Time-dependent spectral diffusion

First, as the molecule on which the chromophore sits rotates, this projection will change. Second, the magnitude of the transition dipole may depend on bath coordinates, which in analogy with gas-phase spectroscopy is called a non-Condon effect For water, as we will see, this latter dependence is very important [13, 14]. In principle there are off-diagonal terms in the Hamiltonian in this truncated two-state Hilbert space, which depend on the bath coordinates and which lead to vibrational energy relaxation [4]. In practice it is usually too difficult to treat both the spectral diffusion and vibrational relaxation problems at the same time, and so one usually adds the effects of this relaxation phenomenologically, and the lifetime 7j can either be calculated separately or determined from experiment. Within this approach the line shape can be written as [92 94]... 

DIR spectra have been obtained by the Fayer group on HOD/H20 [53 55]. They characterize the extent of spectral diffusion by the waiting time dependence... 

Time-dependent correlation functions are now widely used to provide concise statements of the miscroscopic meaning of a variety of experimental results. These connections between microscopically defined time-dependent correlation functions and macroscopic experiments are usually expressed through spectral densities, which are the Fourier transforms of correlation functions. For example, transport coefficients1 of electrical conductivity, diffusion, viscosity, and heat conductivity can be written as spectral densities of appropriate correlation functions. Likewise, spectral line shapes in absorption, Raman light scattering, neutron scattering, and nuclear jmagnetic resonance are related to appropriate microscopic spectral densities.2... 

Fig. 5.4.11 [Cal 11 ] Modulated gradient NMR for probing spectral densities of diffusive translational motion. The pulse sequence (left) consists of a CPMG echo train with interdispersed gradient pulses G(t) which produces the time-dependent wave vector k(t). The spectrum K(co) of k(t) probes the spectral density of diffusive motion at a single frequency (right).

The time dependence of the interaction can arise from variations in the interspin vector, r, due to the relative translational motions of the / and 5 spins. It can be shown that if the spins I and S are in different molecules and can be treated as diffusing independently, an expression for the reduced spectral density 7)1 =7d,co/- d,o can be obtained. The result is—... 

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