RKR method

The long-range part of the halogen-halogen potential correlating with the B3ITou excited state of the diatomic molecule has been obtained by the RKR method, yielding C5, Cz, and C coefficients for I -I,143 Br- -Br, and Cl- C1.144... 

Finally, we note that this discussion of the RKR method has been given in energy units (J). The equations must be divided throughout by he if the equivalent expressions in wavenumber units, for example, are required. 

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... 

EBK) semiclassical quantization condition given by Eq. (2.72). In contrast to the RKR method for diatomics, a direct method has not been developed for determining potential energy surfaces from experimental anharmonic vibrational/rotational energy levels of polyatomic molecules. Methods which have been used are based on an analytic representation of the potential energy surface (Bowman and Gazdy, 1991). At low levels of excitation the surface may be represented as a sum of quadratic, cubic, and quartic normal mode coordinates (or internal coordinate) terms, that is,... 

Fig.2 Test of the rotational RKR method. Solid and open dots refer to inner and outer turning points for J=0-30 in steps of 5. Residuals are riven for (a) Lennard-Jones (b) Morse (c) no iterative refinement. (Taken irom ref.5 with permission).

A test of this method for 1-D radial potentials is shown in Fig. 2. Here we have taken an assumed intermolecular potential (shown in solid line) for a weakly bound diatomic molecule (which for realism had well depths and radial minima similar to a psuedo diatomic treatment of Ar-HF), and solved exactly for the J = 0, 5, 10, 15, 20, 25, and 30 eigenvalues for v=0 by exact close coupling quantum calculations. These eigenvalues are then taken as input into the rotational RKR method, which attempts to regenerate the initial potential. 

To capture the flavor of the method, consider the limit of a M-HX complex in which the intermolecular potential is mostly isotropic, but with sufficient anisotropy so the nearly free internal HX rotor motion is oriented in the body fixed frame. The ground state of such a complex would look like a j=0 HX rotor (i.e. an "s" orbital) bound to M, whereas the three lowest excited HX bending states would approximate the three j l rotor wave functions (i.e. three "p" orbitals) oriented with respect to the end-over-end plane of rotation of the M-HX centers of mass, one in a S and two in a II configuration. The j=0 HX rotor state probes predominantly the isotropic part of the intermolecular radial potential, whereas j=l HX rotor states (the S and either one of the II configurations) begin to sample in addition the lowest order anisotropic parts of the potential. The radial dependence of the intermolecular potential for each of these three states can be determined from rotational RKR method. In principle, these curves contain sufficient information to determine the three lowest... 

Diatomic molecules are a special case. Firstly, the dynamics of atomic collisions can usually be calculated accurately, and there are some inversion techniques that allow one to predict the potential from the experimental data the RKR method of analysing spectroscopic data is the most well known of these [1]. Secondly, the potential energy functions are one dimensional and even "complicated functions are simple compared with those of polyatomic molecules. 

---