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Vibrational properties of ultralong Rydberg Cs$_2$ molecules are investigatedon corresponding potential curves obtained by perturbation theory. The RydbergCs$_2$ molecules are associated by a Rydberg Cs($nS/nP$) atom $(n=30-70)$ and aground state Cs($6s$) atom. The starting point for the perturbation treatmentof corresponding Rydberg molecular potential curves is to generate accurateatomic Rydberg states from realistic {\it ab initio} effective core potential.The calculated results have similar characteristics with available experimentaland theoretical investigations on Rydberg Rb$_2$ molecules. And this is thefirst time that Rydberg molecules are studied at the {\it ab initio} level.

Ultralong Rydberg Cs$_2$ Molecules Investigated by Combined ab initio Calculations and Perturbation Theory