Multidimensional tunneling dynamics of proton transfer in malonaldehyde molecule and its isotopomers

The twenty-one-dimensional Hamiltonian of malonaldehyde molecule and a number of its isotopomers (H/D, ¹³C/¹²C) was reconstructed in the low-energy region (<3000 cm^–1). Parameters of the Hamiltonian were obtained from quantum-chemical calculations of the energies, equilibrium geometries, and eigenvectors and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and transition state. Despite substantial variation of the barrier height calculated using different quantum-chemical methods (from 2.8 to 10.3 kcal mol^–1), the corresponding potential energy surfaces can be matched with high accuracy by scaling only one parameter (the semiclassical parameter , which defines the scales of potential, energy, and action). Scaling invariance allows optimization of the Hamiltonian in such a way that the calculated ground-state tunneling splitting coincides with the experimental value. The corresponding potential barrier height is estimated at 4.34±0.4 kcal mol^–1. The quantum dynamics problem was solved using the perturbative instanton approach without reducing the number of degrees of freedom. The role of all transverse vibrations in proton tunneling is characterized. Vibration-tunneling spectrum is calculated for the ground state and low-lying excited states and mode-specific isotope effects are predicted.