Spectroscopic general valence force field

Let us consider the description of a simple three-atom molecule by the three most frequently used spectroscopic parameterization schemes, the general central force field (GCF), the general valence force field (GVF) and the Urey-Bradley force field (UBF Fig. 2.14). 

The general valence force field of pyramidal XY3-type molecules contains six independent constants. In internal coordinates, these are the stretching and bending force constants f and f , and four interaction constants f r for two adjacent bends, fr and fr . for a stretch and an adjacent and a nonadjacent bend, and fo two bends. Besides the four fundamental frequencies, additional spectroscopic data such as isotopic frequency shifts, centrifugal distortion constants, and Coriolis coupling constants are required to fix a unique set of force constants. Various authors have performed such calculations, and the sets so obtained [13, 14, 25, 26, 35 to 38, 45] agree reasonably well. As a representative example, the symmetry and valence force constants, all in mdyn/A, of Sawodny et al. [25] are presented below. 

Kuchitsu and co-workers5 7 were the first to introduce what is perhaps the simplest and most generally useful model, in which they assume all anharmonic force constants in curvilinear co-ordinates to be zero with the exception of cubic and quartic bond-stretching constants. These may be estimated from the corresponding diatomics, or from a Morse function, or they may be adjusted to give the best fit to selected spectroscopic constants to which they make a major contribution. This is often called the valence-force model. It is clear from the results on general anharmonic force fields quoted above that this model is close to the truth, and in fact summarizes 80 % of all that we have learnt so far about anharmonic force fields. 

Efforts have also been made to devise more sophisticated models, with a few more parameters, because some of the spectroscopic constants generally show a sensitivity to features of the force field which are not present in the valence force model. They range from extended Urey-Bradley models,7 through semi-empirical valency models,1 to an ad hoc introduction of extra anharmonic... 

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