Ground-state, mode-dependent vibronic coupling in some simple, cyanide-bridged transition-metal donor-acceptor complexes

Patterns of the shifts in bridging cyanide-stretching frequencies have been examined in several fully saturated, mu-cyano, bi- or trimetallic transiti on-metal donor-acceptor (D/A) complexes. An earlier (Watzky, M. A.; et al. Inorg. Chem. 1996, 35, 3463) inference that the bridging ligand nuclear and the D/A electronic coordinates are entangled is unequivocally demonstrated by the 32 cm(-1) lower frequency of v(CN) for (NH3)(5)Cr(CNRu(NH3)(5))(4+) than for the cyanopentaamminechromium(III) parent. This contrasts to the 4 1 cm(-1) increase in v(CN) upon ruthenation of (NH3)(5)RhCN2+. More complex behavior has been found for cis and trans trimetallic, donor-acceptor comp lexes. The symmetric combination of CN- stretching frequencies in trans-Cr- III(MCL)(CNRuII(NH3)(5))(2)(5+) complexes (MCL = a tetraazamacrocyclic liga nd) shifts 100-140 cm(-1) to lower frequency, and the antisymmetric combina tion shifts less than about 30 cm(-1). This contrast in the shifts of the s ymmetric and the antisymmetric combinations of the CN stretches persists ev en in a trans complex with no center of symmetry. Two CN stretches have als o been resolved in an analogous cis complex, and both shift to lower freque ncy by about 60 cm(-1). The net shift, summed over all the CN-stretching fr equencies, is about the same for the bis-ruthenates of related dicyano comp lexes. A simple, symmetry-adapted perturbation theory treatment of the coup led vibrations is employed to deal with the opposing effects of the "kinema tic" shifts (delta) of v(CN) to higher frequency, expected in the absence o f D/A coupling, and shifts (f) of v(CN) to lower frequency that occur when D/A coupling is large. The Rh(III)and Cr(III)-centered complexes correspond to different limits of this model: delta > f and delta < f, respectively. When referenced by means of this model to complexes with Rh(III) acceptors, the shifts in trimetallic complexes, summed over the symmetric and antisym metric combinations of CN stretches, are about twice those of bimetallic co mplexes. Similarly referenced and summed over all bridging CN frequencies, the shifts of v(CN) to lower energies are proportional to the oscillator st rength of the electronic, donor-acceptor charge-transfer transition. The si mplest interpretation of this correlation is that the donor-acceptor coupli ng in these systems is a function of the nuclear coordinates of the bridgin g ligand. This behavior of these complexes is semiquantitatively consistent with expectation for CN--mediated vibronic (pseudo-Jahn-Teller) coupling o f neighboring donors and accepters, and the observed Ru-II/CN- CT absorptio n parameters can be used in a simple, semiclassical vibronic model to predi ct shifts in v(CN) that are in reasonable agreement with those observed.