Vibronic envelope

The general constraints for the design of any dyes for ADPM SHG in poled polymer systems rapidly narrow the choice of chromophores. The dyes should be overall charge neutral (to facilitate poling) and highly soluble in polymer matrices. The first excited electronic state should be well separated from higher energy states for two reasons (1) since the vibronic envelope associated with an... 

The vibronic envelope ECWD (v) in Eq. [129] can be an arbitrary gas-phase spectral profile. In condensed-phase spectral modeling, one often simplifies the analysis by adopting the approximation of a single effective vibrational mode (Einstein model) with the frequency Vv and the vibrational reorganization energy Xy. The vibronic envelope is then a Poisson distribution of... 

For POD, the peak frequency is close to the 18,800 cm" peak observed for the HT TCDU spectrum. The frequency shift within the phenylurethane series is, therefore, nearly equivalent to that observed when PDAs such as ETCD or TCDU undergo thermochromic or pressure induced changes. A major difference here, however, is the retention of the fairly well defined vibronic structure characteristic of the LT bandshape. Application of the strain hypothesis of the thermochromic shift in PDA spectra would imply that the strain on the polymer spines would increase in the order DDMU DDU < ETCD < HDU < POD < TCDU. This extreme shift of the LT electronic spectra of the phenylurethane substituted PDAs presents a problem, since, if it is strain induced, it has not caused the disappearance of the "fine structure" in the vibronic envelope which occurs when the HT phase is induced by temperature or pressure. However, it has caused essentially the same shift of energy of the pi transition of the spine as observed in the thermochromics. 

Phenomenologically, strongly coupled systems are characterized by large differences between their absorption spectra and those of their components. These differences appear even in the vibronic envelopes and can thus be recognized even from unstructured spectra. 

In most organic crystals, however, the first absorption regions are less Intense and show weak coupling characteristics. In the anthracene crystal, for instance, the vibronic envelope of that transition is nearly the same as in solution. However, the vibronic bands are individually split, each into two components, with separations from 100-200 cm . With some reservations we may say that the vibronic interaction energies between nearest neighbours in the lattice are of the same order of magnitude. 

In principle, refined and relatively reliable quantum-theoretical methods are available for the calculation of the energy change associated with the process of equation 2. They take into account the changes in geometry, in electron distribution and in electron correlation which accompany the transition M(1 fio) — M+ (2 P/-), and also vibronic interactions between the radical cation states. Such sophisticated treatments yield not only reliable predictions for the different ionization energies 7 , 77 or 7 , but also rather precise Franck-Condon envelopes for the individual bands in the PE spectrum. However, the computational expenditure of these methods still limits their application to smaller molecules. We shall mention them later in connection with examples where such treatments are required. 

Francium, binary carbide not reported, 11 210 Franck-Condon effect, 16 69 energy, 21 180, 188, 189 envelopes, 16 80, 89, 90 hot bands, 16 90 factors, 32 47 principle, 21 179, 181 vibronic replica, 35 370 frd redon, 38 412, 414 Freeze quench EPR spectroscopy (FQ-EPR), CODH/ACS, 47 318 Fremy s salt, 33 106 Friedel-Crafts reaction, 17 194 cyclophosphazene, 21 65, 66 Frontier molecular orbitals, heteronuclear gold cluster compounds, 39 378-381 Frozen solutions, MOssbauer spectra in studies of, 15 101-103... 

In the calculations reported below, the MCTDH method has been employed for all calculations involving more than a single 2/i electronic state, i.e., involving PJT interactions. As a drawback, vibronic line spectra are not directly obtained from this (as with any wave-packet propagation) method. The spectral envelope is, however, easily obtained as a Fourier transform according to Ref. [26] ... 

Many other structures may be observed in the 0-1 reflectivity envelope 6b at 26254 cm-1 is attributed60 to the threshold of the two-particle states at 00 + 1162 cm-, which is a vibration visible in fluorescence and in absorption 9b is the analog for the vibration at 1564 cm-1. Finally, the transitions 0-1 and 0-2 have their vibronic counterparts associated with the vibration at 392 cm-1 (10b and 10a) for the 0-1 transition. 

Alternatively, Formulae (12 ), (27 ) or (29) can be used numerically to fit the ct(E)/E of triatomic molecules, even if the interpretation of the fitted parameters is not yet possible. The results presented below show that the numerical improvement obtained by using Formulae (12), (27) or (29) (all have 4 parameters and are able to describe the asymmetry of a a E)/E) is comparable with the improvement observed for CI2 (the Chi /DoF is reduced by typically up two orders of magnitude see Section 4). Here, it is essential to note that the reflection models are only able to describe the envelope of the XS, (corresponding to very short time evolution (f < 10 fs (femtosecond)) of the wavepacket after the photon absorption) and not the vibronic structures which are specific to each molecule and correspond to some vibrational (and or vibronic) oscillations at a time scale of several hiuidred femtoseconds. 

From a dynamical (and/or spectroscopic) perspective, we may ask ourselves how to describe and predict the vibronic structures which are superimposed on many low resolution Abs. Cross Sections. These vibronic structures are deeply linked to the time evolution of the wavepacket, after the initial excitation, over typical times of a few hundreds of femtoseconds as discussed by Grebenshchikov et al. [31]. In ID, for a diafomic molecule, fhe fime evolufion is rafher simple when only one upper electronic state is involved. In contrast, for friafomic molecules fhe 3D character of the PESs makes the wavepacket dynamics intrinsically complex. So, for most of the polyatomic molecules, the quantitative interpretation of fhe vibronic structures superimposed to the absorption cross section envelope remains a hard task for two main reasons first because it requires high accuracy PESs in a wide range of nuclear coordinates and, second, it is not easy to follow fhe ND N = 3 for triafomic molecules) wavepackef over several hundred femtoseconds,... 

In order to determine excited state distortions of large metal-containing molecules, two approaches can be taken. The first is to explore new methods of improving the resolution of the vibronic components in the electronic spectra. The second is to use different spectroscopic methods for obtaining the required information even when only broad envelopes in the electronic spectra can be obtained by the usual methods. We briefly discuss methods of improving resolution here. The application of additional spectroscopic methods, especially resonance Raman spectroscopy, forms the basis of the bulk of this chapter. 

Intersystem crossing from the 82 envelope of vibronic states is thought to occur from the lowest vibrational level, or perhaps the lowest two or three such levels. Given the lower relative energies of >lu and states, transitions to each of... 

The spectral behavior of the PDA phenylurethanes indicates that understanding of the electronic properties of these systems, and PDAs in general, still requires development. Calculations simulating strain on the backbone have not been able to address the observed distribution of intensity amongst the vibronic levels nor the changes in the vibrational frequencies or their distribution (6-9). While a substantial blue shift has been calculated, it is unclear what the strain should do to the shape of the electronic band envelope. The higher energy spectrum has previously been taken to be that of the HT form. 

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