Vibrational energy rotational spectra

The vibrational energy levels depend on the nuclear mass through the term M, of Equation 4.7. A vibrational or rotational spectrum is thus considerably changed when the isotope is changed, but in a predictable way. 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

Both absorption and emission may be observed in each region of the spectrum, but in practice only absorption spectra are studied extensively. Three techniques are important for analytical purposes visible and ultraviolet spectrometry (electronic), infrared spectrometry (vibrational) and nuclear magnetic resonance spectrometry (nuclear spin). The characteristic spectra associated with each of these techniques differ appreciably in their complexity and intensity. Changes in electronic energy are accompanied by simultaneous transitions between vibrational and rotational levels and result in broadband spectra. Vibrational spectra have somewhat broadened bands because of simultaneous changes in rotational energy, whilst nuclear magnetic resonance spectra are characterized by narrow bands. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

From precise wavelength measurements of the fluorescence spectrum (which may be performed e. g. by interferometric methods accurate values for the molecular constants can be obtained since the wavelength differences of subsequent lines in the fluorescence progression yield the energy separation of adjacent vibrational and rotational levels as a function of v . From these spectroscopically deduced molecular constants, the internuclear distance can be calculated A special computer programm developed by Zare ) allows the potential curve to be constructed from the measured constants and, if the observed fluorescence progression... 

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