Probing highly excited vibrational eigenfunctions using a modified single Lanczos propagation method: Application to acetylene (HCCH)

A modified version of the single Lanczos propagation method is proposed, which allows both energies and overlaps between multiple target functions and all eigenfunctions to be computed from a single Lanczos recursion with no explicit construction of the eigenfunctions. This method is employed to help assigning some highly excited bending levels of acetylene (HCCH) using a six-dimensional exact quantum Hamiltonian and target functions designed to extract information about the shape of the eigenfunctions. In the special case of the Ã-state vibrational eigenfunctions being the target functions, the Ã→X̃ resonance emission spectra are obtained. The assignments on the Bramley et al. [J. Mol. Spectrosc. 157, 301 (1993)] potential energy surface show a strong resemblance to the experimentally observed normal-to-local mode transition in the bending overtones, while that of Halonen et al. [Mol. Phys. 47, 1097 (1982)] supports no such transition in the same energy range.