Vibrationally adiabatic potential curves

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. 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

The energies of the nine features in Table 4 all correspond closely to the energies of maxima in the vibrationally adiabatic potential curves (8). Table 5 illustrates the agreement between the energies predicted by the spectroscopic constants and maxima, max, in the quantal density of reactive states. 

Figure 4 Vibrationally adiabatic potential curves for O + H2 with v, = 1, J = 0, and v2 = 0, 2, 4, and 6. From the bottom up the curves correspond to the [10°], [12°], [14°], and [16°] states. (Reprinted with permission from Ref. 14.)...

Variational Transition State Theory, Vibrationally Adiabatic Potential Curves, and Tunneling... 

The ground-state adiabatic potential is used in the reactant channel for values of s up to the location of the maximum in the ground-state adiabatic potential curve. The classical turning point in the reactant channel for energy E, so(E), is still defined by Eq. [175]. In the product channel, we define the excited-state vibrationally adiabatic potential curve with quantum number np for each initiation point So by... 

The full computation of the coupled partition function using the adiabatic approximation can be problematic. For each set of quantum numbers describing excitations of the fast vibrational modes, a distinct vibrationally adiabatic potential curve is generated for the torsion. In prineiple, this may... 

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) ...

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. 

Figure 6 (a) Vibrationally adiabatic potential energy curves with v-, = 0 for the... 

Figure 7a Vlbratlonally adiabatic potential curves as a function of R for 1 20, Y 0.5856 for CO vibrational states u 0-4.

The ground-state adiabatic potential curves in Fig. 27.3 are constructed by adding accurate anharmonic zero-point energies for the stretch and bend modes to V]y[gp. On the reactant side the shapes of Vmep and are very similar with the adiabatic potential being shifted up by approximately the zero-point energy for the FI2 stretch vibrations, 6.2 kcal mokk Near the saddle point this contribution decreases markedly for the FI -1- H2 reaction, to 2.9 kcal mokh causing the adia-... 

The vibrational eigenstates of neither the diabatic nor the adiabatic potential curve exactly represent the observed levels. Interaction matrix elements between these zero-order levels (eigenstates of either diabatic or adiabatic potentials)... 

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