Unzipped Acetylene Dispersed Fluorescence Spectra: an Unconventional Form of Franck-Condon Analysis

$^{1}$ S.A.B. Solina, J.P. O'Brien, R.W. Field, W.F. Polik. Ber. Bunsen. Phys. Chem. accepted. $^{2}$ M.M. Gallo, T.P. Hamilton, H.F. Schaefer III. J. Am. Chem. Soc. 112 8714 (1990).Author Institution: Massachusetts Institute of Technology, Cambridge, MA 02139; Hope College, Holland, MI 49423By inspection of the set of active resonances found in the IR, Raman, overtone and SEP $spectra^{1}$ for the $\tilde{X}$ state, it can be shown that there remain three conserved quantities or polyad numbers. The traditional spectroscopic coupled harmonic oscillator basis set for acetylene is effectively block diagonalized into groups of zero-order states or "polyads" where the set of resonances connects zero-order states withi each polyad but never betwee polyads. The two particular Franck-Condon active modes in the acetylene $\tilde{A} \rightarrow \tilde{X}$ dispersed fluorescence (DF) spectra, in addition to the particular set of $\tilde{X}$ state resonances lead to a fortuitous coincidenc such that there will be only one bright state per polyad. The pattern formed in the DF spectrum for each polyad is the distribution of the intensity of the zero order bright state, or chromostate, among the ground state molecular eigenstates. Therefore, the intensity pattern within each polyad is solely a function of the ground state resonances, or dynamics. By comparing DF spectra from different intermediate states that prepare the same set of chromostates, but in which the relative intensities of the different chromostates vary, the intensity pattern within each polyad will be the same in each spectrum, but the relative intensity of each polyad pattern as a whole will vary from one spectrum to the next. By taking advantage of this intrapolyad intensity invariance, the polyads may be separated, i.e., the DF spectrum may be unzipped into its component polyads as long as the polyad numbers remain conserved DF spectra of acetylene have been recorded utilizing $\tilde{A}$ State intermediates that have 0, 2, and 3 quanta of excitation in the transbend. These spectra have been unzipped up to at least $16,400 cm^{-1}$ confirming that the three polyad numbers remain good and no total breakdown of the vibrational constants of motions has been observed which might have been an indication of energetic and coordinate access to the vinylidene-acetylene isomerization process, whose classical barrier to rearrangement is $predicted^{2}$ to lie ${\sim}17000 cm^{-1}$