Analysis of long-ranged mixed-valence states at linear polynuclear metal-complexes under electrochemical equilibrium by means of resonance of pi-conjugation

When a quantum chemical technique for analyzing the resonance at pi-conjugated organics was applied to mixed-valence states of linear N-nuclear metal-complexes with pi-conjugated linkers, the theoretical current-potential curves under the steady state showed N waves at negative values of the overlap integral S, as well as at negative values of the interaction energy between the oxidized metal center and the reduced one. The analysis was made as follows: from a linear combination of wavefunctions of electrons relevant to a single electron transfer reaction, equations for a redox state of a given isomer were derived as a function of S, N and pair interaction energies. Analytical solutions of the current-potential curves were obtained only for N = 2 and 3. The curves for N greater than or equal to 4 were computed numerically, exhibiting N waves. Those for a large number of N seemed to show one wave. These results were compared with the appearance of three waves at odd numbers of N and four at even numbers of N by the additive pair model previously presented.