  The successful use of molecular dyes for solar energy conversion requires
efficient charge injection, which in turn requires the formation of states with
sufficiently long lifetimes (e.g. triplets). The molecular structure elements
that confer this property can be found empirically, however computational
predictions using $\textit{ab initio}$ electronic structure methods are
invaluable to identify structure-property relations for dye sensitizers. The
primary challenge for simulations to elucidate the electronic and nuclear
origins of these properties is a spin-orbit interaction which drives
transitions between electronic states. In this work, we present a computational
analysis of the spin-orbit corrected linear absorption cross sections and
intersystem crossing rate coefficients for a derivative set of phosphonated
tris(2,2'-bipyridine)ruthenium(2+) dye molecules. After sampling the ground
state vibrational distributions, the predicted linear absorption cross sections
indicate that the mixture between singlet and triplet states plays a crucial
role in defining the line shape of the metal-to-ligand charge transfer bands in
these derivatives. Additionally, an analysis of the intersystem crossing rate
coefficients suggests that transitions from the singlet into the triplet
manifolds are ultrafast with rate coefficients on the order of $10^{13}$
s$^{-1}$ for each dye molecule.
