Indeterminacies rotational contact transformations

If the values of the parameters for the vibronic state ri,v) are known a priori, the spin-rotational energy levels can be calculated in a straightforward manner from the effective Hamiltonian, equation (7.183), computing the matrix elements in a suitable 

The solution to this problem which is usually adopted in practice is to constrain particular parameters to preset values, usually zero, in a least-squares fit of the Hamiltonian to the data. This has the effect of modifying the values obtained for the other parameters in the Hamiltonian. In order to interpret the results in this situation, it is necessary to subject the effective Hamiltonian to yet another transformation to bring it into the form which is actnally used in the empirical fit. Before we do this, however, let us consider a particular example to help us understand the nature of these indeterminacies. There is a well-known indeterminacy between the parameters y,jv and in the Hamiltonian for a molecule in a 11 state, first pointed out by Veseth [33]. If we confine ourselves to the simple Hamiltonian 

The terms inside the square root part of this expression may be rearranged in increasing powers of z, to give 

If we make measurements of the energy levels for different J values, the coefficients of the different powers of z are determinable. Thus the following combinations can be determined  

The combination in equation (7.237) allows the value for 5 to be determined from the z dependence. With this value, it is possible to determine (A + y + An) from equation 

Conversely, if we choose to constrain A D to zero, we determine a value for the effective 

---