By using the Rayleigh-Schrödinger perturbation theory the rovibrational wave function is expanded in terms of the series of functions 0 , 1 , 2 , . . . n , where 0 is the pure vibrational wave function and are the rotational harmonics. By replacing the Schrödinger differential equation by the Volterra integral equation the two canonical functions 0 and 0 are well defined for a given potential function. These functions allow the determination of (i) the values of the functions at any points; (ii) the eigenvalues of the eigenvalue equations of the functions 0 , 1 , 2 , . . . n which are, respectively, the vibrational energy E v , the rotational constant B v , and the large order centrifugal distortion constants D v , H v , L v . . . .. Based on these canonical functions and in the Born-Oppenheimer approximation these constants can be obtained with accurate estimates for the low and high excited electronic state and for any values of the vibrational and rotational quantum numbers v and J even near dissociation. As application, the calculations have been done for the potential energy curves: Morse, Lenard Jones, Reidberg-Klein-Rees (RKR), ab initio, Simon-Parr-Finlin, Kratzer, and Dunhum with a variable step for the empirical potentials. A program is available for these calculations free of charge with the corresponding author.