Non-Franck-Condon

Adiabatic control of bond distance in selective non Franck-Condon transitions... 

Consider, to be specific, a molecule like Na2. In Fig. 1(a) we show some singlet electronic potential curves. A selective transition between the initial state (x) and the ground state of the excited potential Vn3(a ), o(x), is highly non Franck-Condon and thus involves a large displacement of the molecular bond. If the transition between these states can be adiabatically controlled, then it will be in principle possible to follow or control the bond length as the transition proceeds. The first problem involves the smallness of... 

Figure 1 (a) Singlet electronic states of Na2 between which the chosen non Franck-Condon transition takes place, (b) Potential curves displaced by the photon energies. 

In Fig.2 we show the evolution of the bond length of the molecule as the non Franck-Condon transition proceeds, both in STIRAP and in APLIP for intuitive and counterintuitive sequences. The calculations were obtained by solving the Schrodinger equation using sine square pulses with FWHM a = 5 ps. The results show that the dynamics... 

Here we report our exploration of the possibility of inducing an ultrafast non-Franck-Condon transition, which we defined to be the creation of a wave packet at the other turning point of the above-mentioned oscillation, see Fig. 1(b), faster than the time it takes the Franck-Condon packet to reach that turning point due to the natural (field-free) dynamics. We have explored two possible routes for inducing non-Franck-Condon transitions, namely phase-tailoring of a weak-field ultraviolet (UV) pulse [6] tmd a two-pulse scheme combining a transform limited weak-field UV pulse with a strong infrared (IR) field [7]. 

The above analysis shows that the IR+UV scheme could be a possible way to create ultrafast non-Franck-Condon transitions. In fact, we illustrated the case where the nuclear dynamics was sped up by the IR field only prior to UV excitation. A more efficient scheme would involve an IR-field induced acceleration of the nuclear motion in both electronic states. 

H2 (Nj.Hj)N 100 eV to 13.5 keV n2(h> First negative system vibrational excitation Vibrational distribution non-Franck-Condon at low energies 155... 

Non-Franck—Condon at low energies strong energy-dependent deviations rotational excitation... 

First negative Non-Franck—Condon vibrational excitation strong rotational excitation 400... 

Figure 7. Calculated two-dimensional energy surfaces for heterogeneous non-Franck-Condon transition of the three-dimensional 6-oscillator trikisoctahedral Inner Shells of 3+ and 2+ ions at (A) equal potential energies after ground state energy correction (B) at equal ground state free energies. Barrier height in B +22.9kT at 298 K (+56.9 kJ/mole, +0.59 eV, experimentally +0.59 eV177).

Figure 8. Calculated two-dimensional energy surfaces for heterogeneous non-Franck-Condon transition between H9OT.H2O + e and 5H2O at equal potential energies, before correction for ground states. Barrier height +6.15kT (+15.2 kJ/mole, +0.16 eV) after correction for ground state energies.

Figure 9. Illustration of how change in Fermi energy (Ep) acts on the energy barrier. E = potential energy C = Nuclear configuration p1 = density of filled metallic states in metal electrode. (A). Gurney s model8 with initial (I) and final (F) states at the same potential. (B). Non-Franck-Condon transfer in equilibrium. (C). Non-Franck-Condon transfer out of equilibrium.

A relatively constant Tafel slope for reactions not involving adsorption, and those involving adsorption with complete charge transfer across the double layer, distorted by second order effects, may also be explained in terms of a non-Franck-Condon process. Since adsorbed intermediates in charge transfer processes also show adsorption energies depending on potential in the same way as the potential energy barrier maxima, these should also follow the same phenomena. 

The large branching ratios predicted by the multiple scattering model is certainly an Indication of the poor representation of the R dependence of the molecular ion potential in this model. It is important to note that substantial non-Franck-Condon behavior of this branching ratio occurs at photon energies well above the peak position of the resonance (27). 

Shape-Resonance-Induced Non-Franck-Condon Effects... 

One recent example has been the prediction and experimental confirmation of the role of shape resonances in producing non-Franck-Condon effects in vibrational branching ratios and photoelectron angular distribution. 

An important characteristic of shape resonances is that they cause non-Franck-Condon effects in vibrationally resolved photoionization spectra. These effects are a consequence of the strong R-variation of the transition moment caused by the R-dependence of the form of the continuum molecular orbital. 

Cooper minima axe also responsible for non Franck-Condon vibrational intensity distributions and intensity anomalies observed in both PES and ZEKE spectra. As for atoms, when the photoionization transition corresponds to excitation from a Rydberg orbital having at least one radial node in its wavefunction, the... 

---