Adiabatic potential curve

In conclusion, it is suggested that a spin combination rule may be an important criterion in determining whether or not reactants may follow an adiabatic, potential curve corresponding to a low lying state of an intermediate. This, in turn, may determine whether or not there will be strong attraction or weak, or even a barrier preventing fast reaction at low energy. 

Fig. 1. A schematic diagram of the relationship between adiabatic potential curves and reactive resonances, (a) shows the conventional Feshbach resonance trapped in a well of an adiabatic curve, (b) illustrates barrier trapping, which occurs near the energy of the barrier maximum of an adiabatic curve.

Figure 1. Adiabatic potential curves in the main chain scission of a model compound of poly(isobutylene) 2,2-, 4,4-tetramethylpentane (4). AE3l(=0.61eV), aET,(—0.35eV), and AEf (=2.05eV) are the activation energies of the main chain scission in the lowest singlet excited state (S,), the lowest triplet state (T,), and the ground state, respectively.

Figure 1. Diabatic potential energy curves for Nal with an expanded view of the adiabatic potential curves, e, and Ej, near the diabatic curve crossing.

Fig. 11.24 Adiabatic potential curves for the Rb-Rb system. The initially populated Rb nl Rydberg state can lead to associative ionization if its energy at R = exceeds the minimum of the Rb+ + Rb 5s potential well, as shown.

Figure 3.1 A schematic diagram showing the relationship of reactive resonances to the vibrationally adiabatic potential curve. The upper panel illustrates a Feshbach resonance trapped in a well the lower panel shows a barrier resonance or QBS.

Fig. 3.5. Adiabatic potential curves en(R), defined in (3.31), for the model system illustrated in Figure 2.3. The right-hand side depicts three selected partial photo dissociation cross sections cr(Ef,n) for the vibrational states n = 0 (short dashes), n = 2 (long dashes), and n = 4 (long and short dashes). The vertical and the horizontal arrows illustrate the reflection principle (see Chapter 6). Also shown is the total cross section (Jtot Ef) ...

Fig. 6.4. Schematic illustration of the multi-dimensional reflection principle in the adiabatic limit. The left-hand side shows the vibrationally adiabatic potential curves en(R). The independent part of the bound-state wavefunction in the ground electronic state is denoted by

Fig. 7.1. Schematic illustration of indirect photodissociation for a one-dimensional system. The two dashed potential curves represent so-called diabatic potentials which are allowed to cross. The solid line represents the lower member of a pair of adiabatic potential curves which on the contrary are prohibited to cross. The other adiabatic potential, which would be purely binding, is not shown here. More will be said about the diabatic and the adiabatic representations of electronic states in Chapter 15. The right-hand side shows the corresponding absorption spectrum with the shaded bars indicating the resonance states embedded in the continuum. The lighter the shading the broader the resonance and the shorter its lifetime.

The upper part of Figure 7.10 clearly elucidates the relationship between internal vibrational excitation of NO in the CH30N0(5i) complex on one hand and the resonance structures in the absorption spectrum on the other. It is the two-dimensional analogue of Figure 7.1. The adiabatic potential curves readily provide the correct assignment of the resonance structures. 

The correlation rules for determining what types of molecular electronic states result from given electronic states of the separated atoms were derived quantum mechanically by Wigner and Witmer [1] and are discussed in great detail by Herzberg [2], These correlation rules hold for the adiabatic potential curves of the electronic states1 when Russell-Saunders coupling is valid for the separated atoms as well as the molecule. 

Time evolution of the ground state hole as well as fluorescence spectra initiated by a short pulse laser irradiation in solution has been conventionally explained in terms of the two-dimensional configuration coordinate model by Kinoshita . According to his theory, two adiabatic potential curves corresponding to the ground and excited states are assumed to have the same curvature but have the different potential minimum in the configuration coordinate. 

---