence efficiency and the intramolecular energy transfer from the ligand environment to the central ion.[1-9] At the first stage of photoexcitation process of Ln(III) complexes, singlet excitation is localized on the ligand. The coincidence of the experimental absorption and excitation spectra of Ln(III) complexes with the corresponding spectra of individual ligands,[1-6,43,58,59] as well as numerous experimental and theoretical studies[8,11,22-24]confirm that excited states of Ln(III) complexes are localized on separate ligands. At the next stage, after fast nonradiative relaxation to the local minimum of the lowest singlet state, molecule deactivates either by fluorescence or by intersystem crossing to the nearest triplet state. Then nonradiative relaxation occurs to the local minimum of the lowest triplet state. Finally, the excitation energy transfers to the resonance levels of the Ln(III) ion, which nonradiatively relaxes to the radiative level and emits a photon at a certain wavelength. Structural relaxation of the excited states of Ln(III) complexes is several orders of magnitude faster than energy transfer processes. Therefore, it is necessary to take relaxation into account and optimize the geometry of the excited states.
In recent works,[60-62] advanced DFT and ab initio techniques have been used to numerically evaluate the energy transfer rates constants and demonstrated complex mechanisms of Ln(III) ions’ sensibilization by surrounding ligands. Such mechanisms may include charge transfer states that mainly occur in molecules with electro-donating and electro-accepting units electronically connected via a conjugated skeleton[60] and strongly depend on the solvent polarity. It is still difficult to unambiguously relate the Eu(III) sensitization to the triplet or charge transfer states.
Our previous experimental studies[7-9,30,37,43,56]verified indirect sensitization mechanism in the simulated mesogenic Eu(III) complexes with saturated coordination sphere and did not show the presence of charge transfer excited states. Whereby in the studied complexes prevalent pathway includes intersystem crossing followed by energy transfer from triplet levels of ligands. It is also worth noting that the calculated (not for individual ligand molecules) triplet levels of the ligands in Eu(III) complexes coincide with the experimental values[8,43,44] obtained from the solvent-free phosphorescence spectra of vitrified Gd(III) complexes’ films with the same ligand environment (Table 2).
The energy transfer efficiency and the luminescence quantum yield of Ln(III) complex are determined by the relative positions of the excited states of ligands and the Ln(III) ion. As was mentioned earlier, the greatest contribution to this process is made by the triplet levels of ligands. Therefore, on the next stage of the work the equilibrium geometries of the studied Eu(III) complexes in the ground state were used as the starting point for the calculations of the triplet excited states. According to our previous studies and literature data[8,11,22-24] the excited states of Ln(III) complexes are localized on individual ligands. This statement can be also confirmed by the coincidence of the experimental absorption and excitation spectra of Ln(III) complexes with the corresponding spectra of individual ligands.[1-6,44,58,59]
Optimization of the geometries of the triplet excited states led to corresponding minima and localization of excitation on individual ligands. It was found that the first three triplet excited states are localized on β-diketones, and the last state - on the Lewis base. The average structural parameters of the studied Eu(III) complexes in the optimized geometries of their triplet excited states are presented in Table 1. Figures 3 and 4 show the optimized structures of Eu(CPDK3-5)3Bpy17-17 and Eu(CPDK3­5)3Phen complexes in their ground and triplet excited states with triplet localization on β­diketone CPDK3-5 and Lewis base. Optimized geometries of other complexes can be found in the Supporting Information (Figure S1).
TABLE 2 Vertical energies (ΔE) in Eu(III) complexes and VDP characteristics in the optimized ground-state (S0) and triplet (T1) geometries with the reference of the excited state localization on separate ligands, intramolecular energy transfer (WET) and back-transfer (WBT) rates, theoretical and experimental values of quantum yields (Q)