Uq(2)⊃Uq(1) Description of Vibrational Spectra of Diatomic Molecules

q-deformation of the U(1) dynamical symmetry of U(2) group is introduced for the first time for vibrations of diatomic molecules. The question of pure real and pure imaginary value of q-deformation parameter, often raised in the literature, is found to be related to the particular choice of the constants of the model. The complex q-deformation parameter is allowed, with pure real and pure imaginary values as its special cases. Compared to the other dynamical symmetry O_q(2) of U_q(2), the result of U_q(1) of U_q(2) remains better even when the vibron number in O_q(2) is varied. The role of the vibron number in the two dynamical symmetries of U(2) is shown to be different. In U_q(1) symmetry, the vibron number is fixed by the number of observed states of the system since U_q(1) represents the q-deformation of a truncated anharmonic oscillator. A possible physical meaning to the q-deformation parameter is suggested in terms of higher order anharmonicities of the truncated anharmonic oscillator.