Assessment of TD-DFT and LF-DFT for study of d - d transitions in first row transition metal hexaaqua complexes

Herein, we present the systematic, comparative computational study of the d - d transitions in a series of first row transition metal hexaaqua complexes, [M(H2O)6](n+) (M(2+/3+) = V (2+/3+), Cr(2+/3+), Mn(2+/3+), Fe(2+/3+), Co(2+/3+), Ni(2+)) by the means of Time-dependent Density Functional Theory (TD-DFT) and Ligand Field Density Functional Theory (LF-DFT). Influence of various exchange-correlation (XC) approximations have been studied, and results have been compared to the experimental transition energies, as well as, to the previous high-level ab initio calculations. TD-DFT gives satisfactory results in the cases of d(2), d(4), and low-spin d(6) complexes, but fails in the cases when transitions depend only on the ligand field splitting, and for states with strong character of double excitation. LF-DFT, as a non-empirical approach to the ligand field theory, takes into account in a balanced way both dynamic and non-dynamic correlation effects and hence accurately describes the multiplets of transition metal complexes, even in difficult cases such as sextet-quartet splitting in d(5) complexes. Use of the XC functionals designed for the accurate description of the spin-state splitting, e.g., OPBE, OPBE0, or SSB-D, is found to be crucial for proper prediction of the spin-forbidden excitations by LF-DFT. It is shown that LF-DFT is a valuable alternative to both TD-DFT and ab initio methods.