Rydberg-Klein-Rees potential

Nem Nemes, L., Szalay, P.G. Rydberg-Klein-Rees potential function calculations for the ground (X H) and excited (B X ) states of the methylidyne (CH) radical. Models in Chemistry 136 (1999) 205-214. 

Fig. 4. Rydberg-Klein-Rees potential energy curves of NH and ND a) X 11 and a states from [1], b) X and B states from [2].

The analysis of spectroscopic data for bound states of diatomic molecules gives accurate potential curves if one follows the semi-classical Rydberg-Klein-Rees method. For a review of this see Ref. 126). It is sufficient to note that this gives the two values of r as a function of potential energy by considering the dependence of the total spectroscopic energy on the vibrational and rotational quantum numbers n and J. A somewhat simpler procedure, and the only one plicable to polyatomic molecule, is to use the Dunham expansion of the potential 127). 

The potential curves derived from such calculations can often be empirically improved by comparison with so-called experimental curves derived from observed spectroscopic data, using Rydberg-Klein-Rees (RKR) or other inversion procedures. It is often found, particularly for the atmospheric systems, that the remaining correlation errors in a configuration interaction (Cl) calculation are similar for many excited electronic states of the same symmetry or principal molecular-orbital description. Thus it is often possible to calibrate an entire family of calculated excited-state potential curves to near-spectroscopic accuracy. Such a procedure has been applied to the systems described here. 

Nesbitt, D.J., Child, M.S., and Clary, D.C. (1989). Rydberg-Klein-Rees inversion of high resolution van der Waals infrared spectra An intermolecular potential energy surface for Ar+HF(t = 1), J. Chem. Phys. 90, 4855-4864. 

The Rydberg-Klein-Rees (RKR) procedure is the most widely used method for deriving V(R) from the G(v) and B(v) functions of diatomic molecules. Countless RKR computer programs of independent origin exist, with differences primarily in the way a singularity at the upper limit of integration of Eqs. (5.1.39a or b) and (5.1.40a or c) is handled, all of which give essentially identical results (see Mantz, et al, 1971 for the CO X1E+ potential), except... 

For a diatomic molecule the Rydberg-Klein-Rees (RKR) method may be used to determine the potential energy curve V r) from the experimental vibrational/rotational energy levels (Hirst, 1985). This method is based on the Einstein-Brillouin-Keller... 

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. 

Fitting a Rydberg-Klein-Rees-Vanderslice potential function for the ground state of NH (cf. p. 54) to the empirical Lippincott potential function (see [39]) resulted in Dq = 3.45 0.14eV [40]. 

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