Title: Determination of Triplet State Energy and the Absorption Spectrum for a Lanthanide Complex

Abstract: The usual depiction of energy transfer from an antenna of a lanthanide complex, LnL_{n}, to the lanthanide ion, Ln^{3+}, such as Eu^{3+} or Tb^{3+}, is illustrated by an energy diagram matching the complex and metal ion levels. Other than direct singlet energy transfer (ET), relaxation to the lowest triplet state, T_{1}, may be followed by ET. The determination of the zero phonon line triplet state energy, T_{1}, is thus essential for the rationalization of the ET processes of lanthanide ions. It is also useful to calculate the electronic absorption spectra of lanthanide complexes to pinpoint maximum absorption. The triplet state energy and the energies of absorption bands have not been thoroughly investigated by calculation and compared with experimental results in a critical manner previously. In order to study and provide guidelines on these points, we have made an experimental and theoretical investigation of the energy levels of lanthanide complexes in the solid state and in solution by employing well-characterized compounds. It is found that time dependent–density functional theory (TD-DFT) methods do not provide a good indication of the complex absorption spectrum, but reasonable agreement is achieved from multireference methods or more rapidly from the Zerner’s intermediate neglect of differential overlap (ZINDO/S) semiempirical method for calculating excited states. Although the absorption spectra of the complexes may be similar for different lanthanide ions and may be fairly similar to those of the ligands, the use of a fragment scheme to calculate absorption spectra using TD-DFT is generally not accurate. The major absorption bands correspond to higher energy singlet transitions and the energies of the first singlet and triplet states are not well-predicted by the above methods. The calculation of the triplet zero phonon line energy is best performed by the correction of the adiabatic transition energy by the difference in the zero-point vibrational energy of the ground singlet (S_{0}) and the triplet (T_{1}) states: the ΔSCF (self-consistent field) method. The geometry optimization of the complex in each electronic state followed by confirmatory vibrational frequency calculations is thus required. This study lays down the platform for a more accurate description and understanding of the ET processes of lanthanide ions in organic complexes.