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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 Omega 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 NH2OH with one inverter is presented and a complete set of the formulas necessary to write down the Hamiltonian of more complex molecules, like NH2NH2 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.

In the series of articles15 we have developed a semiclassical self-consistent approach to calculation of the highly excited rotational states in vibration-rotation (VR) spectra of polyatomic molecules. The central idea of the semiclassical approach is based on the introduction of the auxiliary time-periodical fields which transfer interactions between rotational and vibrational molecular degrees of freedom. This procedure leads to separation of variables in the VR Hamiltonian and, as a result, to simplification of the initial problem interpretation, which is reduced now to an independent solution of two nonsteady Schrodinger equations. In the first of them the Hamiltonian describes a motion of the molecular angular momentum J in some time-periodical field and does not depend on the vibrational coordinates explicitly, in the second -the Hamiltonian is a sum of usual vibrational energy and some additives, which describe a motion of the vibrational collective variables in auxiliary fields and do not depend on the angular coordinate explicitly.Further, using the theoretical field generalization of the WKB method the quantization rules are obtained for the VR energy of a molecule. They correspond to the semiclassical approximation of the initial quantum mechanical problem. In adiabat ic approximat ion, i . e. when the variat ion of fields in time is small in comparison with values of fields, these rules may be written asJ {v} where a(C) is the Berry's phase for the rotational problem, ' (C) is the {v) Berry's phase for the vibrational problem, {v} is the set of the quantum numbers, describing a given vibrat ional state, I J + 0. 5 , J is the angular momentum quantum number, N(C) is the integers running a series of values over the range (0,1,. . . ,J-l,J), p(C) is the Maslov's index.The closed circuit C in the parameter space of field variables can not be selected arbitrary, because it satisfies the classical energy conservation law. As a result a parameter space or, that is almost the same, the phase one of a molecular angular momentum is divided into four invariant regions. In two of them the Maslov's index p(C 2 for the corresponding circuits, in other two -p(C ) In fact, the circuits in a parameter space are the trajectories (orbits), which are described by the angular momentum vector in its phase space.The Berry's phases (C) and ' (C) with the condition (1) and the mean- {v) field configurations of the auxiliary fields are linked by the self-consistent procedure.Owing to orbit periodicity, the quantization rules (1) coincide for the first two regions and have the form 168 / SPIE Vol. 1811 High-Resolution Molecular Spectroscopy (1991) 0-8194-101 1-X/92/$4.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/04/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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