ИСТИНА

With the development of laser technology, accurate descriptions of highly excited states of polyatomic molecules becomes one of the most important problems in the field of molecular spectroscopy and dynamics. Traditional methods of description of anharmonic vibrations of polyatomic molecules, such as those based on the Watson Hamiltonian and perturbation theory, have limited predictive accuracy due to the breakdown of the normal mode description for highly excited states and divergence of expansions of the potential energy surface. [1] The Morse oscillator model is very useful in describing molecular anharmonicity; its levels coincide with ones obtained with normal modes and a quartic potential. For highly excited states a molecular motion can be described in terms of local modes and can be approximated by expansion of the Morse coordinate instead of the normal coordinate. However, representation of physical observables using the Morse oscillator leads to non-sparse matrices. An efficient approach to this problem comes with su(2) algebra and a Morse Hamiltonian in the second quantization [2]. Different forms of ladder operators were proposed in [3-5], using SUSY and factorization method. However, ladder operators proposed in [3] cannot express the coordinate, while operators proposed in [4] change the coefficients of the potential. Bordoni et al. [5] proposed a set of Morse-like basis functions and gave a realization to non-compact Lie algebra su(1,1). Lemus et al. [2,6] proposed linearization of Morse-oscillator ladder operators. We have performed a critical analysis of existing approaches for representing the Morse oscillator in the second quantization. We have shown that linearization of ladder operators in the framework of Morse-coordinate based Meyer-Günthard-Pickett Hamiltonian leads to numerically equivalent results with the perturbative model based on an harmonic oscillator.