The Wavepacket Picture of Resonance Raman Scattering

Although evaluating the matrix element for resonance Raman scattering by Eq. (12.13) is staightforward for a molecule with only one or two vibrational modes, it rapidly becomes intractable for larger molecules, and a wavepacket treatment similar to the one described for absorption in Chap. 11 becomes increasingly useful. To recast Eq. (12.13) in a time-dependent form, we first note that the factor 

1 / - Ea(g) - hve - ihfT2) that appears in each term of the sum is times 

This function has the same form as the function we used in Sect. 2.5 to represent a wavefunction that decays exponentially with time (Eqs. 2.66-2.67 and Appendix A3). The decay time constant T in Eqs. (2.66) and (2.67) corresponds to T-2l2ti in Eq. (12.15). 

Let s now construct an excited-state wavepacket X f) as in Eqs. (11.46) and (11.47) but with a dephasing time constant of T2, so that 

Note that the products of vibrational overlap integrals in this expression are the same as those in Eq. (12.13). 

---