Vibrational sublevels

Figure Bl.3.4. The two fully resonant doorway stages for resonanee Raman seattering (RRS), in wlheh the manifold of vibrational sublevels for eaeh eleetronie state is indieated. (a) Doorway stage iii...

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

Because of the dense spectrum of the highest vibrational sublevels and their rapid vibrational relaxation in the A2 state, this radiationless transition (RLT) is irreversible and thus it may be characterized by a rate constant k. The irreversibility condition formulated by Bixon and Jortner [1968] reads... 

Fig. 21. Top The general Jablonski diagram for the flavin chromophore. The given wavelengths for absorption and luminescence represent crude average values derived from the actual spectra shown below. Due to the Franck-Condon principle the maxima of the peak positions generally do not represent so-called 0 — 0 transitions, but transitions between vibrational sublevels of the different electronically excited states (drawn schematically). Bottom Synopsis of spectra representing the different electronic transitions of the flavin nucleus. Differently substituted flavins show slightly modified spectra. Absorption (So- - S2, 345 nm S0 -> Si,450nm 1561) fluorescence (Sj — S0) 530 nm 156)) phosphorescence (Ty Sq, 605 nm 1051) triplet absorption (Tj ->Tn,...

The width of a band in the absorption spectrum of a chromophore located in a particular microenvironment is a result of two effects homogeneous and inhomogeneous broadening. Homogeneous broadening is due to the existence of a continuous set of vibrational sublevels in each electronic state. Inhomogeneous broadening results from the fluctuations of the structure of the solvation shell... 

In Figure 1, we present energy-level polarization state diagrams corresponding to the one form of VCD and the four forms of CP ROA. In the case of VCD, only a single photon is involved in the vibrational transition from state gO to state gl in the ground electronic state. For ROA, two photons are involved for a transition between the same two vibrational sublevels of the... 

Schematic diagram for a typical electronic potential energy U as a function of some significant interatomic bond distance R. Also shown are the first four vibrational sublevels of the electronic energy, with vibrational quantum numbers v=0, 1, 2, 3.

Figure 4-12. Energy curves for the ground state and an excited state, showing the range of nuclear separations and the different energies for the various vibrational sublevels. The vertical arrow represents a transition that is caused by the absorption of a photon and that is consistent with the Franck-Condon principle. In this text we will use the same energy spacing between vibrational sublevels in both the ground state and the excited state of some molecular species (the spacing actually tends to decrease for the higher excited sublevels).

Quantum-mechanical calculations beyond the scope of this text lead to somewhat different conclusions, especially for the lowest vibrational sublevel. 

Suppose that the spacing in wave numbers (see Problem 4.2) between vibrational sublevels for the transition depicted in Figure 4-12 is 1.2 x 105 m-1 and that the most probable absorption predicted by the Franck-Condon principle occurs at 500 nm (the main band). 

A. What are the wavelength positions of the satellite bands that occur for transitions to the vibrational sublevels just above and just below the one for the most probable transition ... 

A. What is the splitting between vibrational sublevels in the excited state ... 

The participation of the lowest vibrational sublevels of both the ground state and the lower excited state of Chi a in the major red band can also be appreciated by considering the minor band adjacent to the major red band in... 

Figure 5-4. Energy level diagram indicating the vibrational sublevels of the ground state (S )) and the lower excited singlet state (S ) of Chi a. Solid vertical lines indicate the absorption of light by Chi a dissolved in ether (Fig. 5-3) dashed lines represent fluorescence at the specified wavelengths (also Fig. 5-3). The lengths of the arrows are proportional to the energy involved in the various transitions.

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