A new exact quantum mechanical rovibrational Hamiltonian operator for molecules exhibiting large amplitudeinversion 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. Theinversion motion of the frame is described in the umbrella-like coordinates, whereas the torsion motion ofthe top is described by the nonstandard torsion angle defined in terms of the nuclear
vectors and one of themolecular axes. The internal coordinates chosen take into account the properties of the inversion and torsionmotions. Vibrational
s and rotational
vectors obtained for the introduced internal coordinates determinethe rovibrational tensor
G defined by simple scalar
products of these
vectors. The
Jacobian of the transformationfrom 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
2OH with one inverter is presented and acomplete set of the formulas necessary to write down the Hamiltonian of more complex molecules, likeNH
2NH
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, obtainedby other methods with much greater efforts.