Tunneling splittings in vibrational spectra of non-rigid molecules: V. Reconstruction of the Hamiltonian from quantum chemical data Original Research Article

The complete set of potential and kinematic coupling constants, characterizing the Hamiltonian of a non-rigid molecule with one-wide-amplitude-coordinate is derived from standard quantum chemical data for the equilibrium geometries, normal frequencies and eigenvectors in the ground and transition states. This Hamiltonian is suitable for the perturbation instanton approach (PIA), developed in previous work [V.A. Benderskii et al., Chem. Phys., 219 (1997) 119, 143; 234 (1998) 153, 173]. The reconstruction of the Hamiltonian is made via the following steps: classification of the generalized coordinates according to the irreducible representations of the group of the non-rigid molecular model; linear transformation of the ground state normal coordinates into the frame of the transition state taking into account the Eckart conditions; perturbative solution of the inverse vibrational problem. As an example, the Hamiltonian for the internal C2-rotation in HNO3 and its isotopomers has been reconstructed. The specific feature of this molecule is a Fermi resonance between the second torsional level (2ν9) and first level of the ONO bending mode ν5. Tunneling splittings in the ground and first excited states of all vibrations are calculated within the PIA and are found to be in good agreement with the available experimental data. Anomalous large isotope effects on the tunneling splittings of excited levels of active transverse vibrations under O18/O16 and N15/N14 substitution are predicted.