Rovibrational Molecular Hamiltonian in Mixed Bond-Angle and Umbrella-Like Coordinates
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- 作者：Jan Makarewicz ; Alexander Skalozub
- 刊名：Journal of Physical Chemistry A
- 出版年：2007
- 出版时间：August 16, 2007
- 年：2007
- 卷：111
- 期：32
- 页码：7860 - 7869
- 全文大小：163K
- 年卷期：v.111,no.32(August 16, 2007)
- ISSN：1520-5215
文摘
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 NH2OH with one inverter is presented and acomplete set of the formulas necessary to write down the Hamiltonian of more complex molecules, likeNH2NH2 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.
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 NH2OH with one inverter is presented and acomplete set of the formulas necessary to write down the Hamiltonian of more complex molecules, likeNH2NH2 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.