Excitation Energies of Metal Complexes with Time-dependent Density Functional Theory

After a brief introduction to the theory of time-dependent density functional theory (TDDFT), an overview is given of the recent literature on calculations of the electronic absorption spectra of transition-metal complexes. Various types of complexes are treated – organometallic complexes with carbonyl and cyclopentadienyl ligands, oxo and halide complexes (Werner complexes), metal α-diimine complexes and metallotetrapyrroles. The performance of the various GGA and hybrid functionals is discussed, as well as that of special shape-corrected functionals for the Kohn-Sham potential. The TM complexes are outside of the range of molecules for which B3LYP is parameterized, and this functional does not perform better than pure GGAs. The statistical average of the orbital dependent potentials (SAOP) functional for the Kohn-Sham potential appears to perform best. The strong dependence of the excitation energies on metal-ligand distances is stressed. A consequence is that a full assessment of the accuracy of the TDDFT method will have to include a full vibronic interaction treatment. A conservative estimate is that the accuracy of the best TDDFT methods for TM complexes, where errors of several tenths of an eV often occur, is somewhat lower than for simple benchmark molecules like N 2 , CO, and CH 2 O, where errors are often of the order of 0.1–0.2 eV.