Long-range near-dissociation interactions

Most spectroscopic studies involve the lowest energy vibration-rotation levels, and the determination of the values of the molecular parameters at or near the equilibrium position. This is equally true of most theoretical studies indeed there are many published accurate ab initio calculations of equilibrium properties which do not even extrapolate with the correct analytical form to the dissociation asymptote. Calculations which 

Higher values of n can also arise, but for obvious reasons will seldom be significant in determining the long-range potential. 

Now the integral will be nearly unchanged if the exact potential V(R) is replaced by an approximate function which is accurate near the outer turning point R2(v) in other words the approximation 

After evaluation of the integral this can be rearranged [102] to give the result 

The T functions are tabulated by Abramowitz and Segun [85]. An alternative and more useful version of (6.410) is 

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In a similar fashion the bonding in H2 might be formally regarded as a complementary pair of one-electron donor-acceptor interactions, one in the ot (spin up ) and the other in the 3 (spin down ) spin set.8 In the long-range diradical or spin-polarized portion of the potential-energy curve, the electrons of ot and (3 spin are localized on opposite atoms (say, at on HA and 3 on HB), in accordance with the asymptotic dissociation into neutral atoms. However as R diminishes, the ot electron begins to delocalize into the vacant lsB(a) spin-orbital on HB, while (3 simultaneously delocalizes into Isa on HA, until the ot and (3 occupancies on each atom become equalized near R = 1.4 A, as shown in Fig. 3.3. These one-electron delocalizations are formally very similar to the two-electron ( dative ) delocalizations discussed in Chapter 2, and they culminate as before (cf. Fig. 2.9) in an ionic-covalent transition to a completely delocalized two-center spin distribution at... 

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