Zeta constants

In practice, the result of the perturbation treatment may be expressed as a series of formulae for the spectroscopic constants, i.e. the coefficients in the transformed or effective hamiltonian, in terms of the parameters appearing in the original hamiltonian, i.e. the wavenumbers tor, the anharmonic force constants , the moments of inertia Ia, their derivatives eft , and the zeta constants These formulae are analogous to equations (23)—(27) for a diatomic molecule. They are too numerous and too complicated to quote all of them here, but the various spectroscopic constants are listed in Table 3, with their approximate relative orders of magnitude, an indication of which parameters occur in the formula for each spectroscopic constant, and a reference to an appropriate source for the perturbation theory formula for that constant. 

Thus the zeta constants are sensitive to the eigenvectors of the vibrational secular equation, and it is clear that this is potentially useful information to add to the observed vibration frequencies or eigenvalues. Unfortunately, it is only when the two vibrations vr and vs are degenerate or nearly degenerate that the rotational structure is sufficiently perturbed to allow one to deduce the value of the zeta constant from rotational analysis. The zetas are dimensionless and of magnitude 1 > f > -1 [from Eq. (3)1. Their values for the interaction between two components of a degenerate vibration in a symmetric top or spherical... 

Figure 6 illustrates the use of an observed zeta constant for ethylene,, to determine the B2U species force field.8 Since the form of Qf is in this case determined by symmetry, the observed zeta may be regarded as a source of information on the form of Qi0, which is one of the two B2u modes Q9 and Ql0 The graph directly illustrates the accuracy with which the force field is determined by the observation. Other examples of molecules where zeta constants for degenerate vibra-... 

FIGURE 6 Use of observed zeta constant f 7 10( ) for ethylene to determine the force field. 

The vibrational dependence of the inertia defect is given by formulas developed by Laurie and Herschbach20 and also by Oka and Morino21 involving the harmonic vibration frequencies and the Coriolis zeta constants ... 

Coriolis zeta constant angular momentum quantum numbers see additional information below 1... 

In addition to the vibration frequencies and the zeta constants, Aldous and Mills Included in their determination of the force field the data then available on the centrifugal-... 

An accurate analysis on this point was made by Richardson for the Ng molecule and leads to very interesting conclusions. This author calculated the field gradient by using the Ransil s molecular orbitals in the approximation (i) (zeta constant), (iii) (zeta varied in the molecule), and a new type of molecular orbital [approximation (iv)] with a more extended basis, in which each atomic orbital 2s and 2p of the nitrogen atom is composed of two Slater-type functions with different zeta parameters (double zeta approximation). 

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