[Pt-2(mu-P2O5H2)(4)](4) (Pt(pop)) and its perfluoroborated derivative [Pt-2(mu-P2O5(BF2)(2))(4)](4) (Pt(pop-BF2)) are d(8)-d(8) complexes whose electronic excited states can drive reductions and oxidations of relatively inert substrates. We performed spinorbit (SO) TDDFT calculations on these complexes that account for their absorption spectra across the entire UV-vis spectral region. The complexes exhibit both fluorescence and phosphorescence attributable, respectively, to singlet and triplet excited states of ds*ps origin. These features are energetically isolated from each other (similar to 7000 cm(-1) for (Pt(pop-BF2)) as well as from higher-lying states (5800 cm(-1)). The lowest (3)d sigma*p sigma state is split into three SO states by interactions with higher-lying singlet states with dpps and, to a lesser extent, ppps contributions. The spectroscopically allowed d sigma*p sigma SO state has similar to 96% singlet character with small admixtures of higher triplets of partial dpps and ppps characters that also mix with (3)d sigma*p sigma, resulting in a second-order (1)d sigma*p sigma-(3)d sigma*p sigma SO interaction that facilitates intersystem crossing (ISC). All SO interactions involving the ds*ps states are weak because of large energy gaps to higher interacting states. The spectroscopically allowed d sigma*p sigma SO state is followed by a dense manifold of ligand-to-metalmetal charge transfer states, some with ppps (at lower energies) or dpps contributions (at higher energies). Spectroscopically active higher states are strongly spin-mixed. The electronic structure, state ordering, and relative energies are minimally perturbed when the calculation is performed at the optimized geometries of the (1)d sigma*p sigma and (3)d sigma*p sigma excited states (rather than the ground state). Results obtained for Pt(pop) are very similar, showing slightly smaller energy gaps and, possibly, an additional (1)d sigma*p sigma (3)d sigma*p sigma second order SO interaction involving higher (1)d pi p sigma* states that could account in part for the much faster ISC. It also appears that (1)d sigma*p sigma -> (3)d sigma*p sigma ISC requires a structural distortion that has a lower barrier for Pt(pop) than for the more rigid Pt(pop-BF2).