TDDFT 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 TDDFT 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 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, followed by investigation on “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 lead to a slight correction of the spectral shape, while only including the spin-orbit coupling 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