ANHARMONICALLY-COUPLED LOCAL MODE TO NORMAL-MODE HAMILTONIAN TRANSFORMATIONS - BEYOND THE X,K-RELATIONS

Attention is focused on the quantitative relationships between the par ameters of the normal mode and the local mode effective Hamiltonian mo dels of anharmonic stretching vibrations. R. G. Della Valle (1988, Mol ec. Phys., 63, 611) has demonstrated the general relationship between the harmonically coupled anharmonic (Morse) oscillators (HCAO) model a nd the normal mode model of X-H (or X-D or other weakly coupled) stret ching vibrations of polyatomic molecules. Here we consider more fully the relationship between the normal mode and the anharmonically couple d local mode models for X-H stretching vibrations. The local mode Hami ltonian is expressed in terms of boson shift operators and these opera tors are then transformed into the corresponding normal mode model ope rators. Such relationships have already been derived for the special c ases of H2X (Baggott, J. E., 1988, Molec. Phys., 65, 739), XH3 (C-3v) and XH4 (T-d) (Law, M. M., and Duncan, J. L., 1994, Molec. Phys., 83, 757) and here they are derived systematically for arbitrary local mode stretching systems. Explicit relationships are derived for molecules of the symmetry types of allene, ethylene and benzene respectively. Th ese relationships between the unconstrained normal mode and anharmonic ally coupled local mode models allow for more reliable schemes for the relaxation of the HCAO x,K-relations than those suggested hitherto. I n an application to the ethylene-d4 overtone spectrum a much improved fit to experimental data is obtained using a compact anharmonically co upled local mode model and the consequences for the corresponding norm al mode model demonstrated. The generality of our results is emphasize d by the application to systems involving non-equivalent bonds, illust rated with reference to HCN/DCN. Approximations in these local to norm al mode transformations (such as the assumption of a unitary transform ation) are discussed. The models presented here may be supplemented wi th appropriate matrix elements to take account of Fermi resonances in the same straightforward manner as the HCAO model.