Mullikens Classification of Predissociations

Mulliken (1960) has distinguished several classes of predissociation based on the location of the curve crossing (Ec, Rc) relative to the dissociation energy (D°) and the Re of the predissociated state. Cases b, a, and c correspond to Ec D°,Ec = D°, and Ec D°, respectively. The superscripts —, i, +, and 0 specify the cases Rc Re,Rc = Re-, Rc Re, and non crossing potentials, respectively. For the present discussion, it is useful to retain only Mulliken s —, +, and 0 classifications. It is immaterial whether the predissociating curve is partly attractive or completely repulsive. These three classes of predissociation 

at any iZ-value, the centrifugal energy is identical for all potential curves, Rc does not change with J. Consequently, the J-dependent energy of the curve crossing is given by 

At the right of Fig. 7.22 is a plot of the calculated variation of T versus E at a constant J-value, designated as Jmax- The oscillations in T versus J within a given u-level are rapid for hydrides because of their large rotational constants. For heavier molecules such as O2, the linewidths show only a slight, 7-dependence (Lewis, et al., 1980). The linewidth maximum occurs at an energy 

To a good approximation, the vibrational overlap integral is determined in the region near Rc, the point of stationary phase. This means that (Xv,j Xe,j) will be a function of the energy difference, Evj — Ec(J), and will be largely insensitive to the values of v and 7. However, 

The rates of oscillation of the linewidth and level shift versus Ev j — Ec(J) depend on the difference in the slopes of the two potentials at Rc [Eq. (7.6.3)]. Murrell and Taylor (1969) describe many examples of the variation of T with v. Several exceptions to the expected strong fluctuation in T of outer limb crossing will be discussed in Section 7.14. 

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