Two-Dimensional Electronic Correlation and Relaxation Spectra: Theory and Model Calculations

Abstract

Hybl et al. demonstrated a technique for recording two-dimensional Fourier transform electronic correlation and relaxation spectra based on detecting phase modulation of the signal electric field in a noncollinear femtosecond four-wave mixing experiment. A theoretical analysis of 2D correlation and relaxation experiments is presented for a system consisting of two electronic states each having two or more sublevels. The separation between absorption and dispersion mode 2D spectra in these experiments is investigated in detail for nonzero pulse duration and compared to related 2D NMR experiments based on a nonlinear optical definition of coherence order. Phase-twisted peaks, which mix absorption and dispersion line shapes, can occur under some circumstances. A 1D projection of the complex 2D spectrum is shown to equal the transient grating signal field, and the real part of this projection is related to the spectrally resolved pump−probe signal. Calculated 2D spectra for a two-level Bloch model, an underdamped Brownian oscillator, and a few models of polar solvent dynamics based on the correlation function approach to the nonlinear response developed by Mukamel and co-workers are presented. The real parts of the 2D spectra are primarily positive (indicative of ground state bleaching and excited state emission) but contain negative regions arising from excitation of coherent superposition states (e.g. vibrational wavepackets) in both the ground and excited electronic states. Assignment of the 2D spectra displaying wavepacket motion at the vibronic level is discussed, and the manifestations of wavepacket motion and vibrational relaxation in the 2D spectra are explored. As suggested by Hybl et al., an increase in pulse duration is found to affect a 2D spectrum primarily as a spectral filter that limits the range of the spectrum. The Gaussian correlation function characteristic of inertial solvent motion is found to be faithfully reflected in a homogeneous 2D cross width which is nearly independent of pulse duration. An alternative experimental method for obtaining only the real part of 2D spectra is proposed.