Parallels between multiple population-period transient spectroscopy and multidimensional coherence spectroscopies

Abstract

We have recently shown that homogeneous and heterogeneous kinetics can be distinguished by experiments that compare the evolution of the population of a state over two time intervals [E. van Veldhoven et al., ChemPhysChem 8, 1761 (2007)]. This paper elaborates on the analogy between these multiple population-period transient spectroscopy (MUPPETS) experiments and more familiar spectroscopies based on the evolution of coherences. Using a modified inverse-Laplace transform, a standard kinetics decay is re-expressed as a "rate spectrum." A nonexponential decay creates a linewidth in this spectrum. Mechanisms for line broadening in rate spectra are compared to those for line broadening in frequency-domain spectra. Homogeneous and heterogeneous kinetics are defined precisely and are shown to be the counterparts of homogeneous and inhomogeneous line broadenings in frequency-domain spectra. Homogeneous line broadening mechanisms are further divided into equilibrium and nonequilibrium mechanisms, with equilibrium mechanisms more prevalent in frequency spectra and nonequilibrium mechanisms more prevalent in rate spectra. Spectral representations of two-dimensional MUPPETS experiments are developed that are equivalent to two-dimensional coherence spectroscopies. In particular, spectra equivalent to hole-burning and to correlation spectra are defined. Frequency-domain spectra are often modeled as an inhomogeneous distribution of identical homogeneous line shapes. A parallel homogeneous-heterogeneous model for kinetics is defined. Within this model, MUPPETS has sufficient information to completely separate the homogeneous and heterogeneous contributions to a nonexponential decay, even when the homogeneous contribution is nonexponential.

Thermal gratings and phase in high-order, transient-grating spectroscopy

“…Our previous report on auramine relaxation in BMIM-PF 6 showed important changes when compared to nonionic solvents. 8 In addition to an overall slowing, the decay becomes more disperse, i.e., spread over a wider range of times.…”

“…Both the long-time offset in the magnitude and the timedependent phase can be explained by a long-lived species that is only seen when auramine is in BMIM-PF 6 . The shortand long-species have distinctly different spectra and thus different phases at the probe wavelength.…”

“…(6). This detection operator can be compared to the analogous one for a resonant solute given in Eq.…”

“…[1][2][3] More recently, the extension to two dimensions (2D), i.e., using two excitations, has become important and extensions to higher dimension can be foreseen. [4][5][6] Thermal gratings are a well known component of 1D transient-grating spectroscopy. [4][5][6][7] When applied to a nonexponential decay, MUPPETS can measure the homogenous decay of individual subensembles within a heterogeneous sample.…”

Perspective: Two-dimensional resonance Raman spectroscopy

“…77 In future work, we will investigate whether or not heterogeneity in the geometry translates into heterogeneity in the vibrational cooling rate with pump-repump-probe experiments, which can expose correlations between incoherent relaxation processes. 78,79 …”