Local mode behavior in the acetylene bending system

The bending eigenfunctions of the acetylene X̃1Σg+ state, as represented by our recently reported effective Hamiltonian [J. Chem. Phys. 109, 121 (1998)], are analyzed up to Evib=15 000 cm−1. A transition from normal to local mode behavior is observed around 8000–10 000 cm−1, such that above these energies, the eigenstates are better described in terms of local mode quantum numbers. The local mode behavior in the bend degrees of freedom of acetylene that is described here is in many ways analogous to the local mode behavior that has been observed in the stretching degrees of freedom of many ABA molecules. However, the local mode behavior in the acetylene bend degrees of freedom, because it involves two two-dimensional rather than two one-dimensional vibrational modes, encompasses a richer range of motions. Specifically, in the “local” limit, the bending eigenfunctions are describable in terms of a continuum of motions ranging from local bend (one hydrogen bending) to counter-rotation (the two hydrogens executing rotations in opposite directions).