A simple vibrational Hamiltonian expressed in terms of curvilinear internal coordinates has been used to model both stretching and bending vibrations in pyramidal XH3 molecules. The pure stretching part is expressed as harmonically coupled anharmonic oscillators and the pure bending part as harmonically coupled harmonic oscillators. The stretching and the bending modes are coupled with each other by Fermi resonance terms which contain contributions both from the kinetic and potential energy part of the full vibrational Hamiltonian. Only resonance couplings are included. The Hamiltonian matrices are symmetry factorized by employing symmetrized basis functions which consist of products of stretching oscillator and valence angle bending oscillator functions. This model is applied to observed vibrational term value data of arsine (AsH3). The least squares method is used to optimize potential energy parameters. The results obtained are in good agreement with ab initio calculations. All observed arsine overtone and combination bands have been assigned.
Rotational energy level structures of stretching vibrational states have been investigated in the XH2, XH3, and XH4 type symmetrical hydrides. Transformations from standard vibration–rotation normal coordinate Hamiltonians are made to internal coordinate representations which explicitly give the terms responsible for rotational coupling between the different local mode states. It is shown that the local mode relations between the vibration–rotation parameters as given by Lehmann [J. Chem. Phys. 95, 2361 (1991)] and by Halonen and Robiette [J. Chem. Phys. 84, 6861 (1986)] make these Hamiltonians diagonal in the local mode basis. The effective vibration–rotation parameters of overtones are then proved to obey the local mode relations closer and closer as the vibrational excitation increases. A simple vibrational model accounts well for the vibrational dependencies of vibration–rotation constants in the case of SiH4, GeH4, and SnH4.
The third stretching overtone region of a natural sample of stibine, SbH3, has been studied with high resolution infrared spectroscopy and the fifth and the sixth overtone region with Ti:Sapphire ring laser intracavity photoacoustic spectroscopy. The third overtone consists of a local mode pair of bands (400A1/E) which have been rotationally assigned both for 121SbH3 and 123SbH3 with a vibration-rotation model based on rectilinear normal coordinates. The vibrational dependencies of the model parameters are explained well with a simple block diagonal vibrational model. An extension of the standard vibration-rotation model is used to show that the upper state rotational energy level structures of both isotopic species are close to the rotational structure of an asymmetric rotor. High resolution laser spectrum of the fifth overtone consisting of a local mode pair of bands (600A1/E) shows severe perturbations in the upper state rotational structure. The (510A1/E) and (700A1/E) bands have been recorded with low resolution. All experimentally known vibration-rotation band origins of 121SbH3 have been reproduced well with a curvilinear internal valence coordinate system based Fermi resonance local mode model. The potential energy surface obtained agrees well with recent ab initio results.
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.
Articles you may be interested inGlobal threedimensional potential energy surfaces of H2S from the ab initio effective valence shell Hamiltonian method An internal coordinate quantum Monte Carlo method for calculating vibrational ground state energies and wave functions of large molecules: A quantum geometric statement function approach Application of an inverse method to the determination of a twodimensional intermolecular potential energy surface for the Ar-OH(A 2Σ+, v=0) complex from rovibrational spectra This paper presents a formulation of seminumerical contact transformations for rovibrational spectroscopy. Effective rotational Hamiltonians are obtained starting from a rovibrational Hamiltonian with an exact kinetic energy operator in curvilinear internal valence coordinates. Like the accuracy of the variational methods, the accuracy of this method can be increased by using more computational power. Error estimates are also calculated. Main motivations for using seminumerical contact transformations in rovibrational spectroscopy are considered. As an example, a calculation is carried out for H 2 S. No remarkable deviations between the calculated and the observed effective constants were observed for the states considered ͑ground states,
We explain the unexpected behavior of the generalizations of cellular automation traffic models introduced in [H. Fukś and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We analyze the steady-state flow in R(m,k) as a function of the initial density; we show that these rules correspond to a system with an infinite number of different kinds of virtual particles interacting according to complex annihilation rules. From simple considerations, we are able to predict the unexpected cutoff of the average flow at unity observed by Fukś and Boccara. We present an efficient algorithm for determining the exact final flow from a given finite initial state. An analysis of this algorithm in the infinite limit using generating functions yields an exact polynomial equation between the flow and density for R(m,k), of maximally 2(m+k)th degree in both.
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