Tunneling splittings in vibrational spectra of non-rigid molecules: IX. Malonaldehyde and its isotopomers as a test case for fully coupled multidimensional tunneling dynamics

Abstract

Twenty one dimensional potential energy surfaces (PES) and the tunneling coordinate dependent kinematic matrices of malonaldehyde and of several of its isotopomers (D, 13C) are constructed in the low-energy region (<3000 cm −1) using quantum-chemical data. Even though the barrier heights calculated with different methods differ strongly (from 2.8 to 10.3 kcal mol −1), all PES become near identical after scaling, fitting only one semiclassical parameter γ, which defines the scales of potential, energy and action. The results of dynamical calculations carried out in dimensionless variables are therefore quite insensitive to the choice of the quantum-chemical method used for the construction of the Hamiltonian. Choosing the value of γ such that the calculated tunneling splitting in the ground state coincides with the experimental value, the corresponding barrier height is determined as 4.30 kcal mol −1 and the vibrational spectrum of the transition state is obtained. The perturbative instanton approach developed in the previous papers of this series is used to solve the dynamical problem without reducing the number of degrees of freedom. The role of all 20 transverse vibrations in proton tunneling is characterized. The tunneling path and globally uniform semiclassical wave functions are evaluated from the fourth-order Hamilton–Jacobi equation and the second-order transport equation. Tunneling splittings in the ground and low-lying excited states are calculated and isotope effects of H/D and 13C/12C substitutions are predicted.