Quantum mechanical investigation of the inner-sphere reorganization energy of cyclooctatetraene/cyclooctatetraene radical anion. Part I

Abstract

The inner-sphere reorganization energy of the electron self-exchange of the couple cyclooctatetraene/cyclooctatetraene radical anion has been investigated by quantum mechanical calculations. The more stable Jahn Teller distorted B 2 g conformation of the radical anion has been used in this study. Two different theories have been applied in this first part. The harmonic approximation in the classical Marcus scheme has been modified by using projected force constants, which are obtained from the complete force constant matrix and the geometry changes of the molecule during the ET (introduced by Mikkelsen). A different approach (introduced by Nelsen) combines the different energies of the neutral and radical anion with and without relaxation corresponding to the vertical ionization potential and the vertical electron affinity. The electronic energies of the neutral molecule and the radical anion differ dramatically applying three different levels of quantum mechanical calculations (UAM1, UB3LYP, PMP2 with three different basis sets with and without diffuse functions). Nevertheless the Nelsen method gives almost consistent results for the inner-sphere reorganization energies: 120.1 kJ/mol for semiempirical UAM1 method, 159.3 kJ/mol, 156.4 kJ/mol and 158.3 kJ/mol for density functional UB3LYP/6–31G*, UB3LYP/6–31++G* and UB3LYP/AUG–cc–pVDZ calculations and 192.5 kJ/mol for ab-initio PMP2/6–31G* investigations, respectively. These values are in agreement with earlier experimental work supposing the total reorganization energy to be larger than 38 kcal/mol assuming an electron self-exchange rate of 10 4 M −1s −1. The simple harmonic approximation of Marcus relation has not yet been applied for a molecule like cyclooctatetraene with large torsional geometry changes. Using the projected force constants after scaling, considerably different results for the inner-sphere reorganization energy have been calculated: 738.1 kJ/mol for the UB3LYP/6–31G*, 743.3 kJ/mol for UB3LYP/6–31++G* and 759.1 kJ/mol for UB3LYP/AUG–cc–pVDZ level of theory. Comparison with our concentration dependent EPR experiments are controversial to the earlier experimental results, but the latter supports the assumption that the electron self-exchange occurs in a time scale so that the molecules cannot complete their vibrational motions. Therefore the projected Marcus relation is not valid for cyclooctatetraene/cyclooctatetraene radical anion including a large torsional change during the electron transfer.