Studies on density functional theory for the electron-transfer reaction mechanism between M-C6H6 and M+-C6H6 complexes in the gas phase

Density functional theory (DFT) is used to theoretically investigate the electron-transfer (ET) reactions between M (Li, Na, Mg)–C6H6 and M+–C6H6 complexes in the gas phase. The geometry optimization of the metal–benzene complexes and the encounter state in the process of ET reaction was performed at the 6-31G basis set level. The metal atoms (or metal ions)–benzene molecule separation distances computed using DFT method were found to agree with second-order Møller–Plesset (MP2) results. The precursor complex has C6 symmetry, the distances between acceptor and donor is about 3.0–3.6 Å, which yields a bonding energy of approximately 0.9–1.5 eV. It shows there are relatively strong interactions between them. Additionally, the geometry of transition state is also obtained by the linear coordinate method. From the analysis of the charge on the transition state and the isolated state, the reaction mechanism was derived. Also the activation energy and the coupling matrix element of the rate constant of the ET reaction are calculated. According to the reorganization energy of the ET reaction, the values obtained from George–Griffith–Marcus (GGM) method (the contribution only from diagonal elements of force constant matrix) are larger than those obtained from Hessian matrix method (including the contribution from both diagonal and off-diagonal elements), which suggests that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.