Isotope effect on a vibrational level

The electronic factor can also provide an explanation for a nonperturbation and a test of a vibrational assignment (Robbe, et al., 1981). However, this factor can only be computed ab initio or, sometimes, estimated semiempiri-cally. This dependence on theoreticians for the electronic factor is in contrast to the situation for the vibrational factor, which is routinely calculable by the 

The ultimate test of a deperturbation consists of (1) a demonstration that all observed perturbation matrix elements have the v, J -dependence required by the factorization into electronic and vibrational parts (2) agreement between the observed and ab initio values of Hf2 Rc) (3) verification that the molecular constants for both electronic states are internally consistent [isotope shifts, Dv values calculable from G v) and Bv functions] (Gottscho, et al, 1979 Kotlar, et al, 1980). 

Most spectroscopists are comfortable using RKR and Franck-Condon programs as black boxes. Since these programs are widely available, inexpensive to run, and generate more accurate vibrational factors than semiclassical or model potential approaches, the application-minded reader is advised to skip Sections 5.1.1 and 5.1.2. 

Given a potential energy curve, it is possible to locate (iteratively) the vibrational energy levels using the semiclassical quantization condition 

The JWKB wavefunction defined by Eq. (5.1.3) is appropriate for either bound (two turning points) or unbound states (one turning point), provided that R is restricted to the region where E V (R). The normalization factor for the unbound yJWKB at energy E is 

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Figure 5.1 Isotope effect on a vibrational level of the B,2II state of the PO molecule.

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