The x-axis in the bifurcation diagram, is the polyad number, in this case the total number of bend quanta N_bend = (n₄ + n₅), with 4 and 5 referring to the trans- and cis-bend, respectively. The y-axis is a little more difficult to describe. The top represents pure zero-order trans-bending; the bottom, pure cis-bending. In the middle, at y = 0, there is an equal amount of zero-order trans- and cis- bend. Up to about polyad 9, the system is described by pure trans- and cis-bend normal modes. But then, these bifurcate, at slightly different polyad numbers. The trans-bend bifurcates at the top of the diagram into local modes, and then into a kind of mode called three-dimensional precessional modes. The cis-bend bifurcates into two other kinds of modes, an orthogonal mode and a counter-rotator mode.

It should be noted that these modes have been found by others, using both wave functions from the spectroscopic Hamiltonian, and numerical bifurcation analysis of this Hamiltonian. (M.P. Jacobson, C. Jung, H.S. Taylor, and R.W. Field, J. Chem. Phys. 111, 66, 1999). What is noteworthy about the bifurcation diagram on the next page is that it gives a global map of the bifurcation behavior for all polyad numbers.

Page 2 of 2