Optimization of vibrational coordinates

The enormous progress made in recent years in the techniques for detecting and analysing highly excited vibrational states of polyatomic molecules has prompted development of theoretical quantum mechanical methods to determine and characterize these states. A number of techniques, both approximate and exact, have been proposed for solving the vibrational SchroŽ dinger equation and special attention has been paid to the coordinate system used for describing the vibrational motions of the molecule. The use of good coordinate systems that give the best possible degree of separability of vibrational motions enables us to understand molecular dynamics better and substantially reduces the computational e†ort required to determine excited vibrational states. A number of coordinate systems have been used for triatomic molecules, ranging from the classical rectilinear normal modes to more elaborate curvilinear systems such as valence, Jacobi, Radau etc. The quality of these systems can be improved considerably by making coordinate transformations depending on a certain number of parameters to be optimized. The present study reviews the di†erent techniques proposed for parametrizing and optimizing vibrational coordinates for triatomic molecules and gives speciÐc examples to show their efficiency in determining highly excited vibrational states.