Time-dependent density functional theory modeling of spin-orbit coupling in ruthenium and osmium solar cell sensitizers

We report on the relevance of spin-orbit coupling on the optical properties of Ru(II)- and Os(II)-polypyridyl dyes effectively employed in dye-sensitized solar cells (DSCs). We include relativistic effects on time-dependent density functional theory calculations of selected complexes by using different levels of calculations, i.e., the scalar zero-order regular approximation (ZORA) and the fully relativistic ZORA including spin-orbit coupling, in such a way so as to disentangle and evaluate the spin-orbit effect. The widely investigated [M(bpy)3]2+ (M = Ru(II) and Os(II)) have been selected as benchmark complexes in our calculations; this is followed by investigation of "realistic" dyes used in DSCs, such as the prototypical N3 dye, its Os-based analogue, and a panchromatic Os(II) dye. We find that in Ru(II) complexes, spin- orbit coupling leads to a slight correction of the spectral shape, whereas only when we include the spin-orbit oupling we are able to reproduce the low-energy absorption bands characteristic of the Os(II) complexes. This study allows us to find a quantitative correlation between the strength of spin-orbit coupling and the metal center, highlighting the secondary effect of the different ligands experienced by the metal center.