Linear vibronic coupling model

Fig. 2 Representative cuts through the potential energy surfaces of Bz+ (upperpanel or a) and its mono fluoro derivative, F-Bz+ (lowerpanel or b). The upper panel shows the results for the linear vibronic coupling model, while in the lower one the quadratic coupling terms are also included. In both panels the effective coordinate connects the centre of the Franck-Condon zone to the minimum of the intersection seam between the A and C states of F-Bz" ", and between the X and B states of the parent cation (within the subspace of JT active coordinates)...

A comparison between the measured ° and calculated second band of the photodetachment spectrum of N02 is shown in Fig. 1. The theoretical line spectrum has been generated by employing the linear vibronic-coupling model with parameters determined by ab initio calculations which are more accurate than those previously available. Subsequently, the line spectrum has been convoluted with Lorentzians of suitable width to account for the finite experimental resolution and thermal line broadening effects. The experimental spectral envelope is seen to be very well reproduced by the theory. The theory predicts, moreover, a sub-structure of vibronic lines under most of the peaks of the spectral envelope, which could not be resolved experimentally. 

Interestingly, a conical intersection very similar to that of the S i(n7r ) and S 2(7T7r ) neutral excited states has been found for the n and n hole states of the pyrazine cation.A linear vibronic-coupling model has been constructed for the and states of the pyrazine cation employing many-body Green s function methods for the calculation of the vibronic-coupling parameters. The ah initio calculated photoelectron spectrum of the Ag n ) and states is compared in Fig. 7 with the... 

To account for the first kind of process, we employ the linear vibronic coupling model, where the diabatic potential matrix elements Wkk are approximated by a Taylor expansion with respect to the electronic ground-state equilibrium geometry (see Chapter 7). In lowest order we thus obtain (throughout the article, we set = 1)... 

The accuracy of the linear vibronic coupling model can be improved by adding diagonal quadratic terms 7." Q for the non totaUy-symmetric modes for which the diagonal linear terms vanish [63], In this case, the 7/" constants can be conveniently... 

We have constructed several linear vibronic coupling model Hamiltonians augmented with diagonal quadratic terms for the non-totally symmetric modes. The total Hamiltonian of the molecule in the diabatic representation reads... 

A linear vibronic coupling model Hamiltonian [33], augmented with a diagonal quadratic term along the vioa mode [31] is adopted for the molecular Hamiltonian. Its matrix representation in the basis of the diabatic electronic states reads... 

It is also interesting to mention here the possibility, discussed by Cederbaum and co-workers, of introducing a hierarchy of sequentially coupled modes in the framework of the so-called linear vibronic coupling model (described in Chapter 8) in such a way that a many-mode problem can be truncated to reproduce the required number of moments of the exact absorption spectmm [44, 45]. 

Fig. 3 Diabatic-state populations for the butatriene as a function of time. The Di state is initially excited. Population for the lower state Dq (solid line) and for the upper state Di (dashed line) are presented. Panel A exact 18-mode model. Panel B linear vibronic coupling model (5-mode). Panel C three-effective-mode approach. Panel D quad-ratically extended three-effective-mode approach. [Reproduced from J. Phys. Chem. A. 2012, 116, 2629.]...

Fig. 16.1 The autocorrelation functions for the pyrazine molecule. Solid line exact 24-mode result. Dashed line result for the linear vibronic coupling model (6-mode). Dotted line result for the three effective mode model. Dashdotted line result for our quadradcally extended three effective mode approach...

The enhancement of the total S value by the CT state coupling can be understood using the simplest possible model of the system two excited electronic states and a single vibrational mode. The first state [Qy exciton state) is assumed to carry all the oscillator strength while the second state,(CT state) is dark. In the diabatic representation, the effective Hamiltonian in the linear vibronic coupling model of the excited state surface can be written as " " ... 

Reference (13) uses a linear vibronic coupling model between the and E" states to estimate the asymmetric bend harmonic frequency from experimental data in reference (76). 

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