Application of a symmetry adapted algebraic model to the vibrational spectrum of methane

Recently, a symmetry-adapted version of the vibron model has been developed [14]. The aim of this work is to present the description of all stretching and bending vibrations of the methane molecule in the framework of such a model. In the present algebraic approach a U(2) algebra is associated with each relevant interatomic interaction. For the CH4 molecule we have four U(2) algebras corresponding to the C-H interactions and six more representing the H-H couplings. The assignments and the choice of the Cartesian coordinate system are the same as in []. The molecular dynamical group is then given by the product U1(2)⊗ . . .⊗ U10(2), where each Ui(2) algebra (i = 1, . . . , 10) is generated by the set {Ĝi} ≡ {N̂i, Ĵ+,i, Ĵ−,i, Ĵ0,i}, which satisfies the commutation relations