Quantum analysis of high vibrational overtones of hydrogen cyanide using optimal modes

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Abstract
An accurate two mode model of HCN is used to demonstrate a technique for and the utility of using optimized linear combinations of bond modes to describe molecular vibrational states. While normal modes are exact at zero energy and bond modes describe dissociations conveniently, neither set of coordinates describe accurately the motions of most of the spectroscopically accessible molecular vibrational states of HCN. We present a newly developed method of describing molecular vibrations with an optimized set of linear combinations of bond modes. The Hamiltonian is canonically transformed to these coordinates using the transformation method. Subsequent diagonalization of the rotated Hamiltonian matrix gives the unaltered energies and a much improved description of the molecular vibrations as measured by the projection of the eigenstates onto the zero order states. This technique improves spectroscopic assignments and simplifies visualization of the quantum vibrational motions of molecules. This is illustrated by resolving an apparent intensity anomaly in the overtone spectrum of HCN.

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