Based on the multiple-scattering self-consistent-field theory, we have studied the molecular Rydberg states of the molecules B2,HF,H2O,NH3 and CH4 with Ne as their united atoms. From the united atomic limite of molecular electronic configuration, we set a convention to determine the principal quantum number of fhe initial states of a Rydberg series. The dynamics of the excited molecules are elucidated. The theoretical calculations are in fair agreement with the available experimental results.