Vibrational Spectra of Distorted Structure Molecules by Using Lie Algebraic Techniques: an Application to Copper and Magnesium Octaethyl Porphyrin

Using a U （2） algebraic model the fundamental stretching vibrations of copper octaethyl porphyrin and magnesium octaethyl porphyrin are calculated for 24 vibrational bands. The locality parameter ξ confirms the highly local behavior of the stretching modes of these porphyrin molecules. The model Hamiltonian so constructed appears to describe the vibrational energy levels accurately.     

Vibrational Spectroscopy of CH/CD Stretches in Propadiene: An Algebraic Approach

Using Hamiltonian based on Lie algebraic method, the stretching vibrational modes of C3H4 and C3D4 molecules are calculated up to higher overtones. The model appears to describe C-H and C-D stretching modes with less number of parameters. The locality parameter ξ confirms the highly local behaviour of the stretching modes of these molecules.     

Analysis of vibrational spectra of nano-bio molecules： Application to metalloporphrins

In this paper, we have applied the Lie algebraic model to nano-bio molecules to determine the vibrational spectra of different stretching and bending vibrational modes. The determined vibrational energy levels by the Lie algebraic model are compared with the experimental data. The results from the theoretical mode[ are consistent with the experimental data. The vibrational energy levels are clustering in the excited states.     

Vibrational spectra and intramolecular vibrational redistribution in methane and its isotopomers

An improved U(2) algebraic model is introduced to study the stretching and bending vibrational spectra of methane and its isotopomers.The algebraic model with fewer parameters reproduces the experimental spectra with good precision.Moreover,the obtained parameters describe well the correct behavior of isotopic substitution.It is shown that the Fermi resonance leads to a very fast intramolecular vibrational redistribution among stretches and bends.     

CALCULATIONS OF STRETCHING VIBRATIONAL ENERGY LEVELS OF THE CH3I MOLECULE BY A NONLINEAR MODEL

A nonlinear model, i.e. the quantized discrete self-trapping equation, is applied to calculate the highly excited CH stretching vibrational energy levels of the CH₃I molecule in the liquid phase at the electronic ground state up to n=8. The obtained results agree well with the experimental data and with those obtained from local mode model calculations. We note that the dominant feature of the methyl CH stretching vibrational energy levels of the CH₃I molecule is a pattern of local mode pairs. When n≥7, all the vibrational energy of the CH₃ group can nearly be localized on a single CH bond.     

Three-dimensional ab initio dipole moment surfaces and stretching vibrational band intensities of the XH3 molecules

Stretching vibrational band intensities of XH₃ (X=N, Sb) molecules are investigated employing three-dimensional dipole moment surfaces combined with the local mode Hamiltonian model.The dipole moment surfaces of NH₃ and SbH₃ are calculated with the density functional theory and at the correlated MP2 level,respectively. The calculated band intensities are in good agreement with the available experimental data. The contribution to the band intensities from the different terms in the polynomial expansion of the dipole moments of four group V hydrides (NH₃, PH₃,AsH₃ and SbH₃) are discussed. It is concluded that the breakdown of the bond dipole approximation must be considered. The intensity “borrowing” effect due to the wave function mixing among the stretching vibrational states is found to be less significant for the molecules that reach the local mode limit.     

CALCULATIONS OF STRETCHING VIBRATIONAL OVERTONES AND COMBINATIONS OF ARSINE BY NONLINEAR MODEL

A three-parameter nonlinear model in nonlinear quantum theory,i.e.,the quantized discrete self trapping equation, has been used to calculate the vibrational energy spectrum, including the overtones and combinations with many excited quanta, of AsH stretches of arsine, AsH₃. The model calculations agree well with experiment and other calculations. It is shown that the dominant feature of the energy spectrum of AsH₃ molecule is a pattern of local mode pairs, and that when n≥4, all the vibrational energies are almost localized on a single AsH bond.     

Dynamical potential approach to dissociation of H--C bond in HCO highly excited vibration

The highly excited vibrational levels of HCO in the electronic ground state, \tilde {X}¹A',are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be very useful for interpreting the intramolecular vibrational relaxation (IVR) which operates via the HCO bending motion. The IVR inhibits the dissociation of H atom and enhances the stochastic degree of dynamical character. This approach is from a global viewpoint on a series of levels classified by the polyad number which is a constant of motion in a certain dynamical domain. In this way, the seemingly complicated level structure shows very regular picture, dynamically.     

A NONLINEAR MODEL FOR HIGHLY EXCITED VIBRATIONAL ENERGY LEVELS OF SILANE

The highly excited vibrational energy levels of SiH stretches of silane SiH₄ in the electronic ground state are calculated using a three-parameter nonlinear model, i.e., the quantized discrete self-trapping equation. The obtained results are in good agreements with the experimental data and with those obtained from local mode calculations of others. We note that SiH₄ molecule is a typical molecule close to the local mode limit, and that when n≥3, the molecule could be thought of as vibrating with the four SiH stretching quanta trapped into a single SiH bond.     

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.