Long-range effects in the density of loosely bound states of ion–dipole systems: the gas-phase SN2 complex Cl−⋯CH3Cl

Abstract

We present a methodology for the calculation of the number and density of bound vibrational states close to the dissociation threshold of large polyatomic molecules. It is shown that an evaluation based on the classical phase-space volume dramatically underestimates the number and density of the loosely bound states. The reason for this behaviour is the combination of two effects: the long-range interactions between the fragments and the quantum nature of the intramolecular modes of these fragments in the vicinity of their zero point energy level. Our approach is applied to the Cl⁻⋯CH₃Cl complex, for which multidimensional potential energy surfaces describing the long-range interactions between the Cl⁻ ion and the CH₃Cl molecule are available. The proposed adiabatic method, that combines a quantum treatment of the intramolecular modes and a semi-classical description of the intermolecular modes, is first applied to the two C–Cl stretching degrees of freedom and compared with the semi-classical approach and the exact quantum mechanical results. Then, we extend the methodology to a full-dimensional, but approximate, 12D potential energy surface and compare it with various semi-classical approaches. Finally, the quantum nature of the molecular dynamics in the vicinity of the dissociation threshold of a polyatomic molecule is discussed, in particular with respect to the importance of the density of states when deriving dissociation rates using statistical theories, e.g. RRKM.