Classical characters of highly excited bend dynamics of acetylene in two coupled SU(2) coset spaces

Abstract

The classical characters of the highly excited bend dynamics of acetylene are analyzed in terms of two coupled SU(2)/U(1) coset spaces corresponding to the right and left circular motion of the two C–H bends. The vibrational modes show a wide variety of behaviors that are not observed in the simple SU(2)/U(1) coset case which deals with, e.g., two coupled stretches, in which case the vibrational modes can be characterized as (low-lying) local and (high-lying) normal modes with a so-called local-normal transition in between. For the two coupled SU(2)/U(1) cosets of acetylene, the general trend is that most modes are perturbed local or normal modes, with distinct characters that are not found in the SU(2) dynamics. Details of their classical characters and the dynamical action flow between the two C–H bends were deduced. When the total action number Nb is small (less than 14), normal mode motions dominate, i.e., trans bend modes at the bottom of each polyad and cis bend at the top. At higher Nb, the vibrational modes are more or less of local character though they, individually, do possess very unique characters. Specifically, as Nb ranges from 12 to 22, the characters of the low-lying levels change from the trans character with action asymmetrically distributed in the two C–H bonds to one hydrogen bending, while those of the high-lying levels change from well concerted cis to local counter rotation. These results are consistent with recent quantal and semiclassical results. [M. P. Jacobson, R. J. Silbey, and R. W. Field, J. Chem. Phys. 110, 845 (1999); M. P. Jacobson, C. Jung, H. S. Taylor, and R. W. Field, ibid. 111, 600 (1999)].