Adiabatic energy curve

Dissociation of a resonance state (u 0, v.y, vr) can be viewed as a multi-step non-adiabatic transition from one adiabatic energy curve to a lower one. Whether single quantum jumps, Au = 1, or transitions including more than one vibrational quantum, Au > 1, are more efficient cannot... 

Figure 19.3 Intersection of parabolic diabatic curves for reactant-like and product-like states, together w/ith adiabatic energy curves arising from mixing ofthe diabatic states.

Fig. 8.1. The adiabatic energy curves of the electronic states v,Q) and j Q), as a function of the normal coordinate, Q. The solid up and down vertical arrows are the vertical absorption and emission transitions, respectively. The dashed arrows represent the nonradiative vibrational relaxation. The Stokes shift is twice the reorganization energy.

Fig. 8.4. The adiabatic energy curves for the initial and final states, the vibrational energy levels, the vertical absorption and emission transitions, and the associated intensity of the absorption and emission spectra determined by the Eranck-Condon factors.

The soliton-antisoliton interactions in the excited states are illustrated by the adiabatic energy curves shown in Fig. 10.6. These are obtained by calculating transition energies as a function of the soliton-antisoliton separation, 2no, using the equilibrium values of (and n /no for the state). The two-soliton fit... 

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. 

The potential energy curves (Fig. 1), the non-adiabatic coupling, transition dipole moments and other system parameters are same as those used in our previous work (18,19,23,27). The excited states 1 B(0 ) and 2 B( rio) are non-adiabatically coupled and their potential energy curves cross at R = 6.08 a.u. The ground 0 X( Eo) state is optically coupled to both the and the 2 R( nJ) states with the transition dipole moment /ioi = 0.25/xo2-The results to be presented are for the cw field e(t) = A Yll=o cos (w - u pfi)t described earlier. However, for IBr, we have shown (18) that similar selectivity and yield may be obtained using Gaussian pulses too. 

Figure 61. Adiabatic potential energy curves for the atomic hydrogen transmission through the five-membered ring in the case of center approach. Taken from Ref. [47].

The angular-dependent adiabatic potential energy curves of these complexes obtained by averaging over the intermolecular distance coordinate at each orientation and the corresponding probability distributions for the bound intermolecular vibrational levels calculated by McCoy and co-workers provide valuable insights into the geometries of the complexes associated with the observed transitions. The He - - IC1(X, v" = 0) and He + 1C1(B, v = 3) adiabatic potentials are shown in Fig. 3 [39]. The abscissa represents the angle, 9,... 

FIGURE 35.2 Scheme of diabatic (solid line) and adiabatic (dashed line) free-energy curves for a simple electrochemical redox reaction Ox —> Red. 

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.

Fig. 1. Schematic potential energy curves for a neutral transition metal atom (M) inserting into the H-R bond of a hydrocarbon. Diabatic curves are shown as dashed lines, adiabatic curve shown as a solid line.

Figure 4.67 depicts the potential-energy curve for reaction (4.102) along an adiabatic reaction coordinate (R = /Oimc) obtained by stepping along the H—CH3 stretching coordinate with full optimization of geometries at each step. As shown in Fig. 4.67, the reaction exhibits a substantial barrier ( 20.5 kcal mol-1) and overall exothermicity. 

Let us examine the balance between steric and donor-acceptor forces in greater detail for the case of HF- HF. The graph below plots the adiabatic potential-energy curve for H-bond formation (solid line, circles), as well as the steric repulsion energy37 (dotted line)... 

Figure 5.11 The adiabatic potential-energy curve for F HF hydrogen-bond formation (solid line, circles), with the steric repulsion energy (dotted line) and estimated np - oi ip donor-acceptor attraction (dashed line) included for comparison.

Figure 9.5 Adiabatic potential-energy curve according to Eq. (9.35).

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