Correlation functions single molecule spectroscopy

Fluorescence correlation spectroscopy analyses the temporal fluctuations of the fluorescence intensity by means of an autocorrelation function from which translational and rotational diffusion coefficients, flow rates and rate constants of chemical processes of single molecules can be determined. For example, the dynamics of complex formation between /3-cyclodextrin as a host for guest molecules was investigated with singlemolecule sensitivity, which revealed that the formation of an encounter complex is followed by a unimolecular inclusion reaction as the rate-limiting step.263... 

In this chapter, we developed a stochastic theory of single molecule fluorescence spectroscopy. Fluctuations described by Q are evaluated in terms of a three-time correlation function C iXi, X2, T3) related to the response function in nonlinear spectroscopy. This function depends on the characteristics of the spectral diffusion process. Important time-ordering properties of the three-time correlation function were investigated here in detail. Since the fluctuations (i.e., Q) depend on the three-time correlation function, necessarily they contain more information than the line shape that depends on the one-time correlation function Ci(ti) via the Wiener-Khintchine theorem. 

A useful and common way of describing the reorientation dynamics of molecules in the condensed phase is to use single molecule reorientation correlation functions. These will be described later when we discuss solute molecular reorientational dynamics. Indirect experimental probes of the reorientation dynamics of molecules in neat bulk liquids include techniques such as IR, Raman, and NMR spectroscopy. More direct probes involve a variety of time-resolved methods such as dielectric relaxation, time-resolved absorption and emission spectroscopy, and the optical Kerr effect. The basic idea of time-resolved spectroscopic techniques is that a short polarized laser pulse removes a subset of molecular orientations from the equifibrium orientational distribution. The relaxation of the perturbed distribution is monitored by the absorption of a second time-delayed pulse or by the time-dependent change in the fluorescence depolarization. 

Fairly good agreement exists between the calculated value of 1682 cm-1 and the experimental value of 1650 cm1. Direct correlation does not exist because Hooke s law assumes that the vibrational system is an ideal harmonic oscillator and, as mentioned before, the vibrational frequency for a single chemical moiety in a polyatomic molecule corresponds to the vibrations from a group of atoms. Nonetheless, based on the Hooke s law approximation, numerous correlation tables have been generated that allow one to estimate the characteristic absorption frequency of a specific functionality (13). It becomes readily apparent how IR spectroscopy can be used to identify a molecular entity, and subsequently physically characterize a sample or perform quantitative analysis. 

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