A simple method for the derivation of exact quantum-mechanical vibration–rotation Hamiltonians in terms of internal coordinates

By considering infinitesimal rotations, the well-known G-matrix method is extended for the derivation of exact quantum-mechanical vibration–rotation Hamiltonians in arbitrary vibrational coordinates and molecule-fixed coordinate systems. All rovibrational coefficients can be calculated by dot products, with considerably less algebra than by using conventional methods. Coordinate transformations from one molecule-fixed coordinate system to another are discussed. Hamiltonians are partly derived for XH2 and XH3 (without inversion) type molecules to demonstrate the ease of this approach.