A Model of Ion-Dipole Capture Force Field for Inner-Sphere Reorganization Energy of Transition Metal Hexa-aquocations in Solution

From the view of structure of coordination ions, the effect of the structural reogranization energy （RE） of reactants in electron transfer processes to electron transfer rate may be divided into two parts: inner-sphere factor （contribution from the ion-ligand bond length stretching）and outter-sphere factor （contribution from the solvent）. The outter-sphere RE may be accurately calculated via the Marcus theory of nonequilibrium solvent polarization, but the inner-sphere formalism are George-Griffith’s model whose applicability is usually limited by the paucity of the reliable vibrational spectroscopic data and Tunuli’s formalism of RE of oscillator potential by calculating the force constants of reorganized state in terms of ion-dipole interaction potential which effectively improved RE results. But, there are also some errors in them, the reason is that the change relationship between the energy of complex ions and ion-ligand bond length in solution doesn’t completely satisfy harmonic oscillator model, the bigger the equilibrium displacement, the bigger the energy error. Both of cxperiment and theory indicate that the cubic term correction of harmonic oscillator potential can give a better fit to actual potential curve in a large degree. Based on a simple improved model of reorganization phenomenon and ion-dipole capture force field potential, a new formalism of energy index describing the inner-sphere reorganization effect of hydrated ions in solution involved in electron-transfer processes is presented in this paper, the calculation results indicate that this work effectively improve early ones, and give a better agreement with experimental spectroscopic scale data and photoemission cxperimentul results, and avoid the difficulty to calculate inner-sphere RE under the condition of the scarcity of vibrational spectroscopic data in solution, and present a new simple analysis method by the physical parameters of ions and ligands which is chained easily.