Repulsive curve

If the neon-neon interaction were a pure dispersion one, then the HF-LCAO calculation would give a fully repulsive curve. The fact that the HF-LCAO calculation gives a shallow minimum implies an element of covalency. 

The recombination of He is a special case. We include it here because of the similarities with H3 and because it is the only known example where three-body recombination of a diatomic molecular ion dominates over the binary process. The literature on the helium afterglow is quite large and we will not be able to do justice to all aspects of this problem. Mulliken71 had predicted that fast dissociative recombination of Hej should not occur due to a lack of a suitable curve crossing between the ionic potential curve and repulsive curves of He. Afterglow experiments in pure helium, at sufficient pressure to enable formation of Hej ions, have confirmed this expectation. It does not appear that the true binary recombination... 

Fig. 1.4. Vibrational motion induced by Lochfrass as well as the detection scheme using a repulsive curve of Ij+ [16]...

The attraction and repulsion curves that describe the interaction of a pair of colloidal particles are usually not as evenly matched as those shown in Figure 10. la. Next let us consider... 

Figure 2.9 Potential energy curve for a diatomic molecule, (a) Attractive curve—bonding interaction (b) repulsive curve—antibonding interaction.

The predissociation probabilities for various vibrational levels of the B3Z state have been calculated (726) assuming a repulsive curve that crosses the B3E state near v = 4. Both at 1849 (1011) and at 1470 A (954) the quantum yield of 03 formation is 2, indicating a direct dissociation... 

Figure 8.2 Total interaction energy curves, V(l) and V(2), obtained by the summation of an attraction curve, VA, with different repulsion curves, VR(1) and Vr(2)...

Fig. 3. E as a function of r [Eq. (4)]. Curve A gives the energy of attraction, curve R the energy of repulsion curve W is the resultant curve.

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,... 

C. He2.—Work on Hea and HeJ has been thoroughly reviewed recently.7 The repulsive curve has been extensively studied in the past, and the various components have been analysed. The recent calculations by Bertoncini and Wahl90 and McLaughlin and Schaefer,01 who studied the long-range attraction, have been supplemented by two recent studies not reviewed in ref. 7. Liu and McLean02 have... 

In the case of noble-gas compounds HeB+, NeB+, and ArB+, repulsive curves were computed,296 but it was suggested that XeB+ might be bound. Finally, an extensive SCF calculation near the HF limit was reported by Liu and Schaefer for KrF and KrF+ 296,297 KrF+ is predicted to be bound (Re = 1.68 A De = 0.02 eV). First-order wavefunctions still predict KrF to be repulsive, but for KrF+, Rc = 1.75 A, De = 1.90 eV. The latter has been observed experimentally (DfXF i 1.58 eV) and KrSbFi2 (KrF+SbF ) has been synthesized. Several molecular properties were computed in this work. 

Figure 28. The HCl excited-state repulsive curve is plotted adjacent to the H-OCO curve obtained by having the H atom approach CO along its axis, with its nuclei fixed at the equilibrium positions (see Figure 18a). The initial Cl-O separation is that of the COj-HCl weakly bonded complex. Note the overlap of the curves.

Kittel s simple theory gives rise to the prediction of purely repulsive interaction curves. This is in marked contrast to the defect force theories which predict the existence of minima in the interaction function. Kittel argues that repulsive curves are required to explain infinite adaptability. For if minima were present in the interaction function, those solutions whose compositions corresponded to interplanar spacings considerably displaced from the minimum would be unstable with respect to separation into two phases, one of whose composition gave a separation nearer to the minimum. The argument cannot be faulted granted thermodynamic control of the ordering in these structures. It is, however, far from certain that kinetic factors do not play a decisive role in the structure of these compounds. 

Also the A n state involves two dominant configurations. The interaction between the boron (2s) (2p) ground state and hydrogen is repulsive in this symmetry. A attractive potential between the excited boron (2s) (2p) configuration and hydrogen crosses over the repulsive curve, resulting in an... 

With respect to the last quotation, it is known from the literature on the Be2 bond, for example. Refs. [95, 103], and is verified here again as part of a series of calculations, that a CASSCF calculation that uses (2s, 2p as the active set of zero-order spin orbifals yields essentially a repulsive curve. This fact has been emphasized in Ref. [95], who carried out not only large-scale calculations but also an in-depth analysis of fhe origin of the Be-Be bond, by emphasizing that "the binding in Be2 is contingent on the effects of dynamical electron correlation, which is uncommon and therefore of considerable interest." ([95], p. 8687). 

FIGURE 9-1 Total interaction energy curves (obtained by summation of attraction and repulsion curves) for two repulsion curves of different heights. 

As long as the two parameters A and b or A and n are chosen so that the repulsive curve crosses the bound curve at the same point, Rc, and with the same slope, overlap factors obtained from either form of the potential are nearly identical (Julienne and Krauss, 1975). In practice, the two parameters of Eqs. (7.6.1) or (7.6.2) axe varied until optimal agreement with the experimental vibration-rotation dependence of T (or r) is obtained. 

If V and the form of

turning points (Child, 1973, 1974). This method is useful for obtaining an initial approximation for the repulsive potential. However, if only a few experimental r -values are known, it is difficult to identify unambiguously the oscillatory frequency of T versus v. For example, in Fig. 7.20 the number of vibrational levels sampled is insufficient to determine the actual shape of r . 

For a crossing on the left side (repulsive branch) of the bound potential, an inner crossing or one of Mulliken s a-, c, or b predissociation cases, a single oscillation of r will extend over many vibrational levels so that, in practice, only a small variation with v (and J) can be sampled (see Fig. 7.23). The reason for this is that the slopes of the bound and repulsive curves at Rc are much larger and more nearly equal for an inner rather than an outer wall crossing. Consequently, as EVtj—Ec increases, the innermost maximum of Xv,j(R) moves to smaller R much more slowly than the outermost maximum sweeps to larger R. 

It is insufficient, having obtained an approximate shape for the dissociative curve from the study of the relative variation of T (or r), for the interpretation of the predissociation to be complete. An equally important but often quite difficult step consists of accounting for the absolute value of T. The mere presence of a crossing by a repulsive curve is not sufficient to cause predissociation of bound levels. A value for the electronic interaction He may be deduced from an experimental value for r j if the calculated value of (Xv,j Xe,j) is introduced into Eq. (7.5.16). This semiexperimental value for He may be compared to a calculated or estimated value. The few cases that have been completely interpreted are listed in Tables 7.3 and 7.4. 

One should not be left with the impression that electronically nonadiabatic processes are limited to predissociation. Figure 1(a) shows a crossing between two excited repulsive curves in the photolysis of methyl iodide. If the surface hopping process is efficient enough, it can even influence a dissociating molecule that passes the curve crossing within a few femtoseconds, as is the case for methyl iodide photodissociation. 

C) where B is at its equilibrium bond distance from one of the other atoms. Actually this resonance has a finite energy for all distances. This means that the repulsion curve II, Figure 48, includes a small resonance effect, and the resonance curve (IV) gives... 

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