Appendix Energy of the Separated Pair Function

The only permutations Pr which give non-zero contributions to (118) are those which permute the co-ordinates of an electron pair function, and transpositions Pwhich correspond to a term g from (117). The normalization integral is given simply by 

Matrix elements of H between separated pair functions which differ in the spin coupling index k are given by 

The earliest anharmonic force field calculations on polyatomic molecules were made by Pliva and co-workers.1-2 More recently, Kuchitsu and Morino and co-workers,4-7 Overend and co-workers,8-10 Cihla and Chedin,11 and Hoy, Mills, and Strey12 have developed the techniques of calculation and applied them to a wide variety of molecules many other workers have reported calculations on particular molecules, as discussed in Section S. A recent review by Pliva12 contains reference to most published calculations on particular molecules up to 1973. 

The primary motive for attempting calculations of this kind is simply our desire to determine the potential function V(r) more accurately and over a wider range of co-ordinate space. Even if our immediate ambition is only to determine the equilibrium configuration and the harmonic force field, our ability to withdraw this information from spectroscopic data is limited by the need to make corrections arising from the cubic and quartic anharmonic force field. 

A secondary motive is our general desire to verify and extend our understanding of vibration-rotation interactions in molecular spectra, and particularly to interpret data on different isotopic species in a consistent manner. Consider, for example, a constants (which measure the dependence of the rotational constant B on the vibrational quantum numbers vr) determined experimentally for several isotopic species of the same molecule. It is clear that these constants are not all independent, since they are related to the potential function which is common to all isotopic species. However, the consistency of the data and of our theoretical formulae can only be tested through a complete anharmonic force field calculation (there are at this time no known relationships between the a values analogous to the Teller-Redlich product rule). Similar comments apply to many other vibration-rotation interaction constants. 

---