Vibrational factors

The isotope effects of reactions of HD + ions with He, Ne, Ar, and Kr over an energy range from 3 to 20 e.v. are discussed. The results are interpreted in terms of a stripping model for ion-molecule reactions. The technique of wave vector analysis, which has been successful in nuclear stripping reactions, is used. The method is primarily classical, but it incorporates the vibrational and rotational properties of molecule-ions which may be important. Preliminary calculations indicate that this model is relatively insensitive to the vibrational factors of the molecule-ion but depends strongly on rotational parameters. 

Thus, the efficiency (rate) of internal conversion and intersystem crossing depends on both electronic and vibrational factors ... 

Vibrational factors involve the operation of the vibrational wave-function overlap with the radiationless transitions. 

Thus for a diatomic molecule, the vibrational factor is always symmetric with respect to E and so does not play any part in the symmetry classification scheme. 

Each molecular vibration factor in Equation (3) is a type of molecular time correlation function for the internal vibrational dynamics. In the harmonic approximation, i) and f) would reduce to the harmonic vibrational eigenstates and the qj would be the actual molecular normal modes. Then one has the simplification... 

The rotational and vibrational factors in the partition function of the diatomic molecule A are given by equations (16.24) and (16.30), respectively. These are independent of the pressure (or volume) and require no adjustment or correction to the standard state. 

The vibrational factors f0, gi and g j of (4.5) can be expressed in terms of creation operators at, of SSANMV operating on the ground state function of noninteracting phonons namely... 

A, Rc = 1.915 A, and vibrational factors calculated using eigenfunctions of the deperturbed adiabatic potentials. 

The observability of a perturbation between levels 1, Vi,J 2, vj, J requires that both the electronic and vibrational factors be nonzero. For example,... 

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... 

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. 

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