Vibrational predissociation, collinear

Woodmff, S.B. and Thompson, D. (1979) A quasiclassical trajectory study of vibrational predissociation of van der Waals molecules Collinear He-T2(5 fl), J.Chem.Phys. 71, 376-380. 

The linearly structure (HCN)2 cluster was studied by SCF and Cl calculations. Results available so far are within the framework of a collinear model only, given the fact that a full, reliable potential surface for this system is not available yet. We note that calculations of vibrational predissociation lifetimes that we carried out for this system in the framework of a preliminary collinear treatment have shown that to obtain lifetimes compatible with the experimental ones, the energy released from the excited C-H stretching mode must necessarily be mostly dumped into C-H bending and rotational excitation of the fragments. This means that the collinear treatment is unacceptable even qualitatively for describing the predissociation dynamics. However a collinear treatment may be a reasonable approximation for the spectroscopy of those modes that do not involve bending excitations. Table 1 shows the results of SCF and Cl calculations for several of the transition frequencies. Jacobi ("collision") coordinates seemed an intuitively reasonable choice for the SCF calculation, and were employed here. 

Ab initio MCHF calculations have been carried out (49) for the predissociative C2N2 (Cl]lu) state (see the appendix). The initially prepared state was found to remain linear. As a first approximation, the collinear dissociation has been studied thus neglecting bending vibrations and rotations. 

For the predissociative C2N2 (C- TIU) state in the collinear approximation, the nuclear wavefunction is approximated by the product of three harmonic oscillator functions describing the normal modes vibrations. The frequencies and normal coordinates of the three linear stretching vibrations were obtained from ab initio MCHF calculations. The validity of the harmonic approximations is supported from experimental data (8) where absorption spectra of C2N2 is found to give a set of equidistant bands. 

Band and Freed have criticized the quasi-diatomic approximation and emphasized that any complete theory of dissodation must involve the use of the correct sets of normal modes Q and O of the molecule in the initial and final states (> and /> respectively. The two sets are not independent, but are related by a co-ordinate transformation. A detailed, quantum mechanical description has been developed in which the set Q in state ( > are taken to be the normal modes of the unexdted parent molecule for direct photodissodation, or the metastable photo-excited molecule for indirect predissociation, and the set Q ) in the state /> are separated into QUQi, wh e Qi is the reaction co-ordinate on the final repulsive surface and IQi are the normal modes in the photofragments. For a linear, triatomic molecule, Qi is simply the vibrational mode of the diatomic fragment and Q) indudes the symmetric and antisymmetric stretching modes (if collinearity is preserved). The matrix elements for the transition from... 

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