Dunham formulation

In place of equation (6.17), the potential energy of a diatomic molecule is usually given in the Dunham formulation ... 

When Dunham [4,5] presented formula 8 for vibration-rotational terms, he derived a functional V + V2 explicitly because in his JBKW formulation the addend V2 results from exact solution of an integral. In contrast, Dunham assumed a functional K(K+l), equivalent to /(/- -1) in contemporary notation, to contain a quantum number K, now J, for rotational angular momentum. To generate an effective potential energy comprising both internuclear potential... 

As we will see later, there is an alternative formulation of the rotational (and vibrational) energies due to Dunham [65], which is often used. 

As already discusf d for the single-oscillator case in Section II.C.2, it is possible to obtain Dunham-like form for the local-mode eigenspectrum (4.33). Given the anharmonic character of the algebraic formulation, we expect to find a certain number of relations between the Dunham coefficients similar to those of the x-K relations of Lehmann [73, 74]. In fact, we can compare the traditional Dunham series for a triatomic molecule... 

Here v and / are the vibrational and rotational quantum numbers, respectively, h is Planck s constant, and c is the speed of light. In this customary formulation the constants B, etc. have dimensions of inverse length in this table they are given in units of cm h Users should note that higher order terms in the above energy expressions are required for very precise calculations constants for many of these terms can be found in the references. Also, if the ground electronic state is not Z, additional terms are needed to account for the interaction between electronic and pure rotational angular momentum. For some molecules in the table the data have been analyzed in terms of the Dunham series expansion ... 

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