Using Lie-algebraic techniques and the simpler expressions of the matrix elements of Majorana operators given by us, we obtain an effective Hamiltonian operator which conveniently describes vibrational spectra of linear tetratomic molecules, including both stretching and bending modes. For a linear symmetrical four-atom molecule C2H2, the highly excited vibrational levels are obtained by applying the u (4) algebraic approach. We have found that the spectra are made up of a clustering structure. The number of levels in one cluster depends on the total quantum number of stretching and bending vibrations. In addition, some other properties, such as the level assignment and the labeling of calculated theoretical results, are also discussed.

The vibrational excitations of linear triatomic molecules, including both bending and stretching vibrations, are studied in the framework of dynamical symmetry groups. In this framework, the dynamical symmetry group of triatomic molecules is U1(4)⊗U2(4). Hence, a Hamiltonian is constructed that includes the second-order combination of the invariant operators. The eigenvalues of the molecular Hamiltonian give relatively little improvement for HCN but significant improvement for OCS. We obtained highly excited vibrational levels of the two molecules.

In this paper, the multiphoton transition Hamiltonian for the linear triatomic molecule HCN is given by using the quadratic anharmonic model and Sudden approximation. From this Hamiltonian we find a dynamic algebra h4. The bond-selective vibrational transition probability of HC and the long-time averaged energy are calculated.

The vibrational excitations of bent triatomic molecules, including both bending and stretching vibrations, are studied in the framework of the U (4) algebra. For the bent triatomic molecules H2O and H2S, the highly excited vibrational levels (up to 14) are obtained using the U (4) algebraic approach. We have found that the spectra are made up of clustering structure. The number of levels in one cluster depends on the total quanta of stretching and bending. In addition, some other properties are also discussed.

The time-independent energy sudden (ES) representation is defined through application of the energy shift operator S=exp[-(h-ωn)ə/əє], where h is the internal (molecular) Hamiltonian. Our introduction of S follows from an earlier study by Chang, Eno, and Rabitz where exp[-iht], which "factors out" internal motion, was used to define the time-dependent ES representation. Exact integral equations for the scattering wave function within the ES representation are derived, the leading terms being the approximate ES wave function. Corrections to the ES wave function are nonsingnlar and involve the generalized potential increment V=S-1VS-V, where V is the interaction potential. Boundary conditions and transition amplitudes are discussed, as is the connection between wave functions in the ES and the original representations.