Vibrational spectra condensed phase

Condensed phase vibrational or vibronie lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide information about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectrum. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

NIST Chemistry WebBook http //webbook.nist.gov/chonistry/ (accessed November 10, 2010). The NIST Chemistry WebBook provides Internet access to chemical and physical property data for nearly 50,000 chonical species (compounds, ions, radicals, etc.). The data are derived from collections maintained by both the NIST Standard Reference Data Program and outside contributors. The available data include thermodynamic, gas phase, IR spectrum, condensed phase, mass spectrum, phase change, UV/Vis spectrum, reaction, vibrational and electronic energy levels, ion enogetics, constants of diatomic molecules, ion cluster, and Henry s Law. 

The objective of this first part of the book is to explain in a chemically intelligible fashion the physical origin of microwave-matter interactions. After consideration of the history of microwaves, and their position in the electromagnetic spectrum, we will examine the notions of polarization and dielectric loss. The orienting effects of the electric field, and the physical origin of dielectric loss will be analyzed, as will transfers between rotational states and vibrational states within condensed phases. A brief overview of thermodynamic and athermal effects will also be given. 

Consequently, many more individual absorption processes can be accommodated on the frequency (energy) axis. Their actual number is indirectly proportional to the line-width. According to (9.2), the quantum of energy associated with the transition that would correspond to a single spectral line is sharply defined. Such a line spectrum is observed, for example, in atomic vapors. On the other hand, spectral lines of more complicated molecules, even in gas phase, are broader. This is due to the fact that the transition between two electronic states is complicated by the presence of multiple vibrational levels within each state. Furthermore, in the condensed phase, these vibrational levels are strongly affected by interactions with the surrounding molecules. 

Vibrational spectra of isolated molecules depend on the presence of certain chemical groups, and finer details extracted from the large wealth of information enclosed in the spectrum permit the better characterization of the molecule, its conformation, its chemical linkage, and the mutual interactions between atoms and the atomic charges, modulated by the intrinsic temperature. When the system is not isolated, the interpretation of the spectrum becomes more complex, as additional factors due to the interaction of the molecule with the surrounding have to be taken into account. This should be kept well in mind when developing any computational approach to vibrational spectra of molecules in a condensed phase. 

So far, this discussion of selection rules has considered only the electronic component of the transition. For molecular species, vibrational and rotational structure is possible in the spectrum, although for complex molecules, especially in condensed phases where collisional line broadening is important, the rotational lines, and sometimes the vibrational bands, may be too close to be resolved. Where the structure exists, however, certain transitions may be allowed or forbidden by vibrational or rotational selection rules. Such rules once again use the Born-Oppenheimer approximation, and assume that the wavefunctions for the individual modes may be separated. Quite apart from the symmetry-related selection rules, there is one further very important factor that determines the intensity of individual vibrational bands in electronic transitions, and that is the geometries of the two electronic states concerned. Relative intensities of different vibrational components of an electronic transition are of importance in connection with both absorption and emission processes. The populations of the vibrational levels obviously affect the relative intensities. In addition, electronic transitions between given vibrational levels in upper and lower states have a specific probability, determined in part... 

Figure 2 Schematic of the electronic absorption spectrum of a single chromophoric site in a condensed phase host environment at low temperatures. An extremely sharp electronic origin, exhibiting a radiatively limited linewidth is accompanied by a phonon sideband with vibrational sidelines. A second electronic excited state lies at higher energies. Vibrational sidelines and the second electronic excited state are lifetime broadened by rapid radiationless deactivation processes...

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectrum of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from Unewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

Consider Eq. (6.84). This result was obtained for a harmonic system of identical and equivalent atoms. We could however reverse our reasoning and define a vibrational spectrum for a dense atomic system from the velocity autocorrelation function according to Eq. (6.84). Since this function can be computed for all systems, including liquids and disordered solids, we may use (6.84) as a definition of a spectrum that may be interpreted as density of modes fimction for such media. We can then use it in expressions such as (4.33), and (6.92). Is this approach to dynamics in condensed phases any good ... 

Since the direct simulation of vibrational relaxation in condensed phases is clearly a difficult and lengthy procedure for molecules with realistic vibrational frequencies, Shugard et al. ° proposed an alternative approach based on work of Adelman and Doll and applied it to relaxation of diatomic impurities in solid matrices. The motion of atoms near the impurity was simulated directly and the effect of more distant atoms was taken into account through a stochastic force, which was constructed from the phonon spectrum of the solid. This method still requires that the relaxation time not be too long compared to the vibrational period (i.e., that the vibrational frequency not be too high) but the calculation is much faster than a full molecular dynamics simulation since only a few degrees... 

Nevertheless, it is possible to give a formal description of a statistical-limit molecule in the same terms as previously used in the strong-coupling case. It is well known that the emission spectrum of large molecules (studied up to now only in condensed phases) is composed of narrow bands (considered as the resonance Raman scattering) and broad-band fluorescence. The relative intensity of the first component is enhanced in presence of fluorescence quenchers (Friedman and Hochstrasser, 1975), or in laser intracavity experiments (Bobovich and Bortkevich, 1977). The first component may be related to the emission from nonstationary s> states with redistribution time shorter than the exciting-pulse duration. The second component would be due to the rapid vibrational redistribution. In the limiting case of nonfluorescent molecules only the resonance Raman spectrum persists. The nonradiative deactivation of the excited state would be more rapid here than the vibrational redistribution. 

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