ABSTRACT
We have seen in previous chapters that spectral lineshapes I(ω) are related via Fourier transformation to time-correlation functions that depend on the dynamics of molecular motion coupled to the spectrum under consideration. For example, as shown in Chapter 5, the lineshape of an infrared absorption band is determined by the vibrational and reorientational dynamics of the dipole moment derivative with respect to normal coordinate. In the time-dependent theory of electronic spectroscopy, discussed in Chapter 12, the frequency distribution of the absorption spectrum and Raman excitation profile derives from the motion of vibrational wavepackets propagating on displaced excited electronic state potential surfaces. Solvent-induced dephasing, population relaxation, vibrational and reorientational motion, and static inhomogeneous broadening can all contribute to the frequency distribution I(ω). Separating these effects without models or assumptions is simply not tenable in the linear regime. Time-dependent spectroscopy, on the other hand, provides insight into the same dynamics that contribute to the lineshape, but are not readily uncovered in the frequency domain. As an extreme example, consider that a typical excited electronic state lifetime of 10 ns translates into a breadth of only 0.003 cm-1, according to the time-energy uncertainty principle, ∆ ∆ν t ≥1. This contribution to the spectral width is insignificant compared to other line broadening effects in the condensed phase, but a 10 ns (or much shorter) lifetime is readily measured in the time domain. Coherent time-domain experiments with a variety of pulse sequences, wavelengths and detection schemes enable the separation of homogeneous and inhomogeneous contributions to the spectral width. Using coherent excitation of vibrational states which beat against one another, the wavepacket motion that underlies electronic and resonance Raman spectroscopy is revealed in real time. Following pulsed excitation, the effect of the solvent environment on the time-evolving transition frequency, known as spectral diffusion, is seen. Spectral diffusion derives from fluctuations in the transition frequency of a molecule, fluctuations like that of the general dynamic variable depicted in the cartoon of Figure 5.1, as a result of interactions with its environment. These dynamics give rise to the frequency fluctuation correlation function (FFCF), δω δω( ) ( )0 t , that influences linear and nonlinear spectra. Time-dependent experiments enable the determination of the effects of solvent and internal dynamics on spectroscopic transitions. Nonlinear and time-resolved experiments offer more information content than steady-state linear spectroscopy, as a result of multiple field-matter interactions. Though we limit our discussion in this chapter to the realm of third-order response, the number of experimental configurations embraced by χ(3) is quite large. We focus here on some of the more widely used techniques.
