Relative Stokes vibrational Raman

Figure 1. Relative Stokes vibrational Raman intensity jor nitrogen for a trapezoidal slit function and various center positions...

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

For any vibrational mode, the relative intensities of Stokes and anti-Stokes scattering depend only on the temperature. Measurement of this ratio can be used for temperature measurement, although this application is not commonly encountered in pharmaceutical or biomedical applications. Raman scattering based on rotational transitions in the gas phase and low energy (near-infrared) electronic transitions in condensed phases can also be observed. These forms of Raman scattering are sometimes used by physical chemists. However, as a practical matter, to most scientists, Raman spectroscopy means and will continue to mean vibrational Raman spectroscopy. 

Raman line intensities are proportional to the number density N of molecules in the initial state /c>, which is in turn proportional to the pertinent Boltzmann factor for that state at thermal equilibrium. Consequently, the relative intensities of a Stokes transition /c> - m> and the corresponding anti-Stokes transition m> -> /c> are 1 and exp — hoj kjkT), respectively. (The factor coicol varies little between the Stokes and anti-Stokes lines, because the Raman frequency shifts are ordinarily small compared to cui.) Hence the anti-Stokes Raman transitions (which require molecules in vibrationally excited initial states) are considerably less intense than their Stokes counterparts, particularly when the Raman shift (o k is large. In much of the current vibrational Raman literature, only the Stokes spectrum is reported (cf Fig. 10.1). 

Mizutani and Kitagawa measured the time-dependent Stokes and anti-Stokes Raman intensities of the heme v4 band after photoexcitation and used the relative intensities to estimate its temperature and thermal relaxation dynamics (30). They found the population relaxation to occur biexponen-tially with 1.9 ps (93%) and 16 ps (7%) time constants. The dominant 1.9 ps population relaxation correlates with a 3.0 ps thermal relaxation, which is a factor of 2 faster than the ensemble averaged temperature relaxation deduced from the near-IR study of band III. The kinetic energy retained within a photoexcited heme need not be distributed uniformly among all the vibrational degrees of freedom, nor must the energy of all vibrational modes decay at the same rate. Consequently, a 6.2 ps ensemble-averaged estimate of the heme thermal relaxation is not necessarily inconsistent with a 3 ps relaxation of v4. 

The vibrational selection rules are the same for Raman spectroscopy as for infrared spectroscopy. In the Stokes process, the intense, monochromatic radiation t es a molecule from the v = 0 state to a virtual state, VO, from which it falls back to the v = 1 state. Similarly, in the anti-Stokes process, the virtual state VI is involved in the overall transfer of the molecule from the v = 1 to the v = 0 state. The Stokes and anti-Stokes transitions lie on the low and high wavenumber sides, respectively, of the exciting radiation. The intensity of the anti-Stokes line, relative to the Stokes transition is very low because of the lower population of the v = 1 state, compared to that of the v = 0 state. Consequently, Raman spectroscopy uses only the Stokes transitions. 

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