Temperature and pressure dependences of tunneling rate constant: density-functional theory potential-energy surface for H-atom transfer in the fluorene-acridine system

Temperature and pressure dependences of rate constants for solid phase tunneling reactions are analytically considered within the framework of modified theory of radiationless transitions, taking into account the intermolecular and soft intramolecular promotive vibrations of reagents. This treatment allows us to describe theoretically the process of atomic tunneling and the effect of temperature on the potential barrier and reorganization of the reagents. The influence of external pressure appears in our treatment as a static reduction of widths and heights of the potential barrier with hydrostatic compression of the matrix, and also as an increase of frequencies of promotive vibrational modes owing to anharmonicity. The theoretical results are used to interpret experimental data concerning the effect of temperature and pressure on the hydrogen-atom tunneling in the fluorene-acridine reaction system. It has been shown that by taking into account the contributions from reorganization of the reagents, which statically reduce the tunneling barrier and are related to four types of promotive vibrations (translational, librational, and two low-frequency intramolecular modes at 95 and 238 cm(-1)), one can reproduce the experimental data available in the literature. The parameters of the reaction system required for this analysis are calculated from two-dimensional potential-energy surfaces generated at the DFT-B3LYP/6-31G* level.