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In the last chapter, we used a steady-state treatment to relate the shape of an absorption band to the dynamics of relaxations in the excited state. Because a period on the order of the electronic dephasing time () will be required to establish a steady state, Eqs. (10.43) and (10.44) apply only on time scales longer than this. We need to escape this limitation if we hope to use spectroscopic techniques to explore the relaxation dynamics themselves. Our first goal in this chapter is to develop a more general approach for analyzing spectroscopic experiments on femtosecond and picosecond time scales. This provides a platform for discussing how pump–probe and photon-echo experiments can be used to probe the dynamics of structural fluctuations and the transfer of energy or electrons on these short time scales.

The vibrational transitions discussed in Chap. 6 occur by absorption of a photon whose energy matches a vibrational energy spacing, . Vibrational or rotational transitions also can occur when a molecule scatters light of higher frequencies; this is the phenomenon of . Raman scattering is one of a group of two-photon processes in which one photon is absorbed and another is emitted essentially simultaneously. Figure 12.1 illustrates the main possibilities. (Fig. 12.1, transition A) is an , in which there is no net transfer of energy between the molecule and the radiation field: the incident and emitted photons have the same energy. Raman scattering is an process in which the incident and departing photons differ in energy and the molecule is either promoted to a higher vibrational or rotational level of the ground electronic state, or demoted to a lower level. Raman transitions in which the molecule gains vibrational or rotational energy, called Raman scattering (Fig. 12.1, transition B), usually predominate over transitions in which energy is lost ( Raman scattering; Fig. 12.1, transition C) because resting molecules populate mainly the lowest levels of any vibrational modes with > . The strength of anti-Stokes scattering increases with temperature, and the ratio of anti-Stokes to Stokes scattering provides away to measure the effective temperature of amolecule. Both Stokes and anti-Stokes Raman scattering increase greatly in strength if the incident light falls within a molecular absorption band (Fig. 12.1, transition D). The scattering then is termed scattering.