Vibronic coupling parameters

Within the SH formalism the MPs (gx, gy, gz, D, E, /tip) are thought of as physical constants associated with each particular system. The electronic-magnetic theory beyond the SH formalism reveals that there are only the electronic-structure parameters (like B, C, ) associated with the electron configuration and the CF parameters [like F2(L) and F4(I)] for each ligand. A more realistic approach brings the orbital reduction factors k (which must be anisotropic) and in a particular case of the degenerate electronic states also the force-field and vibronic coupling parameters (like Kee, Xe, Xee, and eventually Ktt, Xt, Xtt, or even more parameters). 

Fig.4. Potential hypersurfaces of T, (3P0) and r4 (3P,) levels in the e (Q2, Q3) subspace calculated from the Fukuda coupling matrix with the vibronic coupling parameter Are t = 4x 10 9 J/m from Eq. (5) (denoted by b in [84]), the electron (exchange) repulsion parameter G and spin-orbit parameter are both set equal to 0.3 eV...

The vibronic coupling parameter V was roughly evaluated under the assumption that Vi = v2 = 0, t = 0. If the energy... 

Figure 8 Vibrational potential energy vs. configurational coordinate for electron transfer via vibronic coupling betweeg two symmetric states of a single oscillator A, initial state B, vibration-ally excited state B, thermally excited state X9 vibronic coupling parameter E f optical transition energy E t thermal transition energy (Reproduced with permission from Ref 33 Copyright 1987 The Clay Minerals Society) ...

I = vibronic coupling parameter, v = (1/2jt) , k = harmonic vibrational constant). (Ref 19. Reproduced by permission of Klnwer Academic Publishers)... 

There exists a rich variety of essentially untouched vibronic-coupling phenomena in molecules and clusters containing heavy atoms. Since the SO-induced vibronic-coupling parameters can conveniently be computed with ab initio electronic-structure methods, these novel phenomena can be explored irrespective of the availability of experimental spectroscopic data. 

Table 8 Ligand field parameters (in 10 cm ) for the Cu Fg polyhedron in elpasolites A2 ACup6 (A, A alkaline ions), as well as the Cu -F bond length (in A) and the vibronic coupling parameters Aj, Vg in eV A eV A ), derived by DFT from excited...

Fig. 5 Influence of the JT interaction (defined by the vibronic coupling parameter v) on the Zeeman energy pattern in a perpendicular magnetic field (//HC3)...

Figure 6 illustrates the influence of the JTE on the field dependence of the magnetization. The magnetization vs. perpendicular field at T = 0 is presented as a function of the vibronic coupling parameter v that is assumed to satisfy the condition of instability v > = 4 i5 /3. One can see that provided that v = vq... 

Table 1 Linear (V and V, , in cm /A) and quadratic (Lj and in cm / ) vibronic coupling parameters, Jahn-TeUer stabilization energies [Ejr(D4h) and Ejr(D3d) in cm ] and vibronic coupling strengths = En-(D4i,)/hoOj, = Ejp(D3d)/ha)i ] of the T2g <8> Sg and T2g <8> t2g Jahn-TeUer problems in [Ee(CN)5] as deduced from DFT calculations on a charge-compensated model complex, using water as a solvent and a LDA(VWN) functional as well as a triple zeta basis set) ...

In this section we consider several effects that may complicate the extraction of vibronic coupling parameters from resonance Raman data. By refining the analysis, we shall try to remove these complications or turn them into additional sources of information. The effects to be considered concern external parameters such as the temperature and the medium, and parameters that complicate the description of the electronic ground state. 

The preresonance Raman spectra of naphthalene (Ohta and Ito, 1977a) are of special interest since they show evidence of interference involving three electronically excited states. Model calculations for such a system (Zgierski, 1978) are presented in Section VII,A. The evidence for interference is the decrease of the cross section of the big fundamental after an initial increase upon approaching resonance. The same behavior is shown in Fig. 32a, based on observed transition moments and calculated vibronic coupling parameters. 

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... 

Obviously the inclusion of Cl does not have much influence on the results such that for the present systems the calculations considering only the main electron configurations involved will be adequate. In the weakly coupled case of Red the only contributions to the vibronic coupling parameter arise from Cl terms. 

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