## Rovibrational Molecular Hamiltonian in Mixed Bond-Angle and Umbrella-Like Coordinates

journal contribution

posted on 16.08.2007 by Jan Makarewicz, Alexander Skalozub#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitude
inversion and torsion motions is derived. The derivation is based on a division of a molecule into two parts:
a frame and a top. The nuclei of the frame only are used to construct a molecular system of axes. The
inversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion of
the top is described by the nonstandard torsion angle defined in terms of the nuclear vectors and one of the
molecular axes. The internal coordinates chosen take into account the properties of the inversion and torsion
motions. Vibrational

**s**and rotational**Ω**vectors obtained for the introduced internal coordinates determine the rovibrational tensor**G**defined by simple scalar products of these vectors. The Jacobian of the transformation from the Cartesian to the internal coordinates considered and the**G**tensor specify the rovibrational Hamiltonian. As a result, the Hamiltonian for penta-atomic molecules like NH_{2}OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH_{2}NH_{2}with two inverters, is reported. The approach considered is essentially general and sufficiently simple, as demonstrated by derivation of a polyatomic molecule Hamiltonian in polyspherical coordinates, obtained by other methods with much greater efforts.