Multiconfigurational time-dependent Hartree calculations for tunneling splittings of vibrational states: Theoretical considerations and application to malonaldehyde.

Full-dimensional multiconfigurational time-dependent Hartree calculations on the tunneling splitting of the vibrational ground state and the low lying excited states of malonaldehyde are presented. Methodological developments utilizing the symmetry of double well systems for the efficient calculation of tunneling splittings are described and discussed. Important aspects of the theory underlying the previously communicated results for the ground state tunneling splitting [M. D. Coutinho-Neto et al., J. Chem. Phys. 121, 9207 (2004)] are detailed and further developments facilitating the calculation of tunneling splittings for vibrationally excited states are introduced. Utilizing these developments, the 14 lowest vibrational states of malonaldehyde, i.e., seven tunneling splittings, have been computed. The tunneling splittings are found to vary significantly depending on the particular vibrational excitation. This results in a complex pattern of vibrational levels. Studying the dependence of the tunneling splittings on the vibrational excitation, good agreement with available experimental results is found and intuitive interpretations of the results can be given.