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Vibrational properties of ultralong Rydberg Cs molecules are investigated on corresponding potential curves obtained by perturbation theory. The Rydberg Cs molecules are associated by a Rydberg Cs() atom and a ground state Cs() atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential curves is to generate accurate atomic Rydberg states from realistic {\it ab initio} effective core potential. The calculated results have similar characteristics with available experimental and theoretical investigations on Rydberg Rb molecules. And this is the first time that Rydberg molecules are studied at the {\it ab initio} level.

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