Franck-Condon state derivatives

For instance Cr(CO)6+ is formed only during LI. The time-dependent behavior of the ion yields of Cr(CO)6+ is presented in Fig. 13. Deconvolution of the time-dependent ion yield with the instrument function derived from the Xe+ signal provides a measure of the time constant (ij) of 12.5 0.05 fs for the LI level (Table 2). This represents the time it takes for the excited Cr(CO)6 to cross to the repulsive surface through the conical intersection close to the Franck-Condon state. At the Franck-Condon point with Oh symmetry, the only coordinates with nonzero slope are the totally symmetric alg M-C stretch or the Jahn-Teller-active vibrations which have eg or t2g symmetry [32], The time taken for a wavepacket to travel from any... 

In order to correlate the solid state and solution phase structures, molecular modelling using the exciton matrix method was used to predict the CD spectrum of 1 from its crystal structure and was compared to the CD spectrum obtained in CHC13 solutions [23]. The matrix parameters for NDI were created using the Franck-Condon data derived from complete-active space self-consistent fields (CASSCF) calculations, combined with multi-configurational second-order perturbation theory (CASPT2). 

There are thus two indirect indications that the photochemistry of Co (III) ammines derives from thexi rather than from Franck-Condon states. The spectroscopic nature of this state has not been determined. It could be related (after thermal equilibration and possible descent in symmetry) to the first excited ligand field state in Oh, Tig, It could be triplet or quintet in spin multiplicity, however. 

The absorption oscillator strengths for the 0 - 0,1 - 0, and 0-1 bands of the A - X system of PH were calculated by [31] from the radiative lifetime of the A rij state as measured by [23] and from Franck-Condon factors derived from the spectroscopic constants of [8]. 

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. 

The emission spectrum observed by high resolution spectroscopy for the A - X vibrational bands [4] has been very well reproduced theoretically for several low-lying vibrational quantum numbers and the spectrum for the A - A n vibrational bands has been theoretically derived for low vibrational quantum numbers to be subjected to further experimental analysis [8]. Related Franck-Condon factors for the latter and former transition bands [8] have also been derived and compared favourably with semi-empirical calculations [25] performed for the former transition bands. Pure rotational, vibrationm and rovibrational transitions appear to be the largest for the X ground state followed by those... 

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 Franck-Condon principle states that the excited state is formed with the same geometry as that of the ground state from which it derived. The transition is from the ground state to the excited state lying vertically above it. 

If solvent (or environment) relaxation is complete, equations for the dipole-dipole interaction solvatochromic shifts can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres and within the assumption of equal dipole moments in Franck-Condon and relaxed states. The solvatochromic shifts (expressed in wavenumbers) are then given by Eqs (7.3) and (7.4) for absorption and emission, respectively ... 

Fig. 11 Illustration of the excited state relaxation derived from experimental results obtained for poly(dA).poly(dT) by steady-state absorption and fluorescence spectroscopy, fluorescence upconversion and based on the modeling of the Franck-Condon excited states of (dA)io(dT)io. In red (full line) experimental absorption spectrum yellow circles arranged at thirty steps represent the eigenstates, each circle being associated with a different helix conformation and chromophore vibrations.

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

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