In the present paper, we theoretically reinvestigate structural properties, and photo-physical and chemical characteristics and electronic absorption spectra of three kinds of ruthenium polypyridyl complexes [Ru(tpy)[Formula: see text], [Ru(tpy)(bpy)(H2O)][Formula: see text], and [Ru(tpy)(bpy)(Cl)][Formula: see text] complexes in acetone (tpy[Formula: see text]2,2[Formula: see text],2[Formula: see text]-terpyridine and bpy[Formula: see text]2,2[Formula: see text]-bipyridine). In particular, the experimental absorption spectra of these complexes are revisited theoretically in detail and are simulated using the first-order perturbation theory based on time-dependent density functional theory (TD-DFT) where the first-order perturbation term is the spin–orbit (SO) coupling Hamiltonian, and quantum chemistry calculations based on various functionals and basis sets. It was found that in general the theory including SO coupling can reproduce experimental data better than the simple quantum chemistry calculation neglecting SO coupling, which indicates that SO coupling is very important to understand the optical features of these complexes and that therefore the mixing between singlet and triplet states is strong due to the large SO coupling constant of Ru atom involved in these complexes. This suggests the fact that the disagreement between the experimental and calculated absorption spectra was found in TDB3LYP/(SDD with triple-[Formula: see text] for Ru and 6-31G* for others) [Jakubikova EJ et al., Inorg Chem 48:10720, 2009] can be tracked down to the neglect of SO couplings. It was also found that the choice of the DFT functionals and basis sets is crucial for a good theoretical reproduction of experimental data.
Momentum density and its Fourier transform: Relation to the first-order density matrix and some scaling properties
