Franck excitation

An alternative perspective is as follows. A 5-frmction pulse in time has an infinitely broad frequency range. Thus, the pulse promotes transitions to all the excited-state vibrational eigenstates having good overlap (Franck-Condon factors) with the initial vibrational state. The pulse, by virtue of its coherence, in fact prepares a coherent superposition of all these excited-state vibrational eigenstates. From the earlier sections, we know that each of these eigenstates evolves with a different time-dependent phase factor, leading to coherent spatial translation of the wavepacket. 

The coefficients of the 5-fiinction in the sum are called Franck-Condon factors, and reflect the overlap of the initial state with the excited-state i at energy (see figure Al.6.13). Fonnally, equation (A1.6,88i... 

Figure Al.6.13. (a) Potential energy curves for two electronic states. The vibrational wavefunctions of the excited electronic state and for the lowest level of the ground electronic state are shown superimposed, (b) Stick spectrum representing the Franck-Condon factors (the square of overlap integral) between the vibrational wavefiinction of the ground electronic state and the vibrational wavefiinctions of the excited electronic state (adapted from [3]).

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

At this stage we may distinguish between excitation involving different electronic states and excitation occurring within the same electronic (ground) state. Wlien the spectroscopic states are located in different electronic states, say the ground (g) and excited (e) states, one frequently assumes the Franck-Condon approximation to be applicable ... 

The state may decay by radiative (r) or non-radiative (nr) processes, labelled 5 and 7, respectively, in Figure 9.18. Process 5 is the fluorescence, which forms the laser radiation and the figure shows it terminating in a vibrationally excited level of Sq. The fact that it does so is vital to the dye being usable as an active medium and is a consequence of the Franck-Condon principle (see Section 7.2.5.3). 

The ZEKE-PE process shown in Figure 9.50(c) can be modified as shown by changing the wavenumber Vj of the first laser to excite the molecule to an excited vibrational level of M. Then the Franck-Condon factors for the band system are modified. This can allow... 

Resonance Raman Spectroscopy. If the excitation wavelength is chosen to correspond to an absorption maximum of the species being studied, a 10 —10 enhancement of the Raman scatter of the chromophore is observed. This effect is called resonance enhancement or resonance Raman (RR) spectroscopy. There are several mechanisms to explain this phenomenon, the most common of which is Franck-Condon enhancement. In this case, a band intensity is enhanced if some component of the vibrational motion is along one of the directions in which the molecule expands in the electronic excited state. The intensity is roughly proportional to the distortion of the molecule along this axis. RR spectroscopy has been an important biochemical tool, and it may have industrial uses in some areas of pigment chemistry. Two biological appHcations include the deterrnination of helix transitions of deoxyribonucleic acid (DNA) (18), and the elucidation of several peptide stmctures (19). A review of topics in this area has been pubHshed (20). 

Excited-State Relaxation. A further photophysical topic of intense interest is pathways for thermal relaxation of excited states in condensed phases. According to the Franck-Condon principle, photoexcitation occurs with no concurrent relaxation of atomic positions in space, either of the photoexcited chromophore or of the solvating medium. Subsequent to excitation, but typically on the picosecond time scale, atomic positions change to a new equihbrium position, sometimes termed the (28)- Relaxation of the solvating medium is often more dramatic than that of the chromophore... 

Solvatochromic shifts are rationalized with the aid of the Franck-Condon principle, which states that during the electronic transition the nuclei are essentially immobile because of their relatively great masses. The solvation shell about the solute molecule minimizes the total energy of the ground state by means of dipole-dipole, dipole-induced dipole, and dispersion forces. Upon transition to the excited state, the solute has a different electronic configuration, yet it is still surrounded by a solvation shell optimized for the ground state. There are two possibilities to consider ... 

Table I. Distribution of Excited H2+ Produced by Franck-Condon Electron Impact Processes with 50-Volt Ionizing Electrons...

Even where the promotion is to a lower vibrational level, one that lies wholly within the 2 curve (such as Vi or V2), the molecule may still cleave. As Figure 7.2 shows, equilibrium distances are greater in excited states than in the ground state. The Franck-Condon principle states that promotion of an electron takes place much faster than a single vibration (the promotion takes... 

Franck and Gustav Hertz passed electrons through mercury vapor at low pressure to determine the minimum kinetic energy required to produce the excited state that emits ultraviolet light at 253.7 nm. What is that minimum kinetic energy What wavelength is associated with electrons of this energy ... 

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