Critical points bifurcation analysis of high-l bending dynamics in acetylene

The bending dynamics of acetylene with pure vibrational angular momentum excitation and quantum number l not = 0 are analyzed through the method of critical points analysis, used previously [V. Tyng and M. E. Kellman, J. Phys. Chem. B 110, 18859 (2006)] for l = 0 to find new anharmonic modes born in bifurcations of the low-energy normal modes. Critical points in the reduced phase space are computed for continuously varied bend polyad number N(b) = n(4) + n(5) as l = l(4) + l(5) is varied between 0 and 20. It is found that the local L, orthogonal O, precessional P, and counter-rotator CR families persist for all l. In addition, for l > or = 8, there is a fifth family of critical points which, unlike the previous families, has no fixed relative phase ("off great circle" OGC). The concept of the minimum energy path in the polyad space is developed. With restriction to l=0 this is the local mode family L. This has an intuitive relation to the minimum energy path or reaction mode for acetylene-vinylidene isomerization. With l > or = 0 included as a polyad number, the l = 0 minimum energy path forms a troughlike channel in the minimum energy surface in the polyad space, which consists of a complex mosaic of L, O, and OGC critical points. There is a division of the complete set of critical points into layers, the minimum energy surface forming the lowest.