H-1 NMR spectra of the paramagnetic cyanide-bridged mixed-valence compound [(eta(5)-C5H5)Fe(CO)(2)(mu-CN)Ru(NH3)(5)](CF3SO3)(3) (I) have been obtained in several solvents. When traces of partially deuterated water are present, instead of a single cyclopentadienyl (Cp) resonance shifted by the hyperfine interaction, numerous well-resolved resonances are observed. The spectra were simulated satisfactorily by giving the appropriate statistical weight to 140 possible H/D isotopomers formed by deuteration in the five ruthenium(III) ammine ligands. The proliferation of distinct resonances occurs because (a) the hyperfine shifts (HSs) due to each sequential deuteration in a single ammine are different and (b) while deuteration in an ammine cis to the cyanide bridge causes a downfield shift, in the trans ammine it causes an upfield shift that is nearly twice as large. All of these shifts exhibit a 1/T dependence, but temperature-independent components, due to large second-order Zeeman effects at the Ru-III center, are also present. Combining the results of density functional theory calculations with data from metal-metal charge-transfer optical transitions and with the effect of solvent-induced NMR HSs, it is argued that Fermi contact shifts at the Cp protons are insignificant compared to those due to the dipolar (pseudocontact) mechanism. Analytical expressions are presented for the dependence of the HS on the tetragonal component of the ligand field at the Rum ion. The tetragonal field parameter, defined as the energy by which the 4d(xy) orbital exceeds the mean t(2g) orbital energy, was found to be 147, 52, and 76 cm(-1), in dimethylformamide, acetone, and nitromethane, respectively. The effects of deuteration show that there is a significant component of hyperconjugation in the Ru-ammine interaction and that ND3 is a weaker pi donor than NH3. A single deuteration in an axial ammine increases the tetragonal field parameter (nu) by +2.8 cm(-1), resulting in a HS of -37 ppb in the Cp proton resonance, whereas a single deuteration in an equatorial ammine decreases the field by -1.5 cm(-1) with a HS of +20 ppb, despite a nominal separation of seven chemical bonds. We analyze the origin of this remarkable sensitivity, which relies on the favorable characteristics of the Ru-III low-spin t(2g)(5) configuration, having a spin-orbit coupling constant zeta approximate to 950 cm(-1).