Time-Dependent Approach to Resonance Raman Scattering.

The time-dependent theory of resonance Raman scattering (RRS) with its wavepacket interpretation forms the central theme of this dissertation. We extend the original theory, as developed by Lee and Heller, and apply it in numerical calculations to a wide variety of systems. In the Lee -Heller theory, the static and dynamic contributions to RRS are distinguished. The former is due to non-constancy of the transition moment, while the latter is due to wavepacket dynamics on the resonant Born-Oppenheimer (BO) surface. The incident light frequency governs the time scale of the relevant dynamics, according to (DELTA)(omega)(.)(DELTA)t(TURNEQ)1, where (DELTA)(omega) is the mismatch between the incident light and the resonant BO surface. In Chapter 1 we review the Lee-Heller theory and discuss the role of symmetry in the theory. Symmetry selection rules are developed within the time-dependent, Born-Oppenheimer framework. This chapter also provides a detailed comparison of our approach with the venerable Kramers-Helsenberg-Dirac formalism, developed by Albrecht. Chapter II is a comprehensive treatment of the wavepacket approach applied to harmonic potentials. Harmonic oscillator assumptions are the rule, rather than the exception, in treatments of RRS. SWP techniques are exact for multidimensional harmonic oscillators. A plethora of analytic formulas are provided in this chapter, including the "super-simple" formulas-- one-dimensional overlap formulas for matched -frequency oscillators. Chapter III deals with preresonance Raman scattering on two different scales. In Section IIIA the incident photon is preresonant with an entire electronic band and the propagation time is a fraction of a vibrational period. Slopes and curvatures of the resonant BO surface in the Franck -Condon region are probed in these short times. Analytic formulas are given relating preresonant intensities with these surface parameters. In Section IIIB. these ideas are extended to preresonance with a vibrational feature in the electronic absorption band. We propose sequential detuning from a vibrational feature and monitoring the Raman spectrum to probe the pathway of intramolecular mode -mode energy transfer. Relevance to the alkylbenzene experiments of the Smalley group is emphasized. Chapter IV deals with the fitting of experimental absorption spectra.