10484 J. zyxwvutsrqpo Phys. Chem. zyxwvu 1995, 99, zyxwvu 10484-10491 Role of Vibronic Coupling and Correlation Effects on the Optical Properties of Mixed-Valent and Monovalent Dimer Compounds: the Creutz-Taube Ion and Its Monovalent Analogs Alessandro Ferretti,*>? Alessandro Lami: Mary Jo Ondrechen,' and Giovanni Villanit Istituto di Chimica Quantistica ed Energetica Molecolare del CNR, Via Risorgimento 35, I-56126 Pisa, Italy, and Department of Chemistry, Northeastem University, Boston, Massachusetts 02115 Received: December 13, 1994; In Final Form: March 27, 1995@ A three-site, three-harmonic oscillator vibronic model Hamiltonian that includes correlation effects is considered in order to study the optical absorption spectra of the Creutz-Taube ion at various values for the total charge. The model is made by a two band Hubbard Hamiltonian, plus a vibronic interaction that is linear in the nuclear coordinates. We show that the main features of absorption spectra observed experimentally in the near-IR-visible are well reproduced by this model, as far as band position and shape are concerned. An approximate approach to the vibronic problem reveals that, in the present case, the vibronic interaction is strong and good results can be obtained only by solving the full vibronic problem. 1. Introduction A model for the optical absorption spectrum of bridged electron donor-acceptor systems with variable total charge is presented. We consider herein linear trinuclear clusters of the form, donor-bridge-acceptor, hereafter referred to as DBA. We illustrate our method with application to the extensively studied Creutz-Taube ion in three oxidation states: mixed- valent, fully reduced, and fully oxidized. Such complexes have numerous important applications in coordination chemistry, in molecular electronics, and in materi- als design. Electron donor-acceptor pairs joined together by a variable bridging ligand were first synthesized by Taube et a1.I for the purpose of studying inner-sphere electron transfer. A host of related bridged mixed-valent species that possess an odd charge and for which donor D and acceptor A are identical were also reported by the Taube group and These mixed-valent compounds run the gamut from strongly localized (slow electron transfer) to completely delocalized (averaged- valent). Probably the best known bridged mixed-valent dimer is the Creutz-Taube ion, a pyrazine-bridged mixed-valent dimer of ruthenium.6 This compound was the focus of intense contro- versy for more than a decade, but evidence later pointed toward a fully delocalized ground ~tate.~-'O More recently, the Stark effect work of Oh and Boxer" and the resonance RamanI2 and asymmetric c~mplexation'~ work of Hupp and co-workers have contributed strong evidence in support of delocalization (valence averaging) in the ground state. Trinuclear systems of the DBA type were proposed as possible molecular-scale rectifiers in 1974.14 Recently reported evidence on this front is enco~raging.'~ Other molecules in this class recently were proposed as molecular switches with sub- picosecond write times and at least microsecond retention times.'' Lanthanide sandwich compounds, in which a rare earth ion acts as a bridge between two macrocycles with an excess electron (a variation on the bridged mixed-valent theme), have applications in electrochromic devices." Extended-chain analogs of the above systems, in which multivalent metal ions M are joined together with bridging Istituto di Chimica Quantistica ed Energetica Molecolare del CNR. Northeastem University. @ Abstract published in Advance ACS Abstracts, May 15, 1995. 0022-3654/95/2099- 10484$09.00/0 ligands L to form a linear chain of the form..-M-L-M-L.**, have been ~ynthesized.'~.'~ In addition, one-, two-, and three- dimensional assemblies of such systems have been suggested for particular applications in the areas of molecular electronics and nanoscale devices.20,*' In the systems discussed above, we have two chemical means for controlling their properties: (1) synthetic alteration of the bridging ligand and zyxwv (2) variation of the total charge. Chemical changes in the bridging ligand can have profound effects on the spectroscopic and conductive properties of these bridged systems, and any reasonable model must incorporate the coupled bridge orbitals expli~itly.**-*~ Furthermore, whenever transition metals with variable total electron occupation are involved, as is the case in the systems of interest here, a simple one-electron model, such as the Huckel or tight binding models, will not be adequate to describe the system, and the effects of electronic correlation must be taken into a c c o ~ n t . ~ ~ - ~ ~ The Creutz-Taube ion is known to exhibit absorption bands in the near-IR and visible region that strongly depend upon the oxidation state of the two metal ions and hence on the total charge. The fully oxidized form of the complex, the one with both Ru ions in an oxidation state of f3, is characterized by the absence of absorption in the near-IR, while some bands appear above 3 eV. The complex with a total charge +5 still has some features above zyxw 4 eV but exhibits also two bands at 0.8 and 2.2 eV. Finally, the fully reduced form with a total charge of +4 has a spectrum very similar to the +5 species, except that at low frequency, the band at 0.8 eV is absent and the one at 2.2 eV is slightly blue shifted to 2.27 eV.' Early models for this complex considered only the two metal ions and neglected the role of the bridging Further investigation by Ondrechen et al.22-24 revealed that a ligand orbital may play a fundamental role in the spectral features of the Creutz-Taube ion, and they fitted the experimental data for the +5 species with a Huckel Hamiltonian. Recent experimental evidence corroborates the conclusions of their three-site model Hamiltonian for the +5 species."-'3 The role of vibronic interaction with multicenter vibrations on the line shape has been investigated by Piepho for the +5 specie^,^',^^ using a M-L interaction term which is distance-dependent and a MO electronic basis. A recent improvement of the electronic three-site model involves the explicit introduction of the 0 1995 American Chemical Society