Estimates and interpretation of parameters in the effective Hamiltonian

As we explained earlier in this chapter, one of the great merits of the effective Hamiltonian is that it allows the two tasks of fitting experimental data and interpreting the resultant parameters to be separated. In this section we discuss the latter aspect and explain how the quantities obtained from a fit of experimental data can be interpreted in terms of the geometric and electronic structure of the molecule concerned. We have seen how the process of averaging the parameters over the vibrational motion of the molecule leads to additional terms which describe the vibrational dependence of the parameters. We shall assume in what follows that all such vibrational averaging effects have been properly taken into account and that we are left to deal with the equilibrium value of the parameter, Pe, in equation (7.180). 

It is well known, and shown earlier in this book, that the rotational constant of a diatomic molecule is very simply related to its bond length (R) and reduced mass (// ), 

The dominant contribution to the rotational constant is from the nuclear masses. There is also a small contribution from the electrons in the molecule which is of the order ( me/mN)Be = ic4Be 10 413, where me and are the masses of an electron and a 

In effect, the equilibrium bond lengths of different isotopomers are found to be slightly different. As we have discussed elsewhere, Watson [25] has shown that the equihhrium bond length Rg obtained by the use of equation (7.256) can be related to the Bom 3ppenheimer equdibrium bond length Rf (the bond length at the minimum of the potential energy curve) by the equation 

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