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

The inner-sphere reorganization energy of the electron self-exchange of the couple cyclooctatetraene/cyclooctatetraene radical anion has been investig ated by quantum mechanical calculations. The more stable Jahn Teller distor ted B-2g conformation of the radical anion has been used in this study. Two different theories have been applied in this first part, The harmonic appr oximation in the classical Marcus scheme has been modified by using project ed force constants, which are obtained from the complete force constant mat rix and the geometry changes of the molecule during the ET (introduced by M ikkelsen). A different approach (introduced by Nelsen) combines the differe nt energies of the neutral and radical anion with and without relaxation co rresponding to the vertical ionization potential and the vertical electron affinity. The electronic energies of the neutral molecule and the radical a nion differ dramatically applying three different levels of quantum mechani cal calculations (UAM1, UB3LYP, PMP2 with three different basis sets with a nd without diffuse functions). Nevertheless the Nelsen method gives almost consistent results for the inner-sphere reorganization energies: 120.1 kJ/m ol for semiempirical UAM1 method, 159.3 kJ/mol, 156.4 kJ/mol and 158.3 kJ/m ol for density functional UB3LYP/6-3lG*, 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 wor k supposing the total reorganization energy to be larger than 38 kcal/mot a ssuming an electron self-exchange rate of 10(4) M(-1)s(-1). The simple harm onic approximation of Marcus relation has not yet been applied for a molecu le 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 fo r UB3LYP/AUG-cc-pVDZ level of theory. Comparison with our concentration dep endent EPR experiments are controversial to the earlier experimental result s, but the latter supports the assumption that the electron self-exchange o ccurs in a time scale so that the molecules cannot complete their vibration al motions. Therefore the projected Marcus relation is not valid for cycloo ctatetraene/cyclooctatetraene radical anion including a large torsional cha nge during the electron transfer. (C) 2001 Elsevier Science B.V. All rights reserved.