Partial Density of States Ligand Field Theory (PDOS-LFT): Recovering a LFT-Like Picture and Application to Photoproperties of Ruthenium(II) Polypyridine Complexes

摘要

Gas phase density-functional theory (DFT) and time-dependent DFT (TD-DFT)calculations are reported for a data base of 98 ruthenium(II) polypyridinecomplexes. Comparison with X-ray crystal geometries and with experimentalabsorption spectra measured in solution show an excellent linear correlationwith the results of the gas phase calculations. Comparing this with the usualchemical understanding based upon ligand field theory (LFT) is complicated bythe large number of molecular orbitals present and especially by the heavymixing of the antibonding metal e*$_{g}$ orbitals with ligand orbitals.Nevertheless, we show that a deeper understanding can be obtained by a partialdensity-of-states (PDOS) analysis which allows us to extract approximate metalt$_{2g}$ and e*$_{g}$ and ligand \pi* orbital energies in a well-defined way,thus providing a PDOS analogue of LFT (PDOS-LFT). Not only do PDOS-LFT energiesgenerate a spectrochemical series for the ligands, but orbital energydifferences provide good estimates of TD-DFT absorption energies. Encouraged bythis success, we use frontier-molecular-orbital-theory-like reasoning toconstruct a model which allows us in most, but not all, of the cases studied touse PDOS-LFT energies to provide a semiquantitative relationship betweenluminescence lifetimes at room temperature and liquid nitrogen temperature.