Dissociation limiting curve

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

Figures 11.9 and 11.10 compare the performance of the CCSD and CCSD(T) methods, based on either an RFIF or UHF reference wave function. Compared to the RMP plot (Figure 11.7), it is seen that the infinite nature of coupled cluster causes it to perform somewhat better as the reference wave function becomes increasingly poor. While the RMP4 energy curve follows the exact out to an elongation of 1.0A, the CCSD(T) has the same accuracy out to - 1.5 A. Eventually, however, the wrong dissociation limit of the RHF wave also makes the coupled cluster methods break down, and the energy starts to decrease.

Fig. 1.17. Experimentally determined potential energy curve for the state leading to the (2,0) dissociation limit...

BO energy curves of pertinent states we can expect the parallel component an to have singularities atR = 0.9873 and 15.4482 bohr whereas the perpendicular a at / = 1.8886 and 2.9055 bohr. Because all three interacting states have the same dissociation limit, A tends to zero when oo and we can also expect that both polarizability components will escape to infinity with growing R. 

Unfortunately, the failure of RHF is so severe that none of the correlated methods based upon it are able to overcome it (except, of course, full Cl). The MP2 curve diverges to negative infinity at the dissociation limit because of a near-degeneracy between the highest occupied and lowest unoccupied molecular... 

The treatment of loss of R from sterns is trivial dissociation occurs along some kind of bond dissociation curve to give, in the imagined limit, metal and a car-banion. In solution at least, both fragments will interact with the environment at bond distortion energies wefl below the dissociative limit. 

The harmonic approximation is typically a good approximation for low vibrational levels. The adiabatic approximation is often valid for high vibrational levels and even energies in the continuum above the dissociation limit. Both harmonic and adiabatic approximations are expected to fail when the separation between electronic energy curves is small compared to differences between vibrational levels. 

The Hartree-Fock potential energy curves are necessarily unsatisfactory towards the dissociation limit, and the most reliable overall potential energy diagram for Oa is that of Gilmore,8 although it does omit certain states of interest. The curves are reproduced in Figure 1. 

A composite potential curve for the bound stales of NO is shown in Fig. 42. Potential curves, including repulsive slates, are shown in Figs. 43 to 52 for each symmetry type. The low-lying molecular slates of NO and their dissociation limits are given in Table VII. The most important electronic... 

The potential curves for bromine (Fig. 4) are similar to those for chlorine, except that the excited atom, and the 3I70+U state correlating with it, lie higher relative to the ground state Br+Br limit than in the case of chlorine. This means that the minimum of the 3J70+U state is now very close to the dissociation limit of the ground state, rather than being considerably below it as in the case of Cl2. 

In closing the section on non-Hermitean approaches to continuum processes in atomic and molecular physics, we will also mention accurate examinations on resonance parameters in molecular predissociation displaying unexpected resonance overlapping [46,89]. The phenomenon of predissociation by rotation in HgH was analyzed via an isotopically combined potential due to Stwalley [120]. The potential, i.e., a relatively shallow energy curve with a nonzero /-value giving rise to a rotational barrier, supported novel metastable states above the dissociation limit. The Weyl s method was able to resolve the closely lying vibrational states v = 3 and v = 4 for the rotational quantum number K = 9. 

If the motion is not that of a harmonic oscillator, the PE is no longer proportional to the square of the displacement, and the equation describing the motion is now a curve with a plateau approaching a horizontal PE asymptote. This curve is the Morse curve. The asymptote represents the dissociation limit and the energy levels become closer together as the PE increases (Figure 4.19). 

Let us start the discussion with Fig. 15, which presents various levels of the approach to the potential curve of F2. The Hartree-Fock approximation is especially poor in this case because it does not lead to a correct dissociation limit, i.e. to the atoms in the Hartree-Fock ground states. In the case of F2, the proper dissociation is achieved... 

The curves of Figures 5.4 and 5.5 show remarkable dependence on the golden ratio. The attractive and repulsive curves intersect where d = r, at which point the diatomic dissociation energy D = 2r. Again, the limiting curves (marked 1.0 and 0.25(H) in Figure 5.5) are maximally separated at d = 2r,... 

Figure 2 shows that the ionic group curve, 02+0°, is asymptotically flat, going to the O2++O0 dissociation limit. The curve falls rapidly as R gets smaller and reaches a deep minimum at R-1.00A. The individual energy curve behaviors of the covalent and ionic structure groups,... 

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