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.
The rotational invariants constructed by the products of three spherical harmonic polynomials are expressed generally as homogeneous polynomials with respect to the three coordinate vectors in the compact form,where the coefficients are calculated explicitly in this paper.
