Vibronic coupling-models

D. The Vibronic-Coupling Model Hamiltonian IV, Non-Adiabatic Molecular Dynamics... 

A B2u- The vibronic coupling model Hamiltonian is set up using the ground-state... 

The vibronic coupling model has been applied to a number of molecular systems, and used to evaluate the behavior of wavepackets over coupled surfaces [191]. Recent examples are the radical cation of allene [192,193], and benzene [194] (for further examples see references cited therein). It has also been used to explain the lack of structure in the S2 band of the pyrazine absoiption spectrum [109,173,174,195], and recently to study the photoisomerization of retina] [196],... 

In the past decade, vibronic coupling models have been used extensively and successfully to explain the short-time excited-state dynamics of small to medium-sized molecules [200-202]. In many cases, these models were used in conjunction with the MCTDH method [203-207] and the comparison to experimental data (typically electronic absorption spectra) validated both the MCTDH method and the model potentials, which were obtained by fitting high-level quantum chemistry calculations. In certain cases the ab initio-determined parameters were modified to agree with experimental results (e.g., excitation energies). The MCTDH method assumes the existence of factorizable parameterized PESs and is thus very different from AIMS. However, it does scale more favorably with system size than other numerically exact quantum... 

Parameters for the Three Dimensional S,-S2 Vibronic Coupling Model of Pyrazine [208], All Quantities are in eV... 

The Hamiltonian provides a suitable analytic form that can be fitted to the adiabatic surfaces obtained from quantum chemical calculations. As a simple example we take the butatriene molecule. In its neutral ground state it is a planar molecule with Dy, symmetry. The lowest two states of the radical cation, responsible for the first two bands in the photoelectron spectrum, are X2B2g and A1 By The vibronic coupling model Hamiltonian is set up using the ground-state... 

Figure 7. The PES of the X2B2S and A -Bi, states of the butatriene radical cation, (a) Diabatic surfaces, (b) Adiabatic surfaces. The surfaces are obtained as eigenfucations of the vibronic coupling model Hamiltonain that fitted to reproduce quantum chemical calculations. The coordinates are shown in Figure lc. See Section III. D for further details.

Muller and Stock [227] used the vibronic coupling model Hamiltonian, Section III.D, to compare surface hopping and Ehrenfest dynamics with exact calculations for a number of model cases. The results again show that the semiclassical methods are able to provide a qualitative, if not quantitative, description of the dynamics. A large-scale comparison of mixed method and quantum dynamics has been made in a study of the pyrazine absorption spectrum, including all 24 degrees of freedom [228]. Here a method related to Ehrenfest dynamics was used with reasonable success, showing that these methods are indeed able to reproduce the main features of the dynamics of non-adiabatic molecular systems. 

Inclusion of Solvent Effects in a Vibronic Coupling Model for Mixed-Valence Compounds... 

A vibronic coupling model for mixed-valence systems has been developed over the last few years (1-5). The model, which is exactly soluble, has been used to calculate intervalence band contours (1, 3, 4, 5), electron transfer rates (4, 5, 6) and Raman spectra (5, 7, 8), and the relation of the model to earlier theoretical work has been discussed in detail (3-5). As formulated to date, the model is "one dimensional (or one-mode). That is, effectively only a single vibrational coordinate is used in discussing the complete ground vibronic manifold of the system. This is a severe limitation which, among other things, prevents an explicit treatment of solvent effects which are... 

A vibronic coupling model Hamiltonian was constructed using CASSCF (active space and basis set as discussed above for the semi-classical study) (79). The vibrational modes were obtained from a Hartree-Fock frequency calculation of the dianion, and it... 

Fig. 9.29. Schematic diagram of a phonon-vibron coupling model. (Reproduced form J. O M. Bockris and S. u. M. Khan, Surface Electrochemistry, Plenum, 1993, p. 448.)...

Explanations of the frequency upshift were given by Ohno,236ab Orlandi et al.,236c and Mikami and Ito239 in terms of a vibronic coupling model. While the model was quantitatively successful, it did not give... 

In the following, we summarize the pertinent results of our analysis of Refs. [50-53] where we applied the LVC Hamiltonian Eq. (1) in conjunction with a 20-30 mode phonon distribution composed of a high-frequency branch corresponding to C=C stretch modes and a low-frequency branch corresponding to ring-torsional modes. In all cases, the parametrization of the vibronic coupling models is based on the lattice model of Sec. 3.1 and the complementary diabatic representation of Sec. 3.2. 

Ag° atoms isolated in the cubo-octahedral site of rare gas solids. The observation of multiple structure on the 2P 2S absorption and large red spectral shifts for the 2P - 2S emission of site I entrapped Ag° atoms, indicates that the guest-host interactions are markedly different for the 2S and 2P states and can be explained in terms of site I relaxation effects, using a vibronic coupling model similar to that described in detail for Ag° atom rare gas cage complexes (5). 

Vibronic coupling model used to explain the dynamic and energetic properties of the octahedral Ag°06 cage complex (A), appropriate for a silver atom in site 1 of faujasite-type zeolites (5). 

Piepho has responded to the criticisms of the PKS model by developing an improved version, the MO vibronic coupling model for mixed-valence complexes (32). Multicenter vibrations are now considered and a molecular orbital basis set (as with the three-site model) is used. This model was used to calculate band shape and g values for the Cretuz-Taube ion (33). The MO vibronic coupling model is admittedly more empirical than the three-site model but it has the advantage in being applicable to all mixed-valence complexes. 

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)...

The vibronic spectra of Do — Di — D2 electronic states recoded by da Silva Filho et al. [45] revealed resolved vibrational structures of the Do and D2 electronic states and a broad and structureless band for the Di state. A slow ( 3-20 ps) and fast k, 200 fs) relaxation components are estimated for the Dq D2 transition in a (femto)picosecond transient grating spectroscopy measurements [16]. The fast component is attributed to the Do D2 transition and a nonradiative relaxation time of 212 fs is also estimated from the cavity ringdown (CRD) spectroscopy data [42]. Electronic structure results of Hall et al. [107] suggest that the nonradiative Do D2 relaxation occurs via two consecutive sloped type CIs [66,108]. We developed a global model PESs for the Do — Di— D2 electronic states and devised a vibronic coupling model to study the nuclear dynamics underlying the complex vibronic spectrum and ultrafast excited state decay of N +[20]. 

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