Rydberg-Klein-Rees points

The Dunham coefficients Yy are related to the spectroscopical parameters as follows 7io = cOe to the fundamental vibrational frequency, Y20 = cOeXe to the anharmonicity constant, Y02 = D to the centrifugal distortion constant, Yn = oie to the vibrational-rotational interaction constant, and Ym = / to the rotational constant. These coefficients can be expressed in terms of different derivatives of U R) at the equilibrium point, r=Re. The derivatives can be either calculated analytically or by using numerical differentiation applied to the PEC points. The numerical differentiation of the total energy of the system, Ecasccsd, point by point is the simplest way to obtain the parameters. In our works we have used the standard five-point numerical differentiation formula. In the comparison of the calculated values with the experimental results we utilize the experimental PECs obtained with the Rydberg-Klein-Rees (RKR) approach [58-60] and with the inverted perturbation approach (IPA) [61,62]. The IPA is method originally intended to improve the RKR potentials. 

The classical turning points, and r ax. of the vibrational levels have been calculated for the ground state X Z (v = 0 to 6 molecular constants from [6]) assuming a Rydberg-Klein-Rees-Vanderslice potential [7], for the X Z and A Ili states (v and v" = 0 to 8 molecular constants from [8]) assuming Morse and modified Rydberg-Klein-Rees (RKR) potentials [9], and for the b Z and d Z" states (v and v" = 0 to 3 molecular constants from [10]) assuming modified RKR and simplified potentials [11] and [12], respectively. 

---