Primary and secondary isotope effect on tunnelling in malonaldehyde using a quantum mechanical scheme

Primary and secondary isotope effect on tunnelling in malonaldehyde is investigated with reduced-dimensional quantum mechanical models in the saddle-point normal coordinates, where the Hamiltonian takes the imaginary-frequency normal model as the reaction coordinate and uses the relaxed potentials to approximate the normal modes not explicitly included. Our two-dimensional (2D) results of the ground-state tunnelling splitting (Δ₀), as well as the ratio of the Δ₀ in malonaldehyde to that in its isotopologues, are in reasonably good agreement with available experimental data. The experimental deduction about the appreciable impact of secondary isotope effect on tunnelling is further confirmed. Moreover, we find that in most isotopologues, the fundamental excitation of the ring-deformation normal mode, explicitly included in the 2D model, shows a large enhancement of tunnelling relative to the Δ₀.