Energy vertical

Experimental. The vibrational spectrum of an ideal harmonic oscillator would consist of one line at frequency v corresponding to A = hv, where A is the distance between levels on the vertical energy axis in Fig. 10-la. In the harmonic oscillator, AE is the same for a transition from one energy level to an adjacent level. A selection rule An = 1, where n is the vibrational quantum number, requires that the transition be to an adjacent level. 

The barrier to EE between n and c, where the two parabolas cross, is the point with one-fourth the vertical energy gap A, owing to the analytical geometry of a parabola. This value of was incorporated in Eq. (10-57) and is explicitly treated in Problem 10-22. Reference should be made to Fig. 10-11. 

Fig. 13. Diabatic correlation diagram for the dissociation of CH2CI to CH2 + Cl. The vertical energies and assignments of the excited electronic states of CH2CI are from Ref. 115. (From Dribinski et al.11A)...

Figure 4.107 Perturbative interaction diagrams (on a common vertical energy scale cf. Fig. 4.106) depicting significant localized bonding interactions for PtH42 (a) metal hybrid formation (NAO NHO), (b) interaction of bonding hybrids to form bonding (a) and antibonding (a ) NBOs (NHO- NBO), and (c) nH

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

Figure 5. Quantum dynamics for an asymmetric double well under coherent or thermal preparations. Vertical energy separation between the two wells (Ae) is 300 cm1, o> = 100...

First, in the classical treatment a transition leading to e can occur only at distances R, at which the vertical energy difference between the potential curves is equal to e ... 

Scheme 23. Vertical Resonance Energy of the Reference Structure, B(R), for Benzene and Its Relation to the Vertical Energy of Hexatriene, B(h)...

Fig. 6.1. Schematic illustration of the one-dimensional reflection principle. The solid curve on the right-hand side shows the spectrum for a linear potential whereas the dashed curve represents a more realistic case. Ve is the vertical energy defined as V(Re).

Fig. 6.3. Schematic illustration of the two-dimensional reflection principle and the dependence of the width of the spectrum on the gradients dV/dR and dV/dr. The dots indicate the two different excitation points. The vertical energies Ve = V(Re,re) are different in the two cases and therefore the spectra Eire plotted as functions of E — Ve rather than E.

The energy dependence of each one-dimensional cross section g(E, n) can be easily explained by the one-dimensional reflection principle as illustrated in Figure 6.4. The vertical energy en(Re) determines the peak... 

The vertical energy gap of the wells at the initial reaction coordinate is described as the reorganization energy, since it implies the rise in energy as the system moves towards the saddle point X along the reaction coordinate (see Fig. 2). Conceptually, the system starts to resemble the situation it will have when the products are finally formed. 

Even in the non-harmonic case, one may still define 17 as the vertical energy gap Gf — G [35,36], but 17 will no longer be linear in x >, in contrast to Equation (3.79). In this case, the relationship noted by Tachiya [37]... 

Non-vertical energy transfer An energy transfer process which has a low Franck-Condon factor. 

FIGURE 19 Schematic energy level diagram of La( C82- The vertical energy spacing is 1.0 eV. 

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