Vibronic resolution

Most charge-transfer transitions show less vibronic resolution than the examples in Figure 2. Resonance Raman spectroscopy has often been used in these cases to analyze the structural changes between the initial and final states of the transition, an approach especially relevant to metal centers in enzymes and to bioinorganic model compounds. The full ensemble of optical spectroscopic techniques has been applied to the study of the lowest-energy metal-to-ligand charge-transfer (MLCT) bands in Ru(bipyridine)3 and related complexes. Other well-studied cases of MLCT transitions with resolved vibronic structure include a number of W(CO)sL complexes. "... 

Figure Bl.1.2. Spectrum of fonnaldehyde with vibrational resolution. Several vibronic origins are marked. One progression m starting from the origin is indicated on the line along the top. A similar progression is built on each vibronic origin. Reprinted with pennission from [20]. Copyright 1982, American Chemical Society.

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

Conventional spontaneous Raman scattering is the oldest and most widely used of the Raman based spectroscopic methods. It has served as a standard teclmique for the study of molecular vibrational and rotational levels in gases, and for both intra- and inter-molecular excitations in liquids and solids. (For example, a high resolution study of the vibrons and phonons at low temperatures in crystalline benzene has just appeared [38].)... 

Pinan J P, Ouillon R, Ranson P, Becucci M and Califano S 1998 High resolution Raman study of phonon and vibron bandwidths in isotropically pure and natural benzene crystal J. Chem. Phys. 109 1-12... 

Another group of approaches for handling the R-T effect are those that employ various forms of effective Hamiltonians. By applying pertuibation theory, it is possible to absorb all relevant interactions into an effective Hamiltonian, which for a particular (e.g., vibronic) molecular level depends on several parameters whose values are determined by fitting available experimental data. These Hamiltonians are widely used to extract from high-resolution [e.g.. 

Vibrational transitions accompanying an electronic transition are referred to as vibronic transitions. These vibronic transitions, with their accompanying rotational or, strictly, rovibronic transitions, give rise to bands in the spectrum, and the set of bands associated with a single electronic transition is called an electronic band system. This terminology is usually adhered to in high-resolution electronic spectroscopy but, in low-resolution work, particularly in the liquid phase, vibrational structure may not be resolved and the whole band system is often referred to as an electronic band. 

The absoiption spectra of these three materials are shown in the bottom panel of Figure 9-16. From these spectra it becomes clear that the m-LPPP shows the longest effective conjugation length 23 the best resolution of vibronic progression, and the steepest onset of absorption [231. Therefore, one would assume the m-LPPP to be a material of the highest chemical definition. This is indeed con-... 

Recent observations of fluorescence in NpF6 and PuF6 (46) are consistent with the energy-level scheme proposed. However, comparison of the calculated level structure with high-resolution spectra of PuFg (44) confirms that much of the observed structure is vibronic in character, built on electronic transitions that are forbidden by the inversion symmetry at the Pu site. 

The visible absorption spectrum of CV in solution appears to be composed of two bands as shown in Fig. 2A. The origin of the two bands was interpreted in three ways (1) resolution of vibronic structures in one electronic state [46], (2) electronic transition from one ground state to two excited states [47-51], and (3) the existence of two ground-state isomers [5,52-54], We have an over 50 year long dispute among (1), (2), and (3) over an origin of the twofold absorption spectrum. 

With increasing resolution, vibronic line spectra can at least be approximately mimicked by the calculations. Finally, also electronic populations are directly extracted from the time-dependent wave-packet [27]. 

In the present work we aim at a more accurate description and treat the Hamiltonian, equation (9), fully, with all JT and PJT couplings of Table 3 included. Only the inherently low-resolution experimental PE spectra of Refs. [4,6] are available for comparison which is thus confined to the gross overall features of the composite D — EYE band. Nevertheless, it proved necessary to adjust the vertical IPs, since their difference affects the computed vibronic structure [26]. Being a small difference of large numbers, we increased it from the ab initio value of 0.3 eV to a value of 0.45 eV. The PE spectral profile thus obtained with the MCTDH algorithm is depicted in Fig. 4, and compared there with the experimental recording of Ref. [6]. 

Fig. 4. Comparison of lower-resolution spectral profiles for the composite D — E PE band, (a) Experimental recording of Ref. [6]. (b) Result of the present calculation utilizing the parameter values of Table 3 and including the modes v2 and vi6 — f18 with all couplings. The Elu and B2u vibronic symmetries are drawn separately as dashed lines, their 1.4 1 weighted sum is given by the full line (FWHM = 88 meY). (c) Same as (b), but employing the propensity rule Af6 = Af7 = Af8 = 0. For more details see text.

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