Acetylene polyads

R. W. Field Each acetylene polyad contains zero-order states that are easily accessible via plausible direct or multiple-resonance A XAU — X Franck-Condon pumping schemes. Each Vib 16,000... 

Since the factorization of H into H[j res effective Hamiltonian blocks is approximate, each polyad res will describe the low-resolution spectrum of each polyad and the early-time intrapolyad dynamics. Since the acetylene DF spectrum has the special property that each g,l = 0+, 2 polyad is illuminated by exactly one known ZOBS, for example, (0, n, 0,2m0>2,00)0,2, the polyad is specified by the ZOBS quantum numbers... 

The polyad model for acetylene is an example of a hybrid scheme, combining ball-and-spring motion in a two-dimensional configuration space [the two Franck-Condon active modes, the C-C stretch (Q2) and the tram-bend (Q4)] with abstract motion in a state space defined by the three approximate constants of motion (the polyad quantum numbers). This state space is four dimensional the three polyad quantum numbers reduce the accessible dimensionality of state space from the seven internal vibrational degrees of freedom of a linear four-atom molecule to 7 - 3 = 4. 

When more than one anharmonic interaction term couples near-degenerate, zero-order levels, a simple vector orthogonalization technique can be used to generate a complete set of the dynamically important (i.e., approximately conserved) polyad quantum numbers (Fried and Ezra, 1987 Kellman, 1990). For example, in acetylene, HC = CH, where the ratios of normal mode frequencies u2 W3 W4 W5 are approximately 5 3 5 1 1, modes 1, 2, and 3 are stretching modes (respectively symmetric CH stretch, and CC stretch, and antisymmetric CH stretch), modes 4 and 5 are bending modes (trans-bend and cis-bend), each polyad is labeled by 3 polyad quantum numbers,... 

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